Chapter 10: Electro-magnetism
In 1831, in the laboratory of the Royal Institution in London, Michael Faraday took a plain ring of soft iron and wound two separate coils of insulated wire around it, one on each side, as shown in Fig. 10.0-1. The two coils never touched each other at any point.
He joined the first coil to a battery through a switch. He joined the second coil to a galvanometer — an instrument whose needle swings whenever a current passes through it.
Scientists already knew that an electric current could produce a magnetic field around itself. Faraday was chasing the opposite effect. He wanted to make magnetism produce a current.
He closed the switch. The galvanometer needle jumped — and then fell straight back to zero, even though the battery was still connected and current was still flowing steadily in the first coil.
Puzzled, he opened the switch. The needle jumped again, this time the other way, and once more returned to zero.
Nothing lasting had happened at all. The second coil gave a current only in the two brief instants when something was changing.
That small flick of a needle is the reason your house has electricity today. Every power station on earth spins coils near magnets to produce, again and again, exactly the effect Faraday saw that afternoon.
Diagram
Fig. 10.0-1 — Faraday’s Iron Ring Experiment Draw a closed ring of soft iron seen face-on. On the left side of the ring, wind a coil of insulated wire and lead its two ends to a battery through an open switch; label this coil, the battery and the switch. On the right side of the ring, wind a second, separate coil and lead its two ends to a centre-zero galvanometer with its needle shown deflected to one side; label this coil and the galvanometer. Add a label ‘soft iron ring’ with an arrow to the ring, and a note that the two coils are nowhere joined to each other.
10.1 Oersted’s Experiment On The Magnetic Effect Of Electric Current
For a long time, electricity and magnetism were studied as two separate subjects. One dealt with charges and currents, the other with lodestones and compass needles. Nothing seemed to join them.
That separation ended in 1820. Hans Oersted, working with a simple circuit and a compass, observed that when an electric current is passed through a conducting wire, a magnetic field is produced around it. A magnetic field is the region around a magnet, or around a current, in which a magnetic force can be felt.
A magnetic field cannot be seen. Its presence at any point around a current carrying wire is detected with the help of a compass needle, which is itself a tiny freely pivoted magnet.
How A Compass Needle Behaves
You need to be clear about one thing before the experiment makes sense. When no magnetic field acts on it, the needle of a compass can rest in any direction at all. When a magnetic field does act on it, the needle rests only along the direction of that field.
On the surface of the earth there is always a weak magnetic field of the earth itself. That is why a compass needle, left alone, comes to rest along the north–south direction. The needle is telling you both that the earth’s magnetic field exists and which way it points.
10.1.1 The Experiment And Its Observations
The arrangement is shown in Fig. 10.1-1. A straight wire AB is laid along the north–south direction. It is connected to a battery through a rheostat and a tapping key. A rheostat is simply a resistor whose resistance can be varied, so that the current in the wire can be made larger or smaller at will. A tapping key closes the circuit only for as long as it is pressed.
A compass needle is placed just below the wire, so that the wire runs directly over it.
Diagram
Fig. 10.1-1 — Set-Up For Oersted’s Experiment Circuit diagram drawn in plan view. Show a straight horizontal wire AB lying along the north–south direction, with A at the south end and B at the north end. Connect the ends of AB through a rheostat and a tapping key to a battery, completing a rectangular circuit. Place a compass needle just below the wire at the middle of AB, with its north pole marked N and south pole marked S. Label the wire AB, the battery, the rheostat and the key. At one side draw a small compass rose marking N, S, E and W.
What Is Observed
Observation 1. When the key is open, no current passes through the wire. The needle points along the north–south direction, that is, along the earth’s magnetic field, with its north pole pointing towards geographical north. In this position the needle lies parallel to the wire.
Observation 2. When the key is pressed, a current passes in the wire in the direction from A to B, that is, from south to north. The north pole of the needle now deflects towards the west. If the current in the wire is increased using the rheostat, the deflection of the needle also increases.
Observation 3. When the direction of current in the wire is reversed, by interchanging the connections at the terminals of the battery, the north pole of the needle deflects towards the east instead.
Observation 4. If the compass needle is placed just above the wire, everything is turned about. With the current flowing from A to B, the north pole now deflects towards the east; with the current flowing from B to A, it deflects towards the west.
These four settings are drawn together in Fig. 10.1-2, and gathered side by side in Table 10.1 so that the pattern in them stands out.
Diagram
Fig. 10.1-2 — Deflection Of The Needle In Four Cases Four panels, each showing the straight wire AB lying south to north with a compass needle near it and an arrow on the wire marking the direction of current. Panel (a): needle below the wire, current from A to B, north pole of needle deflected towards west. Panel (b): needle below the wire, current from B to A, north pole deflected towards east. Panel (c): needle above the wire, current from A to B, north pole deflected towards east. Panel (d): needle above the wire, current from B to A, north pole deflected towards west. Label each panel with the position of the needle and the direction of current, and mark N and S on every needle.
Read down the table and two rules of thumb appear on their own. Reverse the current and the deflection reverses. Move the needle from below the wire to above it and the deflection reverses again.
10.1.2 Explanation And Inference
The needle is a magnet, and a magnet turns only when a magnetic field acts on it. So the deflection of the needle on passing current through the wire tells us plainly that a magnetic field has been created around the wire.
Placed in this field, the magnetic needle of the compass experiences a turning effect, or torque. It therefore deflects until it lies along the direction of the resultant magnetic field at that point — the combined effect of the earth’s field and the wire’s field together.
The other two observations now explain themselves. On increasing the current in the wire, the deflection of the needle increases, which means the strength of the magnetic field around the wire has increased. On reversing the direction of current in the wire, the direction of deflection of the needle reverses, because the direction of the magnetic field itself has reversed.
Notice how much this one sentence carries. Any current at all — in a torch wire, in a lightning stroke, in the coil of a bell — has a magnetic field wrapped around it, whether or not anyone has put a compass there to look.
10.2 Magnetic Field And Field Lines Due To Current In A Straight Wire
You now know that a magnetic field exists around a current carrying wire. The next question is what shape that field has, and which way it points at each place around the wire.
To answer it we draw magnetic field lines. A magnetic field line is a line drawn in the field such that the tangent to it at any point gives the direction of the magnetic field at that point. A tangent is simply a straight line that just touches a curve at one point without cutting across it.
Field lines are not real threads lying in space. They are a way of drawing a field so that its shape and its direction can be seen at a glance. Around a straight wire they can be traced out very neatly using iron filings.
10.2.1 Tracing The Field With Iron Filings
The arrangement is shown in Fig. 10.2-1. Take a white sheet of smooth cardboard with a hole at its centre. Place it horizontally and pass a thick copper wire XY vertically through the hole, so that the wire stands at right angles to the board.
Between the ends X and Y of the wire connect an ammeter A, a battery B, a rheostat Rh and a key K, in series. The ammeter lets you read the current in the wire, and the rheostat lets you change it.
Now sprinkle some iron filings evenly on the cardboard and pass an electric current through the wire by inserting the plug in the key K. Then tap the cardboard gently.
Diagram
Fig. 10.2-1 — Field Lines Around A Straight Current Carrying Wire Draw a horizontal rectangular sheet of cardboard shown in perspective, with a thick copper wire XY passing vertically through a hole at its centre; mark the upper end X and the lower end Y and show an arrow on the wire giving the direction of current. On the cardboard show iron filings arranged in concentric circles about the wire, with the circles drawn closer together near the wire and farther apart away from it, and an arrowhead on each circle showing the direction of the magnetic field. Place a small compass needle on the board on one of the circles, with N and S marked and the needle lying along the circle. From the ends X and Y lead wires to an ammeter A, a battery B, a rheostat Rh and a key K connected in series; label each of these, and label the cardboard, the wire, the iron filings and the magnetic field lines.
It is observed that the iron filings get arranged along concentric circles around the wire. Concentric circles are circles of different radii sharing the same centre, and here that common centre is the wire itself.
The filings show the shape of the field but not which way round it goes. For that, place a small compass needle anywhere on the board near the wire. The direction in which the north pole of the needle points is the direction of the magnetic field at that point, and it is marked by an arrow on the field line.
10.2.2 Features Of The Field Line Pattern
From the pattern of the magnetic field lines, we note the following.
Feature 1. The magnetic field lines form concentric circles around the wire. The plane of these circles is perpendicular to the straight wire, and their centres lie on the wire.
Feature 2. When the direction of current in the wire is reversed, the pattern of the iron filings does not change at all. The circles are exactly where they were before. But the direction of deflection of the compass needle gets reversed. The north pole of the needle now points in a direction opposite to the previous one, showing that the direction of the magnetic field has reversed.
Feature 3. On increasing the current in the wire, the magnetic field lines become denser, that is, drawn more closely together. The iron filings also get arranged in circles up to a larger distance from the wire. Both of these show that the magnetic field strength has increased, and that the field is now effective up to a larger distance.
10.2.3 The Neutral Point
There is one more thing at work on that cardboard, and it explains why the pattern of filings does not stay circular right out to the edge of the board.
The magnetic field at any point is the combined effect of two fields: the field due to the current in the wire, and the magnetic field of the earth. Over a small region in a horizontal plane the earth’s magnetic field is uniform, and it is directed from geographic south to geographic north.
At points near the wire, the field due to the current in the wire is much the stronger of the two. It predominates, and so the iron filings there arrange themselves in circles. At points far away from the wire, the field due to the current has weakened, while the earth’s field has not. The earth’s field becomes more pronounced compared with the field due to the current, and as a result the filings out there tend to arrange themselves in straight lines. This is drawn in Fig. 10.2-2.
Somewhere between these two regions lies a point where the two fields are exactly equal in magnitude and opposite in direction, so that they cancel.
The behaviour of the needle at that point is the giveaway. With no resultant field to turn it, the needle has no preferred direction left, and settles wherever it happens to be put.
Diagram
Fig. 10.2-2 — Circles Near The Wire, Straight Lines Far From It Plan view of the cardboard seen from above, with the wire shown as a dot at the centre and a cross or dot marking the direction of current. Close to the wire draw several complete concentric circles of iron filings with arrowheads. Further out, draw the filings gradually opening out and finally lying in straight lines running south to north, and label these ‘earth’s magnetic field predominates’. Label the inner region ‘field due to current predominates’. Mark a point on one side where the two fields oppose and label it ‘neutral point’, with a small compass needle drawn there lying in no particular direction. Add a compass rose marking N, S, E and W.
10.3 Rule To Find The Direction Of Magnetic Field
Experimentally, the direction of the magnetic field at a point is detected with the help of a compass needle. That works, but it means you must have the wire, the current and the compass in front of you before you can say anything.
Theoretically, the direction of the magnetic field, and so the direction of the magnetic field lines, produced due to the flow of current in a conductor can be determined by various rules. These rules let you predict the direction from the drawing alone, with no apparatus at all. One such rule is the right hand thumb rule.
10.3.1 Right Hand Thumb Rule
Imagine gripping the wire in your right hand, with your thumb stretched out along the wire and your fingers curled round it. Your thumb then shows one direction and your curled fingers sweep out another. The rule simply says which is which.
Two points are worth fixing before you use it. It must be the right hand, never the left. And the thumb takes the direction of the conventional current, that is, the direction in which a positive charge would flow, from the positive terminal of the cell round to the negative terminal.
The rule is applied in Fig. 10.3-1. Here the direction of current in the conductor XY is upwards, that is, from X to Y. The magnetic field lines are then clockwise around the conductor, as seen from the end X.
Diagram
Fig. 10.3-1 — Right Hand Thumb Rule Draw a vertical straight conductor XY with X at the lower end and Y at the upper end, and an upward arrow on the conductor labelled ‘direction of current’. Show a right hand gripping the conductor, palm towards the wire, with the thumb stretched vertically upwards along the wire and the four fingers curled around it. Draw two or three dashed circles around the wire in the plane perpendicular to it, each carrying an arrowhead in the same sense as the curled fingers, and label them ‘direction of magnetic field lines’.
Notice that the phrase ‘as seen from the end X’ is doing real work in that sentence. A circle looks clockwise from one side and anticlockwise from the other, so a sense of rotation means nothing until you say where you are looking from.
10.4 Magnetic Field Due To Current In A Loop
A straight wire is not a very useful shape. Its field lines are circles that spread out all round it, and the field weakens quickly as you move away.
Bend the same wire into a circle and something better happens. Every part of the loop now sends its field lines through the middle in the same direction, so the effects add up there instead of spreading out. The magnetic field lines due to current in a loop, whether it is made of thick wire or of a circular coil of several turns, can be obtained by the following experiment.
10.4.1 Tracing The Field Of A Loop
Take a piece of thick wire A and bend it in the form of a loop, or coil. Pass it at two points P and Q through a horizontal cardboard C, in such a way that the points P and Q form the diameter of the wire or coil. Half the loop then stands above the board and half below it, and the board cuts the loop along its widest line.
Now sprinkle some iron filings on the cardboard. Connect a battery through a rheostat and a key between the ends X and Y of the loop, as shown in Fig. 10.4-1.
Close the key to pass current through the coil and tap the cardboard gently. It is noted that the iron filings get arranged in a definite pattern, representing the magnetic field lines of the current carrying loop.
Diagram
Fig. 10.4-1 — Magnetic Field Due To Current In A Loop Draw a horizontal rectangular sheet of cardboard C shown in perspective. Pass a loop of thick wire A through the board at two points P and Q lying on a diameter of the loop, so that the upper half of the loop rises above the board and the lower half hangs below it; label the loop A and the points P and Q. On the cardboard show iron filings arranged in the field line pattern: nearly circular closed curves around P and around Q, opening out and passing through the space between P and Q all in the same direction, and nearly straight parallel lines near the centre of the loop. Put an arrowhead on each field line. Lead the two ends X and Y of the wire down to a rheostat, a key and a battery connected in series, and label each. Label the cardboard, the iron filings and the magnetic field lines.
To find the direction of the magnetic field lines, a compass needle is used. The direction of the magnetic field at a point is along the needle, in the direction in which its north pole points. An arrow is marked on each magnetic field line to indicate the direction of the magnetic field. You may verify that the direction so found is the same as the one given by the right hand thumb rule of Section 10.3, applied to any small part of the loop.
10.4.2 Features Of The Field Line Pattern
From the pattern of magnetic field lines, it is noted that:
In the vicinity of the wire at P and at Q, the magnetic field lines are nearly circular. This is expected, because close up, a short piece of the loop looks much like a straight wire.
Within the space enclosed by the wire, that is, between P and Q, the magnetic field lines are all in the same direction.
Near the centre of the loop, the magnetic field lines are nearly parallel to each other. The magnetic field may therefore be assumed to be nearly uniform in a small space near the centre. A uniform field is one that has the same strength and the same direction at every point of that space.
At the centre, the magnetic field lines are along the axis of the loop and normal to its plane. The axis of a loop is the straight line drawn through its centre at right angles to the plane in which the loop lies.
The magnetic field lines become denser, that is, the magnetic field strength is increased, if (i) the strength of current in the loop is increased, and (ii) the number of turns in the loop is increased.
The magnetic field lines pass through the loop in the same direction. They appear to come out from the face of the loop on one side, so that face behaves as a north pole, while the magnetic field lines appear to enter in at the other face, so that face behaves as a south pole.
That last feature is the important one. A dipole is anything with a north pole and a south pole, and a current carrying loop is exactly that. Its magnetic field is similar to that of a magnetised disc of the same radius as the loop.
10.4.3 Clock Rule For The Polarity Of The Faces
The polarity at the two faces of the loop depends on the direction of current in the loop. On reversing the direction of current in the loop, the polarity at the faces of the loop gets reversed. Which face is which is decided by the clock rule.
The rule is applied in Fig. 10.4-2. In part (a), the current at the face of the loop we are looking at is anticlockwise, so that face behaves as a north pole. In part (b), the current at the face is clockwise, so that face behaves as a south pole.
Diagram
Fig. 10.4-2 — Polarities At The Faces Of A Loop Carrying Current Two circular loops drawn side by side, each seen face-on with its two ends brought down and connected to a cell. In part (a), draw arrowheads on the loop showing the current running anticlockwise around the face we are looking at, and write a large letter N inside the loop, drawn so that the strokes of the letter follow the anticlockwise sense; label it ‘anticlockwise current, north polarity’. In part (b), draw arrowheads showing the current running clockwise around the face, and write a large letter S inside the loop, drawn so that its strokes follow the clockwise sense; label it ‘clockwise current, south polarity’.
10.5 Magnetic Field Due To A Current Carrying Cylindrical Coil Or Solenoid
One loop of wire gives one loop’s worth of magnetic field. Stack many loops one behind the other and their fields add along a common axis, giving something far stronger and far more useful.
If a conducting wire is wound in the form of a cylindrical coil whose diameter is less in comparison to its length, the coil is called a solenoid. It looks like a helical spring, that is, a wire wound round and round in a long even spiral.
To obtain the magnetic field lines due to a current carrying solenoid, the following experiment is performed.
10.5.1 Tracing The Field Of A Solenoid
Take a cardboard having two slits PQ and P’Q’, parallel to each other, at a small separation and parallel to its length. Wind a uniform spiral of an insulated thick copper wire through the two slits, in such a way that the axis of the spiral lies in the plane of the cardboard. The board then slices the solenoid lengthwise, so that the pattern it shows is a section taken right through the coil.
Connect a battery through a rheostat and a key between the ends X and Y of the solenoid wire. Sprinkle some iron filings on the cardboard and pass current through the solenoid by closing the key. Gently tap the cardboard.
It is found that the iron filings on the cardboard get arranged in a definite pattern, as shown in Fig. 10.5-1, representing the pattern of magnetic field lines due to the current carrying solenoid. The direction of the magnetic field at a point is determined by using a compass needle, and arrows are marked on these lines in the direction in which the north pole of the compass needle points.
Diagram
Fig. 10.5-1 — Magnetic Field Lines Due To A Solenoid Carrying Current Draw a horizontal rectangular sheet of cardboard shown in perspective, with two parallel slits PQ and P’Q’ cut lengthwise in it; label the slits. Show an insulated copper wire wound as a long even spiral passing through the two slits, so that the axis of the spiral lies in the plane of the board; label it ‘solenoid’ and mark the direction of current with arrowheads on the turns. On the cardboard show iron filings arranged as field lines: inside the solenoid the lines are straight, parallel to the axis and closely spaced; outside they curve out from one end, spread widely round the coil and return to the other end. Put an arrowhead on each line. Mark the end P as the north pole N and the end Q as the south pole S. Lead the ends X and Y of the wire to a rheostat, a key and a battery in series, and label each of these.
10.5.2 Features Of The Field Line Pattern
From the pattern of magnetic field lines, it is found that:
The magnetic field lines inside the solenoid are nearly straight and parallel to the axis of the solenoid. That is, the magnetic field is uniform inside the solenoid.
The magnetic field lines become denser, that is, a strong magnetic field is obtained, on increasing the current in the solenoid.
The magnetic field is increased if the number of turns in the solenoid of a given length is increased.
The magnetic field is also increased if a soft iron rod, called a core, is placed along the axis of the solenoid. The soft iron increases the strength of the magnetic field of the solenoid, because soft iron has a high magnetic permeability, which is a measure of how readily magnetic field lines are set up inside a material.
In Fig. 10.5-1, the end P at which the direction of current is anticlockwise behaves as a north pole (N), while the end Q at which the direction of current is clockwise behaves as a south pole (S). On reversing the direction of current in the solenoid, the polarities at the ends of the solenoid are reversed, because the direction of the magnetic field has reversed.
The last of these is just the clock rule of Section 10.4 applied to the two ends of the coil, and it is worth reading each end from outside the solenoid, looking straight at it along the axis.
10.5.3 Similarities Between A Current Carrying Solenoid And A Bar Magnet
The magnetic field lines of a current carrying solenoid are similar to the magnetic field lines of a bar magnet. Thus, a current carrying solenoid behaves just like a bar magnet. The two patterns are placed side by side in Fig. 10.5-2.
A current carrying solenoid, when suspended freely, sets itself in the north–south direction, exactly in the same manner as a bar magnet does.
A current carrying solenoid also acquires the attractive property of a magnet. If iron filings are brought near the current carrying solenoid, it attracts them.
Diagram
Fig. 10.5-2 — Field Of A Solenoid Compared With That Of A Bar Magnet Two drawings placed side by side. On the left, a current carrying solenoid drawn in section with arrowheads on its turns, its field lines straight and parallel inside the coil and looping widely round the outside from one end to the other, with the ends marked N and S. On the right, a bar magnet of about the same length with its ends marked N and S, and its field lines drawn looping from the N end round to the S end in the same pattern. Put an arrowhead on every field line. Caption the two drawings ‘solenoid carrying current’ and ‘bar magnet’.
10.5.4 Dissimilarities Between A Current Carrying Solenoid And A Bar Magnet
The strength of the magnetic field due to a solenoid can be changed by changing the current in it, while the strength of the magnetic field due to a bar magnet cannot be changed.
The direction of the magnetic field due to a solenoid can be reversed by reversing the direction of current in it, but the direction of the magnetic field due to a bar magnet cannot be reversed.
Both differences come from the same source. The solenoid’s magnetism is borrowed from a current, and a current is something we can turn up, turn down or turn round at a switch. The bar magnet’s magnetism is built into the material itself, and there is no switch on it.
10.6 Electromagnet
A solenoid behaves like a magnet so long as a current passes through it. As soon as the current is switched off, it loses its magnetic behaviour altogether. A current carrying solenoid is therefore a temporary magnet, and it is called an electromagnet.
You already know from Section 10.5 that the magnetic field of a solenoid is considerably increased by inserting a soft iron core in it. Every practical electromagnet is built that way, so the definition of the device names the core as part of it.
The word temporary is the heart of it. The magnetism can be switched on, switched off, made stronger, made weaker or turned round, all from the circuit and without touching the iron.
An electromagnet can be made in any shape, but usually the following two shapes of electromagnet are in use:
- I-shape, or bar, magnet, and
- U-shape, or horse-shoe, magnet.
10.6.1 Construction Of An I-Shaped Or Bar Electromagnet
To construct an I-shaped electromagnet, a thin insulated copper wire XY is wound in the form of a solenoid around a straight soft iron bar PQ. A battery B, through an ammeter A, a rheostat Rh and a key K, is connected between the ends X and Y of the wire, as shown in Fig. 10.6-1.
Diagram
Fig. 10.6-1 — I-Shaped Electromagnet Draw a straight horizontal soft iron bar with its left end labelled P and its right end labelled Q, and label the bar ‘soft iron bar’. Wind a thin insulated copper wire evenly along the bar as a solenoid, with arrowheads on the turns showing the direction of current; label the left-hand end of the wire X and the right-hand end Y. Connect X and Y through an ammeter A, a rheostat Rh, a key K and a battery B in series, and label each. At the end P draw a circular arrow seen end-on running clockwise, and mark P as the south pole S; at the end Q draw a circular arrow running anticlockwise, and mark Q as the north pole N.
When current is passed through the winding of the solenoid by closing the key K, the end P of the bar becomes the south pole (S), since the current at this face is clockwise, while the end Q, at which the current is anticlockwise, becomes the north pole (N). To read either end, look straight at that end face along the bar and note the sense in which the current runs round it, then apply the clock rule. Thus the bar PQ becomes a magnet.
The bar remains magnetised so long as the electric current flows through the solenoid, but it gets demagnetised as soon as the current is switched off. It is therefore a temporary magnet.
Use. A bar shaped electromagnet is commonly used in a relay. A relay is a switching device, in which a small current in the electromagnet’s coil is used to pull a contact across and so switch on a much larger current in a separate circuit.
10.6.2 Construction Of A U-Shaped Or Horse-Shoe Electromagnet
To construct a horse-shoe electromagnet, a thin insulated copper wire XY is spirally wound on the two arms of a U-shaped soft iron core, in such a way that the winding, as seen from the ends, is in opposite sense on the two arms.
In Fig. 10.6-2, the winding on the arm P starts from the front and is in the clockwise direction, when viewed from the bottom. On reaching the upper end of the arm P, the winding starts from the back at the top of the arm Q, and it is in the anticlockwise direction. Between the ends X and Y of the wire, a battery through an ammeter, a rheostat and a key is connected.
The opposite sense of winding is not a detail of workmanship. It is what makes the two arm ends come out as opposite poles, so that the field lines leave one pole and cross the gap straight into the other.
Diagram
Fig. 10.6-2 — Horse-Shoe Electromagnet Draw a U-shaped soft iron core standing with its two arms pointing downwards and the bend at the top; label it ‘soft iron core’ and mark the left arm P and the right arm Q. Wind an insulated copper wire spirally on both arms, drawn so that the winding runs clockwise on the arm P and anticlockwise on the arm Q when each is viewed from below, with arrowheads showing the direction of current; label the wire ends X and Y. Mark the lower end of the arm P as the south pole S and the lower end of the arm Q as the north pole N, and show several magnetic field lines crossing the gap from N to S. Connect X and Y through an ammeter, a rheostat, a key and a battery in series, and label each.
When current is passed through the winding by closing the key, the end of the arm P becomes the south pole S, because the current at this face is clockwise, and the end of the arm Q becomes the north pole N, because the current at this face is anticlockwise. Thus we get a very strong magnetic field in the gap between the two poles, since the two poles face each other across a short distance.
The magnetic field in the gap vanishes as soon as the current in the circuit is switched off. Thus, it too is a temporary magnet.
Use. Horse-shoe magnets are used in gadgets like the d.c. motor, the a.c. generator and the electric bell, all of which you will meet later in this chapter.
The Source Must Be Direct Current
For sending current in the coil, the source must be a d.c. source, that is, a battery. With an a.c. source of frequency 50 Hz, the soft iron core does get magnetised as long as the current is passed, but the polarity at its ends keeps changing 100 times in each second, so the ends do not stay a fixed north and south at all.
10.6.3 Ways Of Increasing The Magnetic Field Of An Electromagnet
The magnetic field of an electromagnet, whether I-shaped or U-shaped, can be increased by the following two ways:
- by increasing the number of turns of winding in the solenoid, and
- by increasing the current through the solenoid.
Both are ways of getting more current threading the same piece of iron, and the rheostat in the circuit is there so that the second of them can be done at the turn of a knob.
10.7 Permanent Magnet
Naturally occurring magnets are permanent magnets, but they are not strong enough, and they are also not of the required shape for many purposes. A lump of magnetic rock is of little use inside an ammeter.
So a strong permanent magnet is made, and it is made in very much the same way as an electromagnet — with one deliberate change of material. A piece of steel is used instead of soft iron, since steel has more magnetic retentivity than soft iron. Retentivity is a material’s ability to hold on to its magnetism after the magnetising field has been taken away.
A coil of insulated copper wire is wound around the steel piece and current is passed in the coil. The steel piece gets magnetised, and is then taken out from the coil, as shown in Fig. 10.7-1. Once it is magnetised in this manner, the steel piece retains its magnetism for a longer period, and is thus used as a permanent magnet.
Diagram
Fig. 10.7-1 — Making A Permanent Magnet From Steel Two drawings side by side. On the left, a straight steel bar lying inside a solenoid of insulated copper wire, the ends of the winding connected through a key to a battery, with arrowheads on the winding showing the direction of current; label the bar ‘steel bar’ and the winding ‘insulated copper wire’, and mark N at one end of the bar and S at the other. On the right, the same steel bar shown alone, taken out of the coil, still marked N at one end and S at the other, with the caption label ‘magnetism retained after removal’.
The permanent magnets so made are used in electric meters, such as a galvanometer, an ammeter and a voltmeter, and in a magnetic compass.
Look at that list again and you will see why a permanent magnet is the right choice there. A meter must give the same reading today as it did last year, so the magnet inside it has to provide a fixed, unchanging field that needs no supply of its own.
10.8 Comparison Of An Electromagnet With A Permanent Magnet
You have now met both kinds of magnet, and it is worth setting them side by side. Almost every difference between them can be traced back to a single choice made at the start: soft iron for one, steel for the other.
Read the table as two stories rather than twelve facts. An electromagnet is a magnet you command: you decide when it exists, how strong it is and which end is north. A permanent magnet is a magnet you accept as it is: always on, always the same strength, always the same way round.
Neither is better in itself. Each is chosen for the job. A crane that must pick up scrap iron and then drop it needs a magnet that can be switched off, and only an electromagnet can do that. A compass needle carried on a boat, with no cell and no wires, needs a magnet that never switches off, and only a permanent magnet can do that.
10.9 Advantages Of An Electromagnet Over A Permanent Magnet
Of all the differences set out in Table 10.3, three amount to real advantages that an electromagnet holds over a permanent magnet. An electromagnet has the following advantages over a permanent magnet:
An electromagnet can produce a strong magnetic field.
The strength of the magnetic field of an electromagnet can easily be changed by changing the current, or the number of turns, in its solenoid.
The polarity of the electromagnet, or the direction of the field produced by it, can be reversed by reversing the direction of current in its solenoid.
The second and third of these are worth pausing over. They mean that a single electromagnet can be made to give a field of any strength up to its maximum, pointing either way, and all of it under the control of a switch and a rheostat. It is this control, rather than sheer strength, that makes the electromagnet the working heart of the machines described in the rest of this chapter.
10.10 Uses Of Electromagnet
Electromagnets are mainly used for the following purposes.
For lifting and transporting heavy iron scrap, girders, plates and the like, particularly when it is not convenient to take the help of human labour. Electromagnets are used to lift as much as 20,000 kg of iron in a single lift. To unload the iron objects at the desired place, the current in the electromagnet is switched off, so that the electromagnet gets demagnetised and the iron objects get detached.
For loading the furnaces with iron.
For separating the iron pieces from debris and ores, where iron exists as an impurity — for example, for separating iron from the crushed copper ore in copper mines.
For removing the pieces of iron from wounds.
In scientific research, to study the magnetic properties of a substance in a magnetic field.
In several electrical devices such as the electric bell, the telegraph, the electric tram, the electric motor, the relay, the microphone and the loud speaker.
Run your eye down that list and one thread joins nearly all of it. In every case the useful step is not the switching on but the switching off. A crane that could only attract, and never let go, would be a poor crane.
10.10.1 Use Of An Electromagnet In An Electric Bell
An electric bell is one of the most commonly used applications of an electromagnet.
Construction And Wiring
An electric bell is shown in Fig. 10.10-1. The main parts of the bell are:
- a horse-shoe electromagnet M, having a soft iron core,
- a soft iron armature A, which is the movable iron piece that the electromagnet pulls on,
- a hammer H,
- a gong G, which is the metal cup that is struck to make the sound,
- a metallic spring strip SS,
- an adjusting screw S′,
- a switch, or bell-push, K, and
- a battery.
Diagram
Fig. 10.10-1 — Electric Bell And Its Wiring Draw a horse-shoe electromagnet M lying on its side with its two pole faces towards the left, and show the coil CC wound on its two arms with the windings in opposite directions; label M, the coil CC and the soft iron core. To the left of the pole faces draw a flat soft iron armature A, with a small gap between it and the poles, and an arrow labelled ‘attraction’ pointing from A towards the poles. Fix A to a vertical metallic spring strip SS, and attach a hammer H to the upper end of the armature, with its head just clear of a gong G drawn as a metal cup at the top. Draw an adjusting screw S′ touching the spring strip SS. Show one end of the coil going from the screw S′ and the strip SS to a terminal T1, and the other end of the coil going directly to a terminal T2. Connect T1 and T2 through a switch K, labelled bell-push, and a battery, in series. Label every part with its letter.
The armature A is fixed to the spring strip SS. The hammer H is attached at the upper end of the armature A. When the switch K is not pressed, the strip SS makes contact with the adjusting screw S′, and there is a gap between the armature A and the poles of the electromagnet.
The coil CC is wound on the two arms of the electromagnet in the opposite direction, as shown in the diagram, so that the two arms end as opposite poles. One end of the coil is connected to the terminal T₁ through the strip SS and the screw S′, while the other end is directly connected to the terminal T₂. A battery is provided in series with the switch K across the terminals T₁ and T₂.
Notice where the contact between SS and S′ sits: it is inside the coil’s own circuit. The bell can therefore switch itself off, and that is the secret of the whole device.
Working And Function Of Each Part
The working of an electric bell is based on the magnetic effect of current.
As the electric circuit is closed by pressing the switch K, the current flows through the coil CC, and the core of the electromagnet gets magnetised. It therefore attracts and pulls the armature A, in the direction of the arrow in Fig. 10.10-1. Due to this movement of the armature A, the hammer H strikes the gong G and the bell rings.
At the moment when the armature A moves towards the electromagnet due to magnetic attraction, the connection between the strip SS and the screw S′ breaks. The flow of current in the coil therefore stops. Consequently the electromagnet gets demagnetised, and the armature A flies back to its original position due to the spring effect of the strip SS.
Now the armature again touches the screw S′, which results in the flow of current in the coil. The electromagnet regains its magnetism, the armature A is again attracted, and so the hammer H again strikes the gong G. This process continues.
The process of make and break of the circuit goes on, and the hammer strikes the gong repeatedly, so the bell rings as long as the switch K is kept pressed. The cycle is set out in FC 10.1.
Flowchart
FC 10.1 — The Make And Break Cycle Of An Electric Bell Switch K pressed → current flows in coil CC → electromagnet M gets magnetised → armature A is attracted towards the poles → hammer H strikes the gong G, and contact between strip SS and screw S′ breaks → current in the coil stops → electromagnet M gets demagnetised → spring strip SS pulls armature A back → contact at screw S′ is remade → cycle returns to ‘current flows in coil CC’ and repeats so long as K is pressed
If an a.c. source is used in place of the battery, the core of the electromagnet will get magnetised, but the polarity at its ends will change. Since the attraction of the armature does not depend on the polarity of the electromagnet — a magnet attracts soft iron whichever way round it is — the bell will still ring on pressing the switch K.
10.11 Force On A Current Carrying Conductor In A Magnetic Field
So far the current has been the master. A current makes a magnetic field, and that field pushes a compass needle about. Now turn the situation round and ask the opposite question: if a magnetic field already exists, what does it do to a current placed inside it?
Lorentz observed that a charge moving in a magnetic field, in a direction other than the direction of the magnetic field, experiences a force. This force was named the Lorentz force.
Since a charge in motion constitutes a current, a conductor carrying moving charges — that is, a conductor carrying a current — placed in a magnetic field in a direction other than the direction of the magnetic field also experiences a force, and this force can produce motion in the conductor.
That last sentence is the seed of the electric motor, and of very nearly every machine that turns electricity into movement.
10.11.1 Demonstrating The Force
The arrangement is shown in Fig. 10.11-1. A thick copper wire AC is suspended horizontally from its ends A and C from a support, by means of two separate threads. The threads matter: the wire must be free to swing, or a force acting on it would show nothing at all.
A magnetic field \(B\) is applied in the vertical direction by keeping the wire AC in between the poles N and S of a strong horse-shoe magnet, with the length AC of the wire normal to the magnetic field lines of the magnet. A current is passed from the end A to the end C of the wire, by connecting a rheostat, a key and a battery in series with it.
The magnetic field \(B\) is in the plane of the paper, which is kept vertical, and points in the upward direction, that is, in the Y direction. The wire also lies in the plane of the paper, with its length AC along the X direction.
Diagram
Fig. 10.11-1 — Force On A Current Carrying Conductor Draw a vertical stand with a horizontal support arm at the top. From two points on the arm hang two separate threads, and from their lower ends suspend a thick horizontal copper wire, with its left end labelled A and its right end labelled C. Between the poles of a strong horse-shoe magnet, drawn with its N pole below and its S pole above so that the field lines run vertically upwards across the wire, place the middle part of the wire; label N, S and mark the field lines B with upward arrows. Show an arrow on the wire from A to C labelled ‘current I’. Show a bold arrow on the wire pointing out of the plane of the paper towards the reader, labelled ‘force F’. Lead the ends A and C through a rheostat, a key and a battery connected in series, and label each.
What Is Observed
When no current flows in the wire, no force acts on the wire and the wire does not move.
When a current \(I\) is passed in the wire in the direction from A to C, that is, in the X direction, a force \(F\) acts on the wire in a direction perpendicular to both the direction of current \(I\) and the direction of magnetic field \(B\). Due to the force \(F\), the conductor begins to move towards the observer, that is, normal to the plane of the paper in the outward direction, which is the Z direction. The three directions are drawn separately in Fig. 10.11-2.
If the direction of current through the wire is reversed, by interchanging the terminals of the battery, the direction of force — and so the direction of movement of the wire — is also reversed. The wire now moves away from the observer, into the plane of the paper, in the \(-Z\) direction.
On reversing the direction of the magnetic field, that is, on reversing the polarities N and S of the horse-shoe magnet, the direction of force is again reversed as compared with observation 2. The wire once more moves in the \(-Z\) direction.
Diagram
Fig. 10.11-2 — Directions Of Current, Field And Force Draw three straight arrows starting from a common point, mutually at right angles, in the style of a set of coordinate axes. Label the arrow pointing to the right X and mark it with the symbol I for the direction of current. Label the arrow pointing upwards Y and mark it with the symbol B for the direction of magnetic field. Label the arrow pointing out of the plane of the paper towards the reader Z and mark it with the symbol F for the direction of force. Add the note that I, B and F are mutually perpendicular to each other.
If the wire is short and is placed between the poles of the magnet with its length along the Y direction, so that the current in it is in a direction parallel to the direction of the magnetic field, then no force acts on the wire and it does not move. A magnetic field pushes only on a current that cuts across it, never on one that runs along it.
10.11.2 Magnitude Of The Force
Before writing any formula, say the relationship in words. A bigger current is pushed harder. A stronger magnet pushes harder. And the longer the piece of wire lying in the field, the more of it there is to push. Experiment bears out all three, one at a time.
It is found experimentally that the magnitude of the force acting on a current carrying wire placed in a magnetic field in the direction perpendicular to its length depends on the following three factors.
a. The force $F$ is directly proportional to the current $I$ flowing in the wire:\[F \\propto I\]
b. The force $F$ is directly proportional to the strength of the magnetic field $B$:\[F \\propto B\]
c. The force $F$ is directly proportional to the length $l$ of the wire lying within the magnetic field:\[F \\propto l\]
Combining these three, \[F \\propto IBl\] or \[F = KIBl\]
where \(K\) is a constant whose value depends on the choice of the unit. In SI units, the unit of \(B\) is so chosen that \(K = 1\). Then
\[F = IBl \\qquad \\ldots (10.1)\]
where \(F\) is the force in newton (N), \(I\) the current in the wire in ampere (A), \(B\) the strength of the magnetic field in tesla (T), and \(l\) the length of the wire lying in the field in metre (m).
This relation holds only when the wire is placed at right angles to the direction of the magnetic field. If the wire lies along the field, the force is zero, as the note above records.
10.11.3 Unit Of Magnetic Field
Equation (10.1) does more than give a force. Rearranged, it gives us a way of saying what we mean by the strength of a magnetic field, and therefore what its unit must be.
From eqn. (10.1), \[B = \\frac{F}{I \\times l}\]
So the SI unit of magnetic field is newton per (ampere × metre), written \(\\text{N A}^{-1},\\text{m}^{-1}\). This unit is also named the tesla, symbol T, and it is the same as weber per metre squared, symbol \(\\text{Wb m}^{-2}\).
A field of one tesla is therefore the field which exerts a force of one newton on a wire one metre long lying at right angles to it and carrying a current of one ampere. In eqn. (10.1), the constant \(K = 1\) exactly when \(B\) is measured in tesla or in \(\\text{Wb m}^{-2}\).
10.11.4 Fleming’s Left Hand Rule
Equation (10.1) gives how big the force is. It says nothing about which way it points. For that we use Fleming’s left hand rule, which fixes the three mutually perpendicular directions on the three fingers of one hand.
The rule is shown in Fig. 10.11-3. Note that all three fingers must be at right angles to one another; held loosely at any other angles, the rule gives nothing.
Diagram
Fig. 10.11-3 — Fleming’s Left Hand Rule Draw a left hand with the forefinger, the central finger and the thumb stretched out mutually at right angles, and the remaining two fingers folded into the palm. Label the forefinger ‘fore finger — field’, with an arrow along it. Label the central finger ‘central finger — current’, with an arrow along it. Label the thumb ‘thumb — motion, that is, force’, with an arrow along it. Beside the hand, repeat the three words Field, Current and Motion against the matching fingers.
10.12 Simple D.C. Motor
We know that in electric gadgets such as a fan, a washing machine, a juicer, a mixer and a grinder, an electric motor is used to produce rotational motion by the use of electricity.
10.12.1 Principle Of The D.C. Motor
A d.c. motor works on the principle that on passing an electric current through a conductor placed normally in a magnetic field, a force acts on the conductor, as a result of which the conductor begins to move and thus mechanical energy, or work, is obtained.
This is exactly the effect of Section 10.11, put to work. The direction of the force on the conductor is obtained with the help of Fleming’s left hand rule.
The one new idea needed here is a couple. A couple is a pair of equal and opposite forces whose lines of action are not the same. Such a pair cannot push a body along, because the two forces cancel, but it can and does turn the body round. A motor is built so that the magnetic force on one side of a coil and the force on the other side form exactly such a pair.
10.12.2 Construction And Its Main Parts
The basic construction of an electric motor is shown in Fig. 10.12-1. The main parts of an electric motor are:
- the armature coil ABCD, mounted on an axle,
- the split parts S₁ and S₂ of a ring — that is, a copper slip ring divided into two parts S₁ and S₂ — which together are known as the split ring commutator,
- a pair of carbon, or copper, brushes B₁ and B₂,
- a horse-shoe electromagnet NS, and
- a d.c. source, that is, a battery.
Diagram
Fig. 10.12-1 — Main Parts Of A D.C. Motor Draw a horse-shoe electromagnet with its N pole face on the left and its S pole face on the right, the two faces vertical and facing each other. Between them place a rectangular armature coil ABCD wound on a soft iron core, mounted on a horizontal axle that runs out of the page; label the corners A, B, C and D and label the core and the axle. Bring the end A of the coil to one half of a divided copper ring labelled S₁, and the end D to the other half labelled S₂; label the pair ‘split ring commutator’. Show two fixed carbon brushes B₁ and B₂ pressing gently against S₁ and S₂ from below. From the brushes lead wires through a key and a rheostat to a battery, marking the positive and negative terminals; label each part.
The armature coil ABCD is wound around a soft iron core, and it is placed in between the pole pieces of a strong horse-shoe electromagnet NS. The coil is free to rotate about its axis.
The ends A and D of the coil are connected respectively to the split parts S₁ and S₂ of the ring. The brush B₁ presses gently against the split ring S₁, and the brush B₂ presses gently against the split ring S₂. A d.c. source is connected across the brushes B₁ and B₂ through a key and a rheostat.
Now hold on to this one moving detail, because everything in the next subsection follows from it. When the coil rotates, the split parts of the ring rotate with it, while the brushes, being fixed, remain at their position and make contact alternately with the split parts of the ring.
A wheel can be mounted on the axle attached along the axis of the armature coil. The wheel axle then rotates the desired part of the machine in which the motor is used.
10.12.3 Working Of The D.C. Motor
The four stages of one complete turn are drawn in Fig. 10.12-2.
Diagram
Fig. 10.12-2 — Working Of A D.C. Motor Four panels drawn side by side, each showing the same horse-shoe electromagnet with N on the left and S on the right, the coil between the poles, the split rings S₁ and S₂ below with brushes B₁ and B₂, and the battery with its positive and negative terminals marked. Panel (a) ‘initial position, plane of coil parallel to the magnetic field’: coil horizontal with corners marked A, B, C, D, current arrows showing the path ABCD, a force arrow into the page on the arm AB and a force arrow out of the page on the arm CD, S₁ touching B₁ and S₂ touching B₂. Panel (b) ‘after 90° rotation, plane of coil normal to the magnetic field’: coil vertical with arm AB in and arm CD out, and a clear gap drawn between each brush and each split ring, labelled ‘no contact, no current’. Panel (c) ‘after 180° rotation’: coil horizontal again with the arms interchanged, current arrows showing the path DCBA, a force arrow into the page on the arm DC and out of the page on the arm BA, with S₁ now touching B₂ and S₂ touching B₁. Panel (d) ‘after 270° rotation’: coil vertical again with the brushes once more out of contact with the split rings. Mark the sense of rotation with a curved arrow on every panel.
From The Start To A Quarter Turn
In Fig. 10.12-2(a), the plane of the coil is horizontal, and the split ring S₁ touches the brush B₁ while the split ring S₂ touches the brush B₂. The brush B₁ is connected to the positive terminal of the d.c. battery, while the brush B₂ is connected to its negative terminal.
When the key is closed, the current flows in the coil in the direction ABCD. The current in the arms BC and DA is parallel to the magnetic field, so these arms do not experience any force. The current in the arms AB and CD is perpendicular to the magnetic field, so each of these arms experiences a force \(F\), given by
\[F = IBl\]
where \(I\) is the current in the coil in ampere (A), \(B\) is the magnetic field strength in tesla (T), and \(l\) is the length of the side AB or CD of the coil in metre (m).
According to Fleming’s left hand rule, the force \(F\) on the arm AB is in the inward direction, perpendicular to the plane of the paper, and the force \(F\) on the arm CD is in the outward direction, perpendicular to the plane of the paper.
The forces on the arms AB and CD are equal and opposite, and they do not act along the same line. They therefore form an anticlockwise couple, due to which the coil begins to rotate, such that the arm AB goes in and the arm CD comes out.
At The Vertical Position
When the coil reaches the vertical position after a rotation of \(90^\\circ\) — that is, perpendicular to the plane of the paper, with the arm CD out and the arm AB in — as shown in Fig. 10.12-2(b), momentarily there is no contact between the brush B₁ and the split ring S₁, or between the brush B₂ and the split ring S₂.
So at this moment, no current flows through the coil, and thus no force acts on the coil. Due to the inertia of rotational motion, however, the coil does not stop in this position, but continues to rotate. Inertia is simply the tendency of a moving body to keep on moving unless something stops it, and here it carries the coil past the dead point.
From A Quarter Turn To A Half Turn
As the coil passes from its vertical position, the split ring S₁ comes in contact with the brush B₂, while the split ring S₂ comes in contact with the brush B₁, as in Fig. 10.12-2(c). The contacts have swapped over, and so the current now flows through the coil in the direction DCBA.
The arms CB and AD, being parallel to the magnetic field, experience no force. On the arm DC a force acts in the inward direction, perpendicular to the plane of the paper, and on the arm BA an equal force acts in the outward direction, perpendicular to the plane of the paper. The force is again maximum, that is \(F = IBl\), when the coil has turned by \(180^\\circ\) from the initial position.
The forces acting on the arms DC and BA of the coil again form an anticlockwise couple, due to which the coil remains rotating in the same direction. This is the point of the whole design: the arms have swapped sides, and the current in them has swapped too, so the turning effect is unchanged.
Completing The Turn
After a rotation of \(270^\\circ\), the coil reaches the vertical position shown in Fig. 10.12-2(d). Again for a moment there is no contact between the brush B₁ and the split ring S₂, or between the brush B₂ and the split ring S₁, and hence no current flows in the coil. But due to the inertia of motion the coil continues to rotate, and again it reaches back to its initial position. The coil keeps rotating as long as current flows in the coil.
The deflecting couple on the coil of the motor is maximum when the plane of the coil is parallel to the direction of the magnetic field. The deflecting couple is zero, or minimum, when the plane of the coil is perpendicular to the magnetic field.
10.12.4 Function Of The Split Ring Commutator
Whenever the coil passes from the vertical position, the direction of current through the coil has to be reversed, so as to keep the direction of the rotating couple unchanged.
This is achieved by the two split parts S₁ and S₂ of a conducting ring, which reverse the direction of current in the coil so that the coil continues to rotate in the same direction. They are called the split ring commutator.
Take the commutator away and the coil would turn half a circle, then find the couple acting the other way, and would simply rock to and fro instead of spinning.
10.12.5 Ways Of Increasing The Speed Of Rotation Of The Coil
The speed of rotation of the coil depends on the magnitude of the deflecting couple formed by the forces acting on the arms AB and CD of the coil. The deflecting couple is given by \(IBAn\), where \(I\) is the current in the coil in ampere (A), \(B\) is the strength of the magnetic field in tesla (T), \(A\) is the area of the coil in metre squared (m²), and \(n\) is the number of turns in the coil. Hence the speed of rotation of the coil is directly proportional to each of these factors.
The speed of rotation of the coil can therefore be increased by the following four ways:
- by increasing the strength of current in the coil,
- by increasing the number of turns in the coil,
- by increasing the area of the coil, and
- by increasing the strength of the magnetic field.
To increase the strength of the magnetic field, a soft iron core is inserted within the coil. The insertion of the core makes the magnetic field strong and radial, that is, the field lines run outwards from the axle like the spokes of a wheel. Due to the radial field, the couple acting on the coil remains almost constant during the rotation of the coil, except in the vertical position of the coil, where there is no current and the couple is zero.
10.12.6 Transformation Of Energy In A D.C. Motor
In a d.c. motor, the electrical energy supplied by the battery to the coil is transferred to mechanical energy, which rotates the coil. The chain is set out in FC 10.2.
Flowchart
FC 10.2 — Energy Transformation In A D.C. Motor Chemical energy stored in the battery → electrical energy carried by the current in the armature coil → magnetic force on the arms of the coil placed in the field → mechanical energy of the rotating coil and axle → useful work done by the machine driven by the axle
10.13 Electromagnetic Induction
We have read that when an electric current is passed through a conductor, a magnetic field is produced around the conductor. Faraday thought that since a magnetic field is produced by an electric current, it should be possible to produce an electric current by a magnetic field.
He performed a number of experiments and observed that whenever there is a change in the number of magnetic field lines linked with a conductor, an electromotive force, written e.m.f., is developed between the ends of the conductor. This e.m.f. lasts only as long as there is a change in the number of magnetic field lines through the conductor. An e.m.f. is the electrical push that drives a current round a circuit, and like potential difference it is measured in volt (V).
This phenomenon is called electromagnetic induction.
The number of magnetic field lines linked with a conductor is called the magnetic flux linked with it. This word will be used constantly from here on, so fix it now: flux means how many field lines thread through the coil, taken all together.
10.13.1 Demonstration Of Electromagnetic Induction
Wind an insulated copper wire in the form of a spiral on a paper or wooden cylinder, so as to form a coil in the form of a solenoid. Connect a centre zero galvanometer G between the two ends of the solenoid, which are labelled A and B. Then place a magnet NS at some distance, along the axis of the solenoid, as shown in Fig. 10.13-1.
Diagram
Fig. 10.13-1 — Demonstration Of Electromagnetic Induction Five panels drawn one below the other. In every panel show a solenoid wound on a paper cylinder lying horizontally, with its left end labelled B and its right end labelled A, its two ends joined below to a centre zero galvanometer G, and a bar magnet drawn to the right of the solenoid along its axis. Panel (a): magnet stationary with N facing the solenoid, marked v = 0, galvanometer pointer at zero. Panel (b): magnet with N facing the solenoid and an arrow marked v showing it moving towards the solenoid, galvanometer pointer deflected to the right, and an arrow in the coil marking current from B to A. Panel (c): magnet with N facing the solenoid, now at rest close to it, marked v = 0, pointer back at zero. Panel (d): magnet with N facing the solenoid and an arrow marked v showing it moving away, pointer deflected to the left, and an arrow in the coil marking current from A to B. Panel (e): magnet turned round with S facing the solenoid and an arrow marked v showing it moving towards the solenoid, pointer deflected to the left. Label each panel with what it shows.
What Is Observed
When the magnet is stationary, that is \(v = 0\), there is no deflection in the galvanometer and its pointer reads zero.
When the magnet, with its north pole facing the solenoid, is moved towards it, the galvanometer shows a deflection towards the right, showing that a current flows in the solenoid in the direction B to A.
As the motion of the magnet is stopped, the pointer of the galvanometer comes to the zero position. This shows that the current in the solenoid flows only as long as the magnet is in motion.
If the magnet is moved away from the solenoid, the pointer of the galvanometer deflects towards the left, showing that the current in the solenoid flows again, but now in the direction A to B, which is opposite to that in observation 2. The current becomes zero as soon as the magnet stops.
If the same movement of the magnet is done rapidly, the deflection in the galvanometer is more than before, although the direction of deflection remains the same. It shows that now more current flows.
If the magnet is brought towards the solenoid keeping its south pole towards it, the pointer of the galvanometer deflects towards the left, showing that the current in the solenoid flows in the direction A to B, which is again opposite to that shown in observation 2.
If the magnet is rapidly moved back and forth, that is oscillated, in this position, a current alternating in direction flows through the coil and the galvanometer.
Exactly similar observations are made in the galvanometer if the magnet is kept stationary and the solenoid is moved instead. This implies that it is the relative motion between the solenoid and the magnet which produces a current, irrespective of whether the magnet moves or the solenoid moves. Faraday repeated the experiment with different magnets, and with coils of different sizes and different numbers of turns.
Conclusions
From the above observations Faraday made the following three conclusions.
A current flows in the coil only when there is a relative motion between the coil and the magnet.
The direction of the current is reversed if the direction of motion, or the polarity of the magnet, is reversed.
The current in the coil is increased by (i) the rapid motion of the magnet or the coil, (ii) the use of a strong magnet, and (iii) increasing the area of cross section of the coil and increasing the number of turns in the coil.
10.13.2 Faraday’s Explanation
When there is no relative motion between the magnet and the coil, the total number of magnetic field lines of the magnet passing through the coil — that is, the magnetic flux linked with the coil — remains constant. Therefore no e.m.f. is induced in the coil and no current flows in it, as in Fig. 10.13-2(a).
When there is a relative motion between the coil and the magnet, the magnetic flux linked with the coil changes. For example, in Fig. 10.13-2(b), the coil is moved towards the north pole of the magnet, so the magnetic flux through the coil increases. Similarly, if the coil is moved away from the north pole of the magnet, the magnetic flux through the coil decreases.
Diagram
Fig. 10.13-2 — Change Of Magnetic Flux Through A Coil Two panels drawn one below the other. Both show a bar magnet on the left with N at its right end and S at its left end, with its field lines spreading out from the N pole towards the right, and a circular coil to the right of it connected to a galvanometer G. Panel (a): the coil is at rest, well away from the magnet, with only a few field lines passing through it, and the galvanometer pointer at zero; label it ‘no relative motion, flux constant, no e.m.f.’. Panel (b): the coil is shown closer to the magnet with an arrow marked ‘motion of coil’ pointing towards the magnet, with many more field lines now passing through it, and the galvanometer pointer deflected; label it ‘coil moved towards magnet, flux increases, e.m.f. induced’.
Due to the change in the magnetic flux linked with the coil, an e.m.f. is induced in the coil. The induced e.m.f. causes a current to flow in the coil if the circuit of the coil is closed.
10.13.3 Energy Transformation In Electromagnetic Induction
Electrical energy has appeared in the coil. It cannot have come from nowhere, and it is worth asking who paid for it.
In electromagnetic induction, the mechanical energy spent — that is, the work done — in moving the coil or the magnet in order to change the magnetic flux, is transformed into electrical energy in the form of current in the coil. The chain is set out in FC 10.3.
Flowchart
FC 10.3 — Energy Transformation In Electromagnetic Induction Mechanical energy spent in moving the magnet or the coil → change in the magnetic flux linked with the coil → e.m.f. induced between the ends of the coil → current in the closed circuit → electrical energy delivered to the circuit
Inducing An E.M.F. Without Moving Anything
The observations above can also be made without any magnet at all, and without moving anything.
Fig. 10.13-3 shows two coils P and S kept near each other. The coil P is joined to a cell, a key and a rheostat, while the coil S is joined to a centre zero galvanometer.
Diagram
Fig. 10.13-3 — Inducing An E.M.F. Using Two Coils Draw two separate coils side by side on the same horizontal line, not touching each other, labelled P on the left and S on the right. Connect the ends of coil P through a key and a rheostat to a cell, labelling each; mark the direction of current in coil P with arrowheads. Connect the ends of coil S to a centre zero galvanometer G, drawn with its pointer deflected to one side. Label coil P ‘primary coil, current varied’ and coil S ‘secondary coil, e.m.f. induced’. Show a few magnetic field lines produced by coil P passing through coil S.
When the current in the coil P is changed, the magnetic field produced by it changes, so the magnetic flux linked with the neighbouring coil S also changes. An e.m.f. is therefore induced in the coil S, due to which a deflection is observed in the galvanometer. The current carrying coil P behaves as a magnet, and a varying current has the same effect as a moving magnet in changing the flux linked with the coils.
The e.m.f. is induced, that is, the deflection lasts, only so long as there is a change in the current in the coil P.
The coil P, in which the current is varied, is called the primary coil, and the coil S, in which the e.m.f. is induced, is called the secondary coil. The direction of the induced e.m.f. in the coil S depends on whether the current in the coil P is increased or decreased. This is the principle which is used in a transformer, studied in Section 10.18.
10.14 Faraday’s Laws Of Electromagnetic Induction
On the basis of the experimental observations of Section 10.13, Faraday formulated the following two laws of electromagnetic induction.
The words ‘rate of change’ in the second law are doing the real work. It is not how much the flux changes that decides the e.m.f., but how quickly it changes. The same magnet pushed in twice as fast gives twice the e.m.f., even though the flux has altered by exactly the same amount.
If the circuit of the coil is closed, a current flows across the ends of the coil due to the total e.m.f. induced, which is equal to the sum of the e.m.f. induced across each turn of the coil.
10.14.1 Factors Affecting The Magnitude Of Induced E.M.F.
The magnitude of the e.m.f. induced in a coil is equal to the product of the rate of change of magnetic flux \(\\phi\) linked with each turn of the coil and the number of turns in the coil. That is,
\[\\text{induced e.m.f.} = \\frac{N \\times \\Delta\\phi}{\\Delta t} \\qquad \\ldots (10.3)\]
where \(N\) is the number of turns in the coil, \(\\Delta\\phi\) is the change in the magnetic flux of each turn in weber (Wb), \(\\Delta t\) is the time in which the magnetic flux changes in second (s), and the induced e.m.f. is in volt (V).
Thus, for a given coil and magnet, the induced e.m.f. depends on the following two factors:
- on the rate of change of magnetic flux linked with each turn, and
- on the number of turns in the coil.
10.14.2 Lenz’s Law
The two laws above tell us how large the induced e.m.f. is. They say nothing about which way round it acts.
The direction of the induced e.m.f., and hence the direction of the induced current, depends on whether there is an increase or a decrease in the magnetic flux. It can be obtained by either of two rules: Lenz’s law, and Fleming’s right hand rule.
Lenz’s law sounds abstract until you apply it to the demonstration of Section 10.13, so let us do exactly that. The two cases are drawn in Fig. 10.14-1.
When the north pole of the magnet is brought towards the end A of the solenoid, the induced current flows in the solenoid in the direction B to A. At the end A this current is anticlockwise, so by the clock rule the end A of the solenoid becomes a north pole. Two north poles repel, so the solenoid now pushes the approaching magnet back. It opposes the motion of the north pole of the magnet towards the solenoid, and that motion is exactly the cause which produced it.
Similarly, when the north pole of the magnet recedes from the end A of the solenoid, the direction of the induced current in the solenoid is from A to B, that is, it is clockwise at the end A. The end A therefore becomes a south pole. A south pole attracts the departing north pole and tries to hold it back, so again it opposes the motion of the magnet away from the solenoid, which is the cause producing it.
Diagram
Fig. 10.14-1 — Lenz’s Law Applied To A Solenoid Two panels drawn one above the other. Each shows a solenoid lying horizontally with its left end B and its right end A, joined to a centre zero galvanometer, and a bar magnet to the right of it on the same axis with its N pole facing the solenoid. Panel (a): an arrow shows the magnet moving towards the solenoid; mark the induced current in the coil as running from B to A, draw a small circular arrow at the end A showing it anticlockwise as seen from the magnet, mark N at the end A, and add two repulsion arrows pointing apart between the magnet and the solenoid with the label ‘induced pole repels the approaching magnet’. Panel (b): an arrow shows the magnet moving away from the solenoid; mark the induced current as running from A to B, draw a small circular arrow at the end A showing it clockwise as seen from the magnet, mark S at the end A, and add two attraction arrows pointing towards each other with the label ‘induced pole attracts the receding magnet’.
Notice that in both cases the solenoid resists what you are trying to do. Push the magnet in and it pushes back; pull the magnet out and it holds on. You must therefore do work against this opposition, and that is where the electrical energy comes from.
Lenz’s law is based on the law of conservation of energy. It shows that mechanical energy is spent in doing work against the opposing force experienced by the moving magnet, and this is transformed into the electrical energy due to which the current flows in the solenoid.
Ask yourself what a violation would mean. If the induced pole attracted the approaching magnet instead of repelling it, the magnet would be pulled in faster, giving a bigger current, which would pull harder still — energy from nothing, which cannot happen.
10.14.3 Fleming’s Right Hand Rule
Lenz’s law is easiest to use when a magnet approaches a coil. When instead a straight conductor is moved across a magnetic field, a second rule is more convenient.
The rule is shown in Fig. 10.14-2. As with the left hand rule, the three fingers must be held at right angles to one another for it to mean anything.
Diagram
Fig. 10.14-2 — Fleming’s Right Hand Rule Draw a right hand with the thumb, the forefinger and the central finger stretched out mutually at right angles and the other two fingers folded into the palm. Label the forefinger ‘fore finger — field’, the thumb ‘thumb — motion of the conductor’, and the central finger ‘central finger — induced current’, with an arrow along each. Beside the hand repeat the three words Field, Motion and Induced current against the matching fingers.
10.15 A.C. Generator
We know the use of an a.c. generator in our house or factory as an alternative source of electricity, when the electric supply from the mains is not available.
The motor of Section 10.12 took electrical energy and gave back motion. A generator does the reverse, and it does so using electromagnetic induction.
10.15.1 Principle Of The A.C. Generator
In a generator, a coil is rotated in a magnetic field. Due to the rotation, the magnetic flux linked with the coil changes, and therefore an e.m.f. is induced between the ends of the coil.
Thus a generator acts as a source of current in an external circuit containing a load, when that circuit is joined between the ends of its coil. A load simply means whatever is being run from the generator — a lamp, a fan, a whole household.
10.15.2 Construction And Its Main Parts
The basic construction of an a.c. generator is shown in Fig. 10.15-1. The main parts of an a.c. generator are:
- a horse shoe electromagnet NS,
- the armature coil ABCD,
- the slip rings S₁ and S₂, and
- the brushes B₁ and B₂.
Diagram
Fig. 10.15-1 — A.C. Generator Draw a horse shoe electromagnet with its N pole face on the left and its S pole face on the right, the two faces vertical and facing each other, and label them ‘poles of horse shoe magnet’. Between the poles place a rectangular armature coil ABCD wound on a soft iron core and mounted on a horizontal axle running out of the page; label the corners A, B, C and D, and label the soft iron core, the armature coil and the axle. Bring the end A of the coil to a metallic ring labelled S₁ and the end D to a second metallic ring labelled S₂, the two rings drawn coaxial and separate, and label the pair ‘slip rings’. Show two fixed carbon brushes B₁ and B₂ pressing against S₁ and S₂ respectively, each held by a small spring. From the outer ends of the brushes lead wires to a load drawn as a resistor, and label it ‘load’.
A horse shoe electromagnet NS. It is a strong magnet with poles N and S, which provides the magnetic field in which the coil turns.
The armature coil ABCD. There is a soft iron core on which a coil ABCD, having a large number of turns of insulated copper wire, is wound. The coil is rotated rapidly in the magnetic field between the poles of the field magnet, by an axle fixed to it.
The slip rings S₁ and S₂. There are two coaxial metallic rings S₁ and S₂ which rotate along with the coil. One end of the coil is connected to the slip ring S₁ and the other end of the coil is connected to the slip ring S₂. During rotation, each ring slips against a brush which is stationary.
The brushes B₁ and B₂. There are two brushes B₁ and B₂ made of carbon, which press gently, with the help of springs, against the slip rings S₁ and S₂ respectively. The other ends of the brushes act as the terminals of the generator, across which the external circuit containing the load is connected. The brushes B₁ and B₂ do not rotate along with the coil and the slip rings.
10.15.3 Working Of The A.C. Generator
The working of an a.c. generator is shown in Fig. 10.15-2. Let the magnetic field be in the plane of the paper, running from the north pole N to the south pole S.
Throughout what follows, the angle \(\\theta\) means the angle which the normal to the plane of the coil makes with the direction of the magnetic field. The normal is the line drawn at right angles to the plane of the coil.
Diagram
Fig. 10.15-2 — Working Of An A.C. Generator Four panels drawn side by side. Each shows the same horse shoe magnet with N on the left and S on the right, field lines running from N to S across the page, the coil ABCD between the poles, the two slip rings S₁ and S₂ below with brushes B₁ and B₂ touching them, and the load connected across the brushes. Panel (a), labelled ‘plane of coil normal to the magnetic field, initial position, θ = 0°’: the coil is drawn edge-on with the arm AB below the plane of the paper and the arm CD above it, and the flux through the coil marked maximum. Panel (b), labelled ‘plane of coil parallel to the magnetic field, after 90° rotation’: the coil is drawn in the plane of the paper, with current arrows marking the path ABCD in the coil and an arrow in the external circuit showing current flowing from brush B₂ through the load to brush B₁; mark the flux as zero and the e.m.f. as maximum. Panel (c), labelled ‘after 180° rotation, θ = 180°’: the coil edge-on again with the arms interchanged, flux maximum, e.m.f. zero. Panel (d), labelled ‘after 270° rotation’: the coil in the plane of the paper with the arms interchanged, current arrows marking the path DCBA and an arrow in the external circuit showing current flowing from brush B₁ through the load to brush B₂; flux zero and e.m.f. maximum in the opposite sense. Mark the sense of rotation with a curved arrow on every panel.
From The Start To A Quarter Turn
Initially, let the normal to the plane of the coil be in the direction of the magnetic field, that is \(\\theta = 0^\\circ\), so that the maximum number of magnetic field lines pass through the coil. In this position the arm AB of the coil is below the plane of the paper, while the arm CD is above it, as shown in Fig. 10.15-2(a).
The end A of the coil is connected to the slip ring S₁ and the end D to the slip ring S₂. The brush B₁ touches the slip ring S₁ and the brush B₂ touches the slip ring S₂. No e.m.f. is induced in the coil when it is at rest.
Let the coil now be rotated clockwise, seen from the load end, by the handle attached to the axle. As the coil starts rotating, the magnetic flux through the coil decreases, and therefore an e.m.f. is induced between the ends of the coil, due to which an induced current flows in the coil.
By Fleming’s right hand rule, the direction of the induced current in the coil is along ABCD. This is because when the coil rotates clockwise, the arm AB moves upwards, that is, from below into the plane of the paper, so the induced current in the arm AB is from A to B; while the arm CD moves inwards, that is, from above into the plane of the paper, so the induced current in it is from C to D. Therefore, in the external circuit, the current flows from the brush B₂ to the brush B₁ through the load.
When the coil has rotated by \(90^\\circ\), the normal to the plane of the coil becomes perpendicular to the magnetic field, that is \(\\theta = 90^\\circ\), as shown in Fig. 10.15-2(b). Now no magnetic field line passes through the coil, so the magnetic flux linked with the coil becomes zero. At this instant the e.m.f. induced in the coil is maximum, because the rate of change of magnetic flux is maximum at this instant.
That statement is worth pausing on, because it seems back to front at first reading. The e.m.f. is greatest exactly where the flux is least. It is not the flux that induces the e.m.f. but the speed at which the flux is changing, and the flux sweeps past zero at its fastest.
From A Quarter Turn To A Full Turn
On rotation of the coil further by \(90^\\circ\), it is at \(180^\\circ\) from its initial position, and the normal to the plane of the coil again becomes parallel to the magnetic field, that is \(\\theta = 180^\\circ\), as shown in Fig. 10.15-2(c). Now the magnetic field lines passing through the coil become maximum. At this position of the coil the rate of change of magnetic flux is zero, and therefore no e.m.f. is induced in the coil.
When the coil gets rotated further, the magnetic flux linked with the coil decreases and the e.m.f. again increases to the same maximum value, but in the opposite direction. When the coil has turned by \(270^\\circ\) from its initial position, as shown in Fig. 10.15-2(d), the e.m.f. induced in the coil is maximum, because the rate of change of magnetic flux is again maximum at this instant.
Now the arms AB and CD of the coil have interchanged their positions. As a result, an induced current flows in the coil in the direction DCBA, that is, in the external circuit from the brush B₁ to the brush B₂ — the opposite way round to before.
On further rotation of the coil, the induced e.m.f. reduces to zero, and the magnetic flux linked with the coil becomes maximum, when the normal to the plane of the coil has been rotated by \(360^\\circ\) and becomes parallel to the magnetic field once more, as in Fig. 10.15-2(a).
The E.M.F. Produced
Thus, as the coil rotates in the magnetic field between the poles of the field magnet, an induced e.m.f. is produced between the ends of the coil. The e.m.f. so produced changes its polarity as well as its magnitude in each rotation of the coil, so it is called an alternating e.m.f.
Due to this induced e.m.f., an alternating current flows in the external circuit connected between the brushes B₁ and B₂. The direction of the current reverses after each half rotation of the coil. Alternating current is abbreviated as a.c.
Two results are worth setting down on their own.
The magnitude of the induced e.m.f. becomes maximum when the magnetic flux linked with the coil reduces to zero from its maximum value. This happens when the plane of the coil lies along the direction of the magnetic field.
The induced e.m.f. becomes zero when the magnetic flux linked with the coil is maximum. This happens when the plane of the coil is normal to the magnetic field.
Fig. 10.15-3 represents the variation in the e.m.f. induced between the ends of the coil with the angle \(\\theta\) which the normal to the plane of the coil makes with the direction of the magnetic field.
Diagram
Fig. 10.15-3 — Generation Of E.M.F. In The Coil Draw a graph with the vertical axis labelled ‘e.m.f. (volt)’ and the horizontal axis labelled ‘angle θ (degrees)’, with the horizontal axis marked at 0°, 90°, 180°, 270° and 360°, and the origin placed at the middle of the vertical axis so that values above and below zero can both be shown. Draw one complete sine curve: starting at zero at 0°, rising to a peak above the axis at 90°, falling back to zero at 180°, dipping to an equal trough below the axis at 270°, and returning to zero at 360°. Label the peak and the trough as the maximum value of the e.m.f. Below the graph, draw four small sketches of the coil between the poles N and S, placed under 0°, 90°, 180° and 270°, showing the coil edge-on at 0° and 180° and face-on at 90° and 270°.
10.15.4 Frequency Of The Alternating Current Generated
In one complete rotation of the coil, we get one cycle of alternating current in the external circuit. Thus, the generated alternating current has a frequency equal to the frequency of rotation of the coil. Frequency is the number of complete cycles produced in one second, and it is measured in hertz (Hz).
If the coil makes \(n\) rotations per second, the magnitude of the induced e.m.f. at any instant \(t\) is given as
\[e = e\_0 \\sin 2\\pi n t \\qquad \\ldots (10.4)\]
and the current is expressed as
\[i = i\_0 \\sin 2\\pi n t \\qquad \\ldots (10.5)\]
where \(e\) is the e.m.f. at the instant \(t\) in volt (V), \(i\) the current at that instant in ampere (A), \(t\) the time in second (s), \(n\) the number of rotations of the coil per second, and \(e\_0\) and \(i\_0\) represent the maximum values of the e.m.f. and of the current respectively.
The maximum value \(e\_0\) of the e.m.f. induced can be increased by:
- increasing the number of turns in the coil,
- increasing the area of cross section of the coil, and
- increasing the speed of rotation of the coil.
Note that the third of these does two things at once. By increasing the speed of rotation of the coil, the frequency of the a.c. generated will also increase, along with the increase in the maximum value \(e\_0\) of the induced e.m.f. Note also that the magnitude of an alternating current changes continuously with time, in a periodic manner — that is, repeating the same pattern over and over.
10.16 Frequency Of A.C. In Household Supplies
In our houses we have an electric supply of frequency 50 Hz. That is, the coil at the generating station turns 50 times each second, and the polarity at the supply terminal changes 100 times a second — 50 times positive and 50 times negative.
Count carefully and the two numbers stop looking contradictory. In each single cycle the terminal goes positive once and negative once, so 50 cycles bring 100 changes of polarity.
10.16.1 Difference Between D.C. And A.C.
If a resistor is connected across the terminals of a battery, a current flows in the resistor whose magnitude remains constant, and it always flows in one direction, from the positive terminal of the battery to its negative terminal.
But if a resistor is connected at the output terminals of an a.c. generator, or at the mains in our house, the magnitude of the current in the resistor changes periodically. The current repeats its value after each time interval equal to \(\\tfrac{1}{50}\\ \\text{s}\). Its direction also changes: it is in one direction for \(\\tfrac{1}{100}\\ \\text{s}\) and then in the reverse direction for the next \(\\tfrac{1}{100}\\ \\text{s}\).
A current of constant magnitude and unique direction is called direct current, abbreviated d.c., while a current changing its magnitude as well as its direction periodically is called alternating current. A battery is a d.c. source, while the a.c. generator and the mains are a.c. sources.
The difference is easiest to see drawn out against time, as in Fig. 10.16-1.
Diagram
Fig. 10.16-1 — Direct Current Compared With Alternating Current Two graphs drawn one above the other at the same scale. Both have the horizontal axis labelled ‘time (s)’ and the vertical axis labelled ‘current (A)’, with the zero line drawn across the middle so that values above and below zero can be shown. The upper graph, labelled ‘direct current from a battery’, shows a straight horizontal line lying wholly above the zero line at a constant height. The lower graph, labelled ‘alternating current from the mains’, shows a smooth sine curve crossing the zero line, rising above it and dipping equally below it, with one complete cycle marked off and labelled ‘one cycle, 0.02 s’. On the lower graph mark the region above the axis ‘current one way’ and the region below ‘current the other way’.
10.16.2 Advantage Of A.C. Over D.C.
- It is cheaper and easy to generate a.c. than d.c.
- The efficiency of an a.c. generator is higher than that of a d.c. generator.
- It is easy to change a.c. into d.c.
- The magnitude of a.c. voltage can easily be increased or decreased by the use of a step up or a step down transformer.
- a.c. can be transmitted over a long distance without much loss in energy in the line wires.
The last two of these are linked, and together they are the real reason the world runs on a.c.
In India, we use 220 volt a.c. in our houses and factories. The use of a.c. is advantageous over d.c. because the voltage of a.c. can be increased by the use of a step up transformer at the power generating station, and then it can be decreased by the use of a step down transformer for transmission within the city. By doing so, the loss of electrical energy as heat in the transmission line wires is reduced. The full chain is set out in FC 10.4.
If d.c. is generated at the power generating station, its voltage cannot be increased for transmission. A high current must then pass through the transmission line wires, and there will be a huge loss of electrical energy as heat in the line wires.
Flowchart
FC 10.4 — Route Of Electrical Energy From The Power Station To A House Mechanical energy of the turbine → a.c. generator at the power station produces a.c. at a moderate voltage → step up transformer raises the voltage → long transmission lines carry the energy at high voltage and small current → step down transformer at the sub-station lowers the voltage → distribution lines within the city → 220 V a.c. supply at the house
10.17 Distinction Between An A.C. Generator And A D.C. Motor
Set Fig. 10.12-1 beside Fig. 10.15-1 and the resemblance is startling. Both machines have a coil wound on a soft iron core, both have that coil turning between the poles of a horse shoe electromagnet, both have rings on the axle and brushes pressing against them. Yet one of them eats electricity and gives motion, while the other eats motion and gives electricity.
The differences are few, but each one matters.
10.17.1 Similarities Between An A.C. Generator And A D.C. Motor
Both in an a.c. generator and in a d.c. motor, a coil rotates in a magnetic field between the pole pieces of a powerful electromagnet.
Both in an a.c. generator and in a d.c. motor, there is a transformation of energy from one form to the other form.
10.18 Transformer
In our daily life we use various electrical appliances which require a working voltage different from the voltage of the mains, that is, from 220 V. A door bell needs 6 V, while the picture tube in a television needs nearly 10,000 V. To obtain a suitable voltage for different appliances from the mains, we use transformers of a suitable type with the appliance.
Note carefully what a transformer does not change. A transformer does not affect the frequency of the alternating voltage; the frequency remains unchanged at 50 Hz. Only the size of the voltage is altered.
10.18.1 Principle Of The Transformer
A transformer works on the principle of electromagnetic induction, and makes use of two coils having different numbers of turns. The two coils are named the primary coil and the secondary coil, exactly as in Fig. 10.13-3.
The given alternating e.m.f., whose magnitude is to be changed, is applied across the primary coil. The appliance, in which the output is to be obtained, is connected across the secondary coil.
When there is a change in the magnetic field due to the varying current in the primary coil, the magnetic flux linked with the secondary coil also changes. Due to this, an induced varying current of the same frequency, but of different magnitude, flows in the secondary coil.
A transformer cannot be used with a direct current source. If the current in the primary coil is constant, as it is with d.c., then the magnetic field due to the primary coil remains constant, no change occurs in the magnetic flux linked with the secondary coil, and hence no e.m.f. is induced in the secondary coil at all. A transformer needs a changing current, and this is the deepest reason why the world’s supply is alternating.
10.18.2 Construction Of A Transformer
A transformer consists of mainly three parts: (i) the primary coil, (ii) the secondary coil, and (iii) the core.
The purpose of the core is to provide maximum magnetic flux linkage between the coils. The core is made from thin rectangular laminated sheets of soft iron of T and U shape, placed alternately one above the other and insulated from each other by a paint, or varnish, coating over them, as shown in Fig. 10.18-1. This forms a simple rectangular core.
Diagram
Fig. 10.18-1 — Laminated Iron Core Draw a stack of thin flat sheets of soft iron shown in perspective, slightly offset from one another so that the separate layers can be seen. Show alternate sheets cut in a T shape and a U shape, fitting together to form a closed rectangular frame. Label one sheet ‘painted sheet’ with an arrow to the thin insulating coating between two layers, and label the whole stack ‘laminated soft iron core’.
On one arm of the core, the primary coil P of insulated copper wire is wound. This coil is connected with the source of alternating e.m.f., that is, at the ends of this coil the input is given.
On the other arm of the core, the secondary coil S of insulated copper wire is wound. The induced alternating e.m.f. is obtained across the terminals of this coil, that is, the output is obtained at the ends of this coil. The arrangement is shown in Fig. 10.18-2.
Diagram
Fig. 10.18-2 — Construction Of A Transformer Draw a closed rectangular core of laminated soft iron. On the left arm wind a coil of insulated copper wire and label it ‘primary coil P’, with its two ends led out to terminals marked ‘input a.c.’. On the right arm wind a second, separate coil of insulated copper wire and label it ‘secondary coil S’, with its two ends led out to terminals marked ‘output a.c.’. Draw a few magnetic field lines running right round inside the closed core, with arrowheads, and label them ‘magnetic field lines confined to the core’. Label the core ‘laminated soft iron core’. Show clearly that the two coils are nowhere joined to each other.
Three features of the core are chosen deliberately, and each prevents a particular waste of energy.
The lamination of the core prevents the loss of energy due to induced currents, called eddy currents, set up in the core itself. The core is a conductor sitting in a changing magnetic field, so currents are induced in it too; splitting it into insulated sheets breaks up the paths these currents could take.
A closed core is used because it gives a closed path for the magnetic field lines. Therefore almost all the magnetic field lines, caused due to the current in the primary coil, remain linked with the secondary coil — that is, the flux linkage is nearly perfect — and the loss of energy is minimum.
The core is made of soft iron so that the loss of energy due to hysteresis in the core gets minimised. Hysteresis loss is the energy spent in magnetising and demagnetising the core over and over again, a hundred times a second, and soft iron loses far less energy in this way than steel would.
10.18.3 Working And The Turns Ratio
When the terminals of the primary coil are connected to the source of alternating e.m.f., a varying current flows through the primary coil. This varying current produces a varying magnetic field in the core of the transformer.
Thus the magnetic flux linked with the secondary coil, which is wound over the same core, varies, due to which an e.m.f. is induced in it. The induced e.m.f. varies in the same manner as the applied e.m.f. in the primary coil varies, and thus the induced e.m.f. has the same frequency as that of the applied e.m.f.
The ratio of the number of turns \(N\_s\) in the secondary coil to the number of turns \(N\_p\) in the primary coil is called the turns ratio, denoted by the symbol \(n\).
\[n = \\frac{N\_s}{N\_p} \\qquad \\ldots (10.6)\]
where \(N\_s\) is the number of turns in the secondary coil and \(N\_p\) the number of turns in the primary coil. Both are simply counts, so the turns ratio has no unit.
Now for the relation that makes a transformer useful. Each turn of wire on the core has the same changing flux threading it, so each turn has the same e.m.f. induced in it. A coil with twice as many turns therefore has twice the e.m.f. across it. In other words, the e.m.f.s are in the same ratio as the numbers of turns. For a transformer,
\[\\frac{E\_s}{E\_p} = \\frac{N\_s}{N\_p} = n \\qquad \\ldots (10.7)\]
that is, \(E\_s = E\_p \\times n\), where \(E\_s\) is the e.m.f. across the secondary coil in volt (V), \(E\_p\) the e.m.f. across the primary coil in volt (V), and \(n\) the turns ratio.
Thus the magnitude of the e.m.f. induced in the secondary coil depends on the following two factors:
- the ratio of the number of turns in the secondary coil to the number of turns in the primary coil, that is, the turns ratio, and
- the magnitude of the e.m.f. applied in the primary coil.
An Ideal Transformer
A transformer does not create energy. For an ideal transformer, when there is no energy loss, the output power will be equal to the input power. That is,
power in secondary coil = power in primary coil
\[E\_s I\_s = E\_p I\_p \\qquad \\ldots (10.8)\]
where \(I\_s\) is the current in the secondary coil in ampere (A) and \(I\_p\) the current in the primary coil in ampere (A).
But \(\\dfrac{E\_s}{E\_p} = \\dfrac{N\_s}{N\_p}\), and therefore
\[\\frac{I\_p}{I\_s} = \\frac{E\_s}{E\_p} = \\frac{N\_s}{N\_p} \\qquad \\ldots (10.9)\]
Read eqn. (10.9) carefully, because it carries the whole bargain of a transformer. The currents go in the opposite ratio to the voltages. Whatever you gain in voltage you give up in current, and whatever you gain in current you give up in voltage.
10.18.4 Step Up Transformer
The transformer used to change a low alternating voltage to a high alternating voltage, of the same frequency, is called a step up transformer. Here \(E\_s > E\_p\).
In a step up transformer, the number of turns in the secondary coil is more than the number of turns in the primary coil, that is \(N\_s > N\_p\), and so the turns ratio \(n > 1\). This is shown in Fig. 10.18-3(a).
As eqn. (10.9) indicates, the current in the primary coil is more than that in the secondary coil, that is \(I\_p > I\_s\). So the wire in the primary coil is kept thicker than in the secondary coil.
The reason for the thicker wire is worth stating plainly. The use of a thicker wire reduces its resistance, and therefore reduces the loss of energy as heat in that coil. This energy loss due to heat is known as copper loss. Whichever coil carries the larger current is the one that must be wound with thicker wire.
10.18.5 Step Down Transformer
The transformer used to change a high alternating voltage to a low alternating voltage, of the same frequency, is called a step down transformer. Here \(E\_s < E\_p\).
In a step down transformer, the number of turns in the secondary coil is less than the number of turns in the primary coil, that is \(N\_s < N\_p\), and so the turns ratio \(n < 1\). This is shown in Fig. 10.18-3(b).
As eqn. (10.9) indicates, the current in the secondary coil is more than that in the primary coil, that is \(I\_s > I\_p\). So the wire in the secondary coil is kept thicker than in the primary coil, again to keep the copper loss small.
Diagram
Fig. 10.18-3 — Step Up And Step Down Transformers Two drawings side by side, each showing a closed rectangular laminated soft iron core with a coil wound on each arm. In panel (a), labelled ‘step up transformer’, wind few turns on the left arm and label it ‘primary, input a.c., thicker wire, fewer turns’, and wind many turns on the right arm and label it ‘secondary, output a.c., thinner wire, more turns’; add the condition Ns greater than Np. In panel (b), labelled ‘step down transformer’, wind many turns on the left arm and label it ‘primary, input a.c., thinner wire, more turns’, and wind few turns on the right arm and label it ‘secondary, output a.c., thicker wire, fewer turns’; add the condition Ns less than Np. Show the input terminals on the left and the output terminals on the right of each panel, and label the core in both.
10.18.6 Distinction Between Step Up And Step Down Transformers
10.18.7 Uses Of Transformers
In our houses, both types of transformers are used with electrical appliances which operate at a voltage other than the voltage supplied by the mains — a door bell needs 6 V, while a television picture tube requires nearly 10,000 V.
Uses Of Step Up Transformers
- In the transmission of electric power at the power generating station, to step up the voltage.
- With a television picture tube.
- With wireless sets.
- With X-ray machines, to provide a high accelerating voltage.
Uses Of Step Down Transformers
- With electric bells, night electric bulbs, mobile phones and computers.
- At the power sub-stations, to step down the voltage before its distribution to the consumers.
Because a step up transformer can raise a voltage to many thousands of volts, the equipment it feeds must be properly enclosed and earthed, and such units are never opened by anyone but a qualified electrician.
10.19 Summary
Hans Oersted, in 1820, observed that when an electric current is passed through a conducting wire, a magnetic field is produced around it. The presence of this field at any point is detected with a compass needle.
A current, or a moving charge, produces a magnetic field around it. This is called the magnetic effect of current. The strength of the field depends on the magnitude of the current, and its direction depends on the direction of the current.
A magnetic field line is a line drawn such that the tangent to it at any point gives the direction of the magnetic field at that point.
The magnetic field lines around a straight current carrying wire are concentric circles, with their plane perpendicular to the wire and their centres lying on the wire. On increasing the current, the lines become denser and are effective up to a larger distance. On reversing the current, the pattern of iron filings is unchanged but the direction of the field is reversed.
A neutral point is a point where the field due to the current and the field of the earth are equal and opposite, so the resultant field is zero and a compass needle rests in any direction.
Right hand thumb rule: if the current carrying conductor is held in the right hand with the thumb pointing along the direction of flow of current, then the fingers encircle the wire in the direction of the magnetic field lines.
For a current carrying loop, the field lines are nearly circular near the wire, are in the same direction within the loop, are nearly parallel and uniform near the centre, and at the centre lie along the axis of the loop, normal to its plane. The field is stronger if the current is increased or the number of turns is increased. The loop acts as a magnetic dipole, with one face a north pole and the other a south pole.
Clock rule: looking at a face of the loop, if the current at that face is anticlockwise the face has north polarity, and if it is clockwise the face has south polarity.
A solenoid is a conducting wire wound in the form of a cylindrical coil whose diameter is small compared with its length. The magnetic field inside a solenoid is uniform and lies along its axis. It is increased by increasing the current, by increasing the number of turns in a given length, and by inserting a soft iron core, since soft iron has a high magnetic permeability.
A current carrying solenoid behaves just like a bar magnet: it has a similar field pattern, it sets itself north–south when freely suspended, and it attracts iron filings. Unlike a bar magnet, the strength of its field can be changed by changing the current, and the direction of its field can be reversed by reversing the current.
An electromagnet is a temporary strong magnet made by passing current in a coil wound around a piece of soft iron. It is an artificial magnet, made either I-shaped or U-shaped. Its magnetic field is increased by increasing the number of turns of the winding and by increasing the current.
A permanent magnet is made by winding a coil around a piece of steel and passing current in it. Steel is used because it has more magnetic retentivity than soft iron, so it keeps its magnetism after the coil is removed. Permanent magnets are used in electric meters and in a magnetic compass.
An electromagnet is made of soft iron and gives a temporary field that can be made very strong, changed in strength, reversed in polarity and switched off. A permanent magnet is made of steel and gives a permanent field which is not so strong and can be neither changed nor reversed nor easily removed.
Electromagnets are used for lifting and transporting heavy iron scrap, for loading furnaces, for separating iron from ores and debris, for removing iron pieces from wounds, in scientific research, and in devices such as the electric bell, the telegraph, the electric motor, the relay, the microphone and the loud speaker.
In an electric bell, the electromagnet attracts the armature so that the hammer strikes the gong. This movement breaks the contact at the adjusting screw, the electromagnet is demagnetised, and the spring strip returns the armature, remaking the contact. This make and break of the circuit repeats for as long as the switch is pressed.
A current carrying conductor placed in a magnetic field, in a direction other than that of the field, experiences a force. The magnitude of the force is given by \[F = IBl\] where \(F\) is the force in newton (N), \(I\) the current in ampere (A), \(B\) the strength of the magnetic field in tesla (T), and \(l\) the length of the conductor in the field in metre (m). This relation holds only when the conductor is at right angles to the field. If the conductor lies along the field, no force acts on it.
The SI unit of magnetic field is \(\\text{N A}^{-1},\\text{m}^{-1}\), also named the tesla (T) or weber per metre squared (\(\\text{Wb m}^{-2}\)).
Fleming’s left hand rule: stretch the forefinger, central finger and thumb of the left hand mutually perpendicular; if the forefinger gives the direction of the magnetic field and the central finger the direction of the current, the thumb gives the direction of the force on the conductor.
An electric motor is a device which converts electrical energy into mechanical energy. It works on the principle that a current carrying conductor placed normally in a magnetic field experiences a force. The forces on the two arms of the coil form a couple which rotates it.
The split ring commutator reverses the direction of current in the coil each time the coil passes the vertical position, so that the direction of the rotating couple is unchanged and the coil keeps turning the same way.
The deflecting couple on the coil of a motor is given by \(IBAn\), where \(I\) is the current in ampere (A), \(B\) the field strength in tesla (T), \(A\) the area of the coil in metre squared (m²) and \(n\) the number of turns. The couple is maximum when the plane of the coil is parallel to the field and zero when the plane of the coil is normal to the field. The speed of rotation is increased by increasing the current, the number of turns, the area of the coil, or the strength of the magnetic field.
The magnetic flux linked with a coil is the number of magnetic field lines passing through it, measured in weber (Wb).
Electromagnetic induction is the phenomenon in which an e.m.f. is induced in a coil if there is a change in the magnetic flux linked with the coil. A current flows only if the circuit of the coil is closed. It is the relative motion between the coil and the magnet that produces the current, whichever of the two moves.
Faraday’s laws of electromagnetic induction: whenever there is a change in the magnetic flux linked with a coil, an e.m.f. is induced, and it lasts only so long as the flux changes; and the magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linked with the coil.
The magnitude of the induced e.m.f. is given by \[\\text{induced e.m.f.} = \\frac{N \\times \\Delta\\phi}{\\Delta t}\] where \(N\) is the number of turns in the coil, \(\\Delta\\phi\) the change in magnetic flux of each turn in weber (Wb), \(\\Delta t\) the time in second (s), and the e.m.f. is in volt (V).
Lenz’s law: the direction of the induced e.m.f., or induced current, is such that it opposes the cause which produces it. Lenz’s law follows from the law of conservation of energy, since the mechanical energy spent in working against the opposing force is what appears as electrical energy.
Fleming’s right hand rule: stretch the thumb, central finger and forefinger of the right hand mutually perpendicular; if the forefinger gives the direction of the magnetic field and the thumb the direction of motion of the conductor, the central finger gives the direction of the induced current.
An a.c. generator is a device which converts mechanical energy into electrical energy using the principle of electromagnetic induction. Its coil rotates in a magnetic field, and its two separate coaxial slip rings keep each end of the coil joined to the same brush.
In a generator the induced e.m.f. is maximum when the plane of the coil lies along the direction of the magnetic field, where the flux is zero and changing fastest; and the e.m.f. is zero when the plane of the coil is normal to the field, where the flux is maximum and momentarily unchanging. The e.m.f. reverses its polarity after each half rotation, so it is an alternating e.m.f.
If the coil makes \(n\) rotations per second, then \[e = e\_0 \\sin 2\\pi n t, \\qquad i = i\_0 \\sin 2\\pi n t\] where \(e\) is the e.m.f. in volt (V) and \(i\) the current in ampere (A) at the instant \(t\) in second (s), and \(e\_0\) and \(i\_0\) are their maximum values. The frequency of the a.c. generated equals the frequency of rotation of the coil. The maximum e.m.f. \(e\_0\) is increased by increasing the number of turns, the area of cross section of the coil, or the speed of rotation.
Household supply in India is 220 V a.c. of frequency 50 Hz, so the polarity at the supply terminal changes 100 times each second.
Direct current has a constant magnitude and flows in one direction, and is obtained from a cell or battery. Alternating current varies in magnitude and reverses its direction periodically, and is obtained from an a.c. generator and from the mains.
a.c. is preferred because it is cheaper and easier to generate, an a.c. generator is more efficient, a.c. is easily changed to d.c., its voltage is easily raised or lowered by a transformer, and it can be transmitted over long distances with little loss of energy as heat in the line wires.
An a.c. generator and a d.c. motor both have a coil rotating in the field of a powerful electromagnet, and in both there is a transformation of energy. They differ in the direction of that transformation, in the principle of working, and in the rings used: slip rings for the generator, split rings for the motor.
A transformer is a device by which the magnitude of an alternating e.m.f. can be increased or decreased. It works on the principle of electromagnetic induction and does not change the frequency. It cannot be used with a d.c. source, because a steady current gives a steady flux and induces no e.m.f. in the secondary coil.
For a transformer, \[\\frac{E\_s}{E\_p} = \\frac{N\_s}{N\_p} = n\] where \(E\_s\) and \(E\_p\) are the e.m.f.s across the secondary and primary coils in volt (V), \(N\_s\) and \(N\_p\) are the numbers of turns in the secondary and primary coils, and \(n\) is the turns ratio, which has no unit.
For an ideal transformer, the output power equals the input power, so \[E\_s I\_s = E\_p I\_p, \\qquad \\frac{I\_p}{I\_s} = \\frac{E\_s}{E\_p} = \\frac{N\_s}{N\_p}\] where \(I\_s\) and \(I\_p\) are the currents in the secondary and primary coils in ampere (A).
A step up transformer has \(N\_s > N\_p\), so \(n > 1\); it increases the voltage and decreases the current, and its primary coil is wound with the thicker wire. A step down transformer has \(N\_s < N\_p\), so \(n < 1\); it decreases the voltage and increases the current, and its secondary coil is wound with the thicker wire. The thicker wire has less resistance and so reduces the copper loss.
The core of a transformer is made of soft iron to reduce hysteresis loss, is laminated to reduce loss due to eddy currents, and is closed so that almost all the field lines produced by the primary coil remain linked with the secondary coil.
Step up transformers are used at power generating stations, with television picture tubes, with wireless sets and with X-ray machines. Step down transformers are used at power sub-stations and with electric bells, night electric bulbs, mobile phones and computers.
Flowchart
FC 10.5 — The Spine Of The Chapter A current produces a magnetic field around it → the field of a straight wire, of a loop and of a solenoid → a solenoid with a soft iron core is an electromagnet → a current placed in a magnetic field experiences a force F = IBl → the forces on a coil form a couple, which is the d.c. motor, converting electrical energy to mechanical energy → a change in the magnetic flux linked with a coil induces an e.m.f., which is electromagnetic induction → a coil rotated in a magnetic field is the a.c. generator, converting mechanical energy to electrical energy → two coils on one core make a transformer, which raises or lowers an alternating e.m.f.
10.20 Key Terms
A.C. generator — a device which converts mechanical energy into electrical energy using the principle of electromagnetic induction.
Alternating current (a.c.) — a current which varies in magnitude and reverses its direction periodically; measured in ampere (A).
Alternating e.m.f. — an e.m.f. which changes both its magnitude and its polarity in each rotation of the generator coil; measured in volt (V).
Armature — the movable piece of soft iron in an electric bell that is attracted by the electromagnet; also the rotating coil of a motor or a generator.
Brushes — the fixed carbon contacts which press against the rings on the axle of a motor or a generator and carry current to or from the coil.
Clock rule — the rule which states that a face of a current carrying loop is a north pole if the current at that face is anticlockwise, and a south pole if it is clockwise.
Copper loss — the energy lost as heat in the windings of a transformer because of their resistance.
Couple — a pair of equal and opposite forces whose lines of action are different, which turns a body without moving it bodily.
Direct current (d.c.) — a current of constant magnitude which flows in one direction only; measured in ampere (A).
Eddy currents — the currents induced in the core of a transformer by the changing magnetic flux, reduced by laminating the core.
Electric motor — a device which converts electrical energy into mechanical energy.
Electromagnet — a temporary strong magnet made by passing current in a coil wound around a piece of soft iron.
Electromagnetic induction — the phenomenon in which an e.m.f. is induced in a coil when the magnetic flux linked with it changes.
Electromotive force (e.m.f.) — the electrical push developed between the ends of a conductor, which drives a current round a closed circuit; measured in volt (V).
Fleming’s left hand rule — the rule giving the direction of the force on a current carrying conductor placed in a magnetic field.
Fleming’s right hand rule — the rule giving the direction of the current induced in a conductor moving in a magnetic field.
Hysteresis — the loss of energy in a core that is magnetised and demagnetised repeatedly, kept small by using soft iron.
Lenz’s law — the law which states that the direction of an induced e.m.f. or current is such that it opposes the cause producing it.
Lorentz force — the force experienced by a charge moving in a magnetic field in a direction other than that of the field; measured in newton (N).
Magnetic effect of current — the production of a magnetic field around a current, or around any moving charge.
Magnetic field — the region around a magnet or a current in which a magnetic force can be felt; its strength is measured in tesla (T).
Magnetic field line — a line drawn in a magnetic field such that the tangent to it at any point gives the direction of the field at that point.
Magnetic flux — the number of magnetic field lines passing through a coil; measured in weber (Wb).
Magnetic permeability — the property of a material which decides how readily a magnetic field is set up inside it; soft iron has a high permeability.
Magnetic retentivity — the ability of a material to keep its magnetism after the magnetising field has been removed; steel has a high retentivity.
Neutral point — a point where the magnetic field due to a current and the magnetic field of the earth are equal and opposite, so the resultant field is zero.
Permanent magnet — a magnet, usually of steel, which retains its magnetism for a long period without any current.
Primary coil — the coil of a transformer, or of a pair of coils, across which the input alternating e.m.f. is applied.
Right hand thumb rule — the rule which states that if a conductor is held in the right hand with the thumb along the current, the fingers encircle it along the field lines.
Secondary coil — the coil of a transformer, or of a pair of coils, in which the e.m.f. is induced and from which the output is taken.
Slip rings — the two separate coaxial rings on the axle of an a.c. generator, each permanently joined to one end of the coil.
Solenoid — a conducting wire wound in the form of a cylindrical coil whose diameter is small compared with its length.
Split ring commutator — the divided ring in a d.c. motor which reverses the current in the coil each half turn so that the couple always acts the same way.
Step down transformer — a transformer with fewer turns in the secondary than in the primary, which lowers the voltage and raises the current.
Step up transformer — a transformer with more turns in the secondary than in the primary, which raises the voltage and lowers the current.
Tesla (T) — the SI unit of magnetic field, equal to one newton per ampere per metre, and the same as one weber per metre squared.
Transformer — a device by which the magnitude of an alternating e.m.f. can be increased or decreased.
Turns ratio — the number of turns in the secondary coil divided by the number of turns in the primary coil of a transformer; it has no unit.
Weber (Wb) — the SI unit of magnetic flux, equal to the flux through an area of one metre squared placed at right angles to a field of one tesla.
10.21 Points To Ponder
Lenz’s law says that an induced current always opposes the change that produces it. Suppose instead that it helped the change along. Follow that supposition through with a magnet falling towards a coil, and work out what would happen to the magnet, to the current, and to the total energy. What does the result tell you about why Lenz’s law has to take the form it does?
In a generator the induced e.m.f. is largest at the very instant when the magnetic flux through the coil is zero, and it is zero when the flux is greatest. Why should nature care about the rate at which the flux changes rather than about how much flux there is? Try to find another quantity in physics that behaves in the same way.
Take the split ring commutator out of a d.c. motor and leave everything else in place. Describe carefully what the coil would then do over one full turn. Could any useful work be got out of that motion, and what sort of machine might use it?
A transformer cannot work on direct current. Imagine that the world’s electricity supply had been standardised on d.c. instead. Working from what you know about transmission losses, describe how power stations, cables and towns would have had to be arranged differently.
Both an electromagnet and a permanent magnet have their uses, and the chapter treats the ability to switch off as the electromagnet’s great advantage. Can you find a situation in which the permanent magnet’s inability to be switched off is itself the advantage, and say exactly why?
A freely suspended compass needle and a freely suspended current carrying solenoid both settle along the north–south direction, because the earth behaves like an enormous magnet. Given that a magnetic field is produced by moving charge, what does the earth’s magnetism suggest about what may be going on inside the earth? What further evidence would you want before accepting such a suggestion?
10.22 Objective Questions
Multiple Choice Questions
Choose the correct option from those given below each question.
- The magnetic field lines around a long straight current carrying wire are: (1 mark)
- straight lines parallel to the wire
- concentric circles in a plane perpendicular to the wire
- ellipses with the wire at one focus
- straight lines radiating outwards from the wire
- A circular loop is viewed face-on and the current in it is seen to run anticlockwise. The face towards the viewer behaves as: (1 mark)
- a north pole
- a south pole
- a neutral point
- neither pole, since a loop has no polarity
- The magnetic field inside a solenoid of a given length will not be increased by: (1 mark)
- increasing the current in the winding
- increasing the number of turns of the winding
- inserting a soft iron core along the axis
- inserting a wooden rod along the axis
- In Fleming’s left hand rule, the thumb indicates the direction of: (1 mark)
- the magnetic field
- the current in the conductor
- the force on the conductor
- the induced current
- The two coaxial slip rings of an a.c. generator serve to: (1 mark)
- reverse the direction of current in the coil every half turn
- keep each end of the coil permanently joined to the same brush
- increase the e.m.f. induced in the coil
- change the frequency of the current produced
- In a step down transformer: (1 mark)
- \(N\_s > N\_p\) and \(I\_s > I\_p\)
- \(N\_s > N\_p\) and \(I\_s < I\_p\)
- \(N\_s < N\_p\) and \(I\_s > I\_p\)
- \(N\_s < N\_p\) and \(I\_s < I\_p\)
Assertion And Reason
In each of the following, choose from: (a) both A and R are true and R is the correct explanation of A; (b) both A and R are true but R is not the correct explanation of A; (c) A is false but R is true; (d) A is true but R is false.
Assertion (A): A transformer changes the magnitude of an alternating voltage but leaves its frequency unchanged. Reason (R): The e.m.f. induced in the secondary coil varies in the same manner as the applied e.m.f. in the primary coil varies. (1 mark)
Assertion (A): The core of a transformer is built from thin sheets of soft iron insulated from one another. Reason (R): Lamination of the core reduces the loss of energy due to eddy currents set up in the core. (1 mark)
Assertion (A): No current flows in a coil when a strong magnet is held stationary inside it. Reason (R): An e.m.f. is induced in a coil only while the magnetic flux linked with it is changing. (1 mark)
Match The Following
- Match each device or rule in Column A with the correct statement in Column B. (4 marks)
| Column A | Column B |
|---|---|
| a. Split ring commutator | i. Gives the direction of the induced current |
| b. Fleming’s right hand rule | ii. Reverses the current in the coil each half turn |
| c. Step up transformer | iii. Has more turns in the secondary than in the primary |
| d. Right hand thumb rule | iv. Gives the direction of the field around a current |
Fill In The Blanks
- Fill in each blank with a suitable word or phrase. (4 marks)
- The point at which the field due to a current and the field of the earth cancel is called a __________.
- A solenoid with a soft iron core through which current is passed is called an __________.
- The direction of an induced current is such that it __________ the cause producing it.
- A transformer cannot be operated on a __________ supply.
True Or False
- State whether each of the following is true or false. (4 marks)
- Reversing the current in a straight wire reverses the direction of its magnetic field.
- The e.m.f. induced in a generator coil is greatest when the flux linked with the coil is greatest.
- A permanent magnet is made of soft iron because soft iron has a high retentivity.
- In an ideal transformer the output power is equal to the input power.
Name The Following
- Name the following. (4 marks)
- The rule used to find the direction of the force on a current carrying conductor placed in a magnetic field.
- The part of a d.c. motor which reverses the current in the coil after every half rotation.
- The currents induced in the core of a transformer, which the lamination is meant to reduce.
- The device which converts mechanical energy into electrical energy.
Give One Word Or Phrase For
- Give one word or phrase for each of the following. (3 marks)
- The number of magnetic field lines linked with a coil.
- A conducting wire wound as a cylindrical coil whose diameter is small compared with its length.
- The ratio of the number of turns in the secondary coil to that in the primary coil of a transformer.
State The SI Unit Of
- State the SI unit of each of the following, with its symbol. (4 marks)
- magnetic field
- magnetic flux
- induced e.m.f.
- the force on a current carrying conductor
Odd One Out
- In each group, pick the odd one out and give a reason for your choice. (2 marks)
- Slip rings, split ring commutator, brushes, laminated core
- Electric bell, relay, loud speaker, permanent magnet compass
10.23 Check Your Concepts
Define the magnetic effect of current, and state the two things on which the magnetic field around a straight wire depends. (2 marks)
State the right hand thumb rule. (2 marks)
Give a reason why the core of an electromagnet is made of soft iron while a permanent magnet is made of steel. (2 marks)
State the SI unit of magnetic field and define it in terms of the force on a current carrying conductor. (2 marks)
Differentiate between a current carrying solenoid and a bar magnet, stating the basis of difference in each case. (3 marks)
Why does no force act on a straight current carrying wire placed with its length along the direction of the magnetic field? (3 marks)
State Fleming’s right hand rule, and state clearly how its use differs from that of Fleming’s left hand rule. (3 marks)
What would happen to the ringing of an electric bell if the current were supplied from an a.c. source instead of a battery? Give a reason for your answer. (3 marks)
State Lenz’s law, and explain how it follows from the law of conservation of energy. (4 marks)
Describe, with the help of an experiment using a magnet, a coil and a centre zero galvanometer, how you would show that an e.m.f. is induced only when the magnetic flux linked with the coil changes. (4 marks)
Explain why a transformer cannot be used with a direct current source, and state what would be observed at the secondary coil if a d.c. supply were connected to the primary and then switched off. (4 marks)
State Faraday’s two laws of electromagnetic induction, with the conditions attached to each, and name the two factors on which the magnitude of the induced e.m.f. in a coil depends. (5 marks)
Explain the working of a simple d.c. motor through one complete rotation of its coil, stating in particular what happens at the two vertical positions and why the coil does not stop there. (5 marks)
10.24 Diagrams, Graphs & Constructions
Draw a labelled diagram of the apparatus used to trace the magnetic field lines around a long straight vertical wire using iron filings, similar to Fig. 10.2-1. Mark the direction of the current and put arrows on the field lines. (4 marks)
Fig. 10.4-2 shows the two faces of a current carrying loop. Redraw a single loop with the current running clockwise as seen by you, mark the polarity of the near face and of the far face, and draw an arrow at the centre showing the direction of the magnetic field there. Name the rule you have used. (4 marks)
Fig. 10.10-1 shows an electric bell. Identify the labelled parts A, H, G, SS and S′, and state in one line the function of each. (5 marks)
Fig. 10.15-3 shows how the e.m.f. induced in a generator coil varies with the angle turned by the normal to the plane of the coil. From the graph, state (a) the values of the angle at which the e.m.f. is zero, (b) the values at which it is maximum, (c) what the change of sign of the e.m.f. means physically, and (d) the position of the plane of the coil relative to the field at the instants found in part (b). (5 marks)
Draw a labelled diagram of a step down transformer, showing the laminated core, the primary and the secondary windings, and the input and output terminals. Mark clearly which winding has the greater number of turns and which is made of the thicker wire. (5 marks)
10.25 Practice With Numericals
A straight wire of length 50 cm carries a current of 3 A and lies at right angles to a uniform magnetic field of strength 0.4 T. Calculate the force acting on the wire. (2 marks)
A coil of 100 turns is linked with a magnetic flux of \(6 \\times 10^{-3}\\ \\text{Wb}\) through each turn. The flux falls steadily to \(2 \\times 10^{-3}\\ \\text{Wb}\) in 0.2 s. Calculate the e.m.f. induced in the coil. (2 marks)
The armature coil of a d.c. motor has 80 turns, each of area \(4 \\times 10^{-3}\\ \\text{m}^2\), and carries a current of 2 A in a magnetic field of 0.25 T. Calculate the deflecting couple acting on the coil when its plane lies along the direction of the field. (3 marks)
The coil of an a.c. generator makes 20 rotations per second. Calculate (a) the frequency of the alternating current produced, (b) the time period of one cycle, and (c) the number of times the current in the load reverses its direction in one second. (3 marks)
A transformer has 1200 turns in its primary coil and 60 turns in its secondary coil, and is connected to a 240 V a.c. supply. Calculate (a) the turns ratio and (b) the output voltage, and name the type of transformer. (3 marks)
An appliance rated 24 V, 60 W is run from a 240 V a.c. mains supply through an ideal transformer. Calculate (a) the turns ratio, (b) the current in the secondary coil, and (c) the current in the primary coil. State which coil must be wound with the thicker wire, and why. (4 marks)
At a power station, an ideal transformer steps up an alternating supply from 400 V to 16 kV in order to transmit 8 kW of power. Calculate (a) the turns ratio, (b) the current in the primary coil, and (c) the current in the secondary coil. (d) If the primary coil has 250 turns, find the number of turns in the secondary coil. (e) State, with a reason, one advantage of transmitting the power at 16 kV rather than at 400 V. (5 marks)