Electromagnetic induction 9.1 Introduction
9.6 Static induction
The induced EMF (Section 9.2) was due to movement. We considered the conductor to move in a stationary field, but of course a similar EMF would be induced if the conductor remained still and the field moved past it. How an EMF can be induced without any physical motion at all is described here.
Consider two coils of wire placed side by side (Figure 9.9), but not touching or in electrical contact with each other. The first coil is connected in series with a battery and a switch, so that a current can be made to flow in it and can then be switched off. The second coil has a measuring instrument connected to its ends.
If the switch in the circuit of the first coil is operated, the instrument connected to the second coil is seen to ‘kick’ and then return to zero. This happens each time the switch is turned on or off, the needle moving in a different direction at each operation. A reference to Figure 9.9 shows the reason for the induced EMF. In Figure 9.9(a), the switch is off and the first coil sets up no magnetic flux. When the switch is on
(a) (b)
(Figure 9.9(b)), the first coil sets up a magnetic flux, some of which passes through, or ‘links with’, the second coil. There has been a change in the flux linking the second coil, which has had an EMF induced in it, just as if the coil had moved into a steady magnetic field. The EMF will only be induced while the magnetic flux is changing. When the flux becomes steady, no EMF is induced.
The value of a statically induced EMF depends on the total magnetic flux change and the time it takes to complete this change. Thus, as indicated in Figure 9.2,
e = t
where e = induced EMF, V; = total magnetic flux change, Wb; and t = time for flux change, s.
Thus it is true to say that the EMF in volts induced at any instant of time is equal to the rate of change of magnetic flux at that instant in webers per second.
Example 9.6
If a current change in a coil of 200 turns induces an average EMF of 25 V, what will be the total flux change if the current takes 50 ms to complete its change?
e =
t so = et
Since the coil has 200 turns and the total induced EMF is 25 V, the induced EMF per turn will be e = 25 200 = 0.125 V = et = 0.125 × 50 × 10−3 = 6.25 × 10−3Wb or 6.25 mWb
If the left-hand coil is fed from a source of alternating current, the magnetic flux set up will be continually changing and an alternating EMF will be induced in the right-hand coil. This is the principle of the transformer, which will be considered in Chapter 10.
A further study of Figure 9.9 will show that a change of magnetic flux linkages has taken place in the left-hand coil, as well as in the right-hand coil. The left-hand coil, like the right-hand coil, will thus have an EMF induced in it, but this EMF will oppose the battery voltage and try to slow the change of current. This self-induced
EMF is sometimes called a back EMF, and any circuit which has the property of
inducing such an EMF in itself is said to be self-inductive, or just inductive. All circuits are, to some extent, self-inductive, but some conductor arrangements give rise to a much greater self-inductance than others. The unit self-inductance, which has
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the symbol L, is the henry (symbol H). The property of self-inductance is discussed fully in Electrical Craft Principles, Volume 2.
9.7 Summary of formulas for Chapter 9
e = Blv B = e lv l = e Bv v = e Bl
where e = induced EMF, V; B = flux density of magnetic field, T; l = length of conductor in the field, m; and v = velocity (speed) of the conductor, m/s.
e = t = et t = e
where e = average induced EMF, V; = total magnetic flux cut or total magnetic flux change, Wb; and t = time taken to cut flux or time taken for flux change, s.
Fleming’s right-hand (generator) rule
• First finger points in the direction of magnetic flux. • Second finger points in the direction of induced EMF.
• Thumb points in the direction of conductor movement through the magnetic field.
9.8 Exercises
1 Examine the diagrams in Figure 9.10 which show a conductor being moved in a magnetic field, and state
(a) the direction of induced EMF for Figure 9.10(a) (b) the direction of induced EMF for Figure 9.10(b) (c) the magnetic polarity for Figure 9.10(c)
(d) the direction of conductor movement for Figure 9.10(d)
(a) (b) (c) (d)
N
S
N
S
S
N
N
S
Figure 9.10 Diagrams for Exercise 1
2 A conductor is moved at a speed of 10 m/s directly across a magnetic field of flux density 15 mT, and has an EMF of 0.3 V induced in it. What is its effective length?
3 At what speed must a conductor of effective length 180 mm be moved at right angles to a magnetic field of flux density 0.6 T to induce in it an EMF of 0.324 V? 4 A conductor of effective length 200 mm connected across a milliammeter of resistance 5 is moved through a magnetic field of flux density 0.5 T. If the milliammeter reads 40 mA, at what speed must the conductor be moving? 5 What EMF will be induced in a conductor of effective length 80 mm which is
moving with a velocity of 15 m/s through a magnetic field of flux density 0.4 T? 6 One conductor of a generator is 500 mm long and moves at a uniform velocity of 20 m/s in the pole flux which as an average density of 0.4 T. What is the average EMF induced in the conductor? If the winding has 200 of these conductors connected in series, what is the total generated EMF?
7 A conductor is subjected to a magnetic flux changing at the rate of 4 Wb/s. What EMF is induced in the conductor?
8 An average EMF of 1.5 V in a conductor while the initial linking flux of 0.25 Wb is falling to zero. How long does the flux take to collapse?
9 A millivoltmeter connected to a conductor reads a steady 20 mV for 3 s while the conductor is subjected to a changing magnetic flux. Calculate the total flux change.
10 When a magnet is being inserted into a coil of wire, what factors govern (a) the direction
(b) the magnitude of the induced EMF?
11 Describe with the aid of a sketch a simple loop generator which consists of a single wire loop rotating between the poles of permanent magnet. Show the output of the loop taken from slip rings, and sketch a graph of the output voltage to a base of time.
12 Draw a diagram to show a simple two-part commutator which can be substituted for the slip rings of the generator of Exercise 11. Describe how the commutator functions, and sketch a graph of the output from the machine.
13 Describe, with the aid of a sketch, the construction and action of a simple direct- current generator. State
(a) the factors on which the generated EMF depends (b) how the generated EMF can be controlled.
9.9 Multiple-choice exercises
9M1 The word ‘induction’ in the electrical sense is taken to mean
(a) the ceremony which is held when someone joins an organisation (b) the production of EMF due to a change in linking magnetic flux (c) the amount of current flowing in a resistor when a voltage is applied (d) the production of magnetic flux when current flows in a coil
9M2 The value of EMF induced in a conductor when it moves through a magnetic field depends on
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(b) the total field flux and the length of the conductor subject to it (c) the shape of the magnetic field and the size of the conductor
(d) the flux density of the magnetic field, the velocity of the conductor and the length of it in the field.
9M3 If a conductor wound in a loop is moved through a magnetic field (a) the induced EMF will be greater than for a single conductor (b) the device will be a kind of electric motor
(c) the induced EMF will be smaller than for a single conductor (d) the individual EMFs in each loop will cancel to give no total EMF 9M4 If a conductor moving at a constant speed of 8 m/s through a magnetic field
of flux density 0.65 T, has an EMF of 1.3 V induced, its length must be
(a) 6.76 m (b) 0.106 m (c) 0.25 m (d) 0.148 m
9M5 A coil of 1000 turns has one side moved through a magnetic field of flux density 50 mT at a speed of 4.2 m/s. If 12 cm of each conductor is subjected to the flux, the total EMF induced in the coil will be
(a) 25.2 V (b) 2.7 kV (c) 21 mV (d) 1.19 V
9M6 A coil of 450 turns carries current which sets up a total magnetic flux of 42 mWb. If an average EMF of 540 V is induced when the current is switched off, the current collapses to zero in
(a) 50.4 ms (b) 3.5 s (c) 28.6 ms (d) 35 ms
9M7 The polarity of the magnet system shown in the diagram below must be (a) both poles positive
(b) north pole at the top (c) north pole at the bottom (d) south pole at the top
9M8 Fleming’s hand rule can be used to relate the directions of the magnetic field, the current and the motion, for induced EMF. This rule can only give the correct results if we use
(a) both hands (b) the left hand (c) the right hand (d) either hand
9M9 When using Fleming’s hand rule the first finger always points the direction of the
(a) induced EMF (b) magnetic field (c) current flow (d) force on the conductor
9M10 The EMF induced in a rectangular loop of wire which rotates in a magnetic field is
(a) alternating (b) very low
(c) direct (d) dangerous
9M11 When a conductor moves at high speed along a magnetic field so that is cuts no magnetic flux, the EMF induced in it will be
(a) zero (b) a maximum
(c) alternating (d) direct
9M12 The automatic changeover switch on the rotor of a DC machine is called the (a) polepiece (b) commuter
(c) brushes (d) commutator
9M13 Static induction is the principle behind the operation of the
(a) generator (b) motor