Electromagnetic induction

Question 1

Induced current

Answer 1

An electric current is caused by an induced e.m.f. In each case, there is a magnetic field and a conductor. When you move the magnet, or the conductor, there is an induced e.m.f. When you stop, the current stops.

Question 2

The size of the induced e.m.f. depends on which factors?

Answer 2

For a straight wire, the induced e.m.f. depends on the:
►magnitude of the magnetic flux density.
►length of the wire in the field.
►speed of the wire moving across the magnetic field.
For a coil of wire, the induced e.m.f. depends on the:
►magnitude of the magnetic flux density.
►cross-sectional area of the coil.
►angle between the plane of the coil and the magnetic field.
►number of turns of wire.
►rate at which the coil turns in the field.

Question 3

Define Magnetic flux density

Answer 3

The force experienced by a current-carrying conductor in a magnetic field per unit length, per unit current , when the current is perpendicular to the direction of the field. Magnetic flux density has the unit Tesla, T.

Question 4

How does current arise due to a conductor cutting magnetic field lines?

Answer 4

In case of a straight wire:
When a wire is moved into the magnetic field (Figure 26.5). As it moves, it cuts across the magnetic field. Remove the wire from the field, and again it must cut across the field lines, but in the opposite direction. We think of this cutting of a magnetic field by a conductor as the effect that gives rise to current caused by induced e.m.f in the conductor. It doesn’t matter whether the conductor is moved through the magnetic field or the magnet is moved past the conductor, the result is the same–there will be an induced e.m.f.
In case of a coil of wire:
For a coil of N turns, the effect is N times greater than for a single turn of wire. With a coil, it is helpful to imagine the number of field lines linking the coil. If there is a change in the number of field lines that pass through the coil, an e.m.f. will be induced across the ends of the coil (or there will be a current caused by induced e.m.f if the coil forms part of a complete circuit).

Question 5

Example - Induced e.m.f and finally induced current from cutting of magnetic field lines

Answer 5

Figure 26.6 shows a coil near a magnet. When the coil is outside the field, there are no magnetic field lines linking the coil. When it is inside the field, field lines link the coil. Moving the coil into or out of the field changes this linkage of field lines, and this induces an e.m.f. across the ends of the coil. Field lines linking the coil is a helpful starting point in our understanding of induced e.m.f. However, as you will see later, a more sophisticated idea of magnetic flux is required for a better understanding of how an e.m.f. is generated in a circuit.

Question 6

Fleming’s left hand (generator) rule

Answer 6

This rule is used to predict the direction of the induced current or e.m.f. in a conductor moved at right angles to a magnetic field: thumb → motion, first finger → magnetic field and second finger → induced conventional current.

Question 7

Detail - Induced e.m.f

Answer 7

When a conductor is not part of a complete circuit, there cannot be a current induced by e.m.f. Instead, negative charge will accumulate at one end of the conductor, leaving the other end positively charged. We have induced an e.m.f. across the ends of the conductor. Is e.m.f. the right term?Should it be potential difference (voltage)? In Chapter 8, you saw the distinction between voltage and e.m.f. The term e.m.f. is the correct one here because, by pushing the wire through the magnetic field, work is done and this is transformed into electrical energy. Think of this in another way: since we could connect the ends of the conductor so that there is a current in some other component, such as a lamp, which would light up, it must be an e.m.f. – a source of electrical energy. Figure 26.10 shows how an e.m.f. is induced. Notice that, within the conductor, conventional current is from negative to positive, in the same way as inside a battery or any other source of e.m.f. In reality, the free electrons within the conductor travel from right to left, making the left-hand side of the conductor negative. What causes these electrons to move? Moving the conductor is equivalent to giving a free electron within the conductor a velocity in the direction of this motion. This electron is in an external magnetic field and hence experiences a magnetic force Bev from right to left.

Question 8

IMPT

Answer 8

Do go through all the ‘Self-assessment’ and ‘Exam-style’ questions for this chapter (and every chapter for every subject)
PLEASE

Question 9

Define magnetic flux

Answer 9

The product of magnetic flux density normal to a circuit and the cross-sectional area of the circuit. Unit: weber (Wb)

Question 10

What is magnetic flux?

Answer 10

We picture magnetic flux density B as the number of magnetic field lines passing through a region per unit area. Similarly, we can picture magnetic flux as the total number of magnetic field lines passing through a cross-sectional area A. For a magnetic field normal to A, the magnetic flux Φ (Greek letter phi) must therefore be equal to the product of magnetic flux density and the area A.
Formula: Φ = BA
where B is the component of the magnetic flux density perpendicular to the area → perpendicular B ko as a base lay rahay hain

Question 11

When the magnetic flux B is not perpendicular to the area

Answer 11

How can we calculate the magnetic flux when B is not perpendicular to A? You can easily see that when the field is parallel to the plane of the area, the magnetic flux through A is zero. To find the magnetic flux in general, we need to find the component of the magnetic flux density perpendicular to the cross sectional area.
magnetic flux Φ = BAcosθ

Question 12

Define magnetic flux linkage

Answer 12

The product of magnetic flux for a circuit and the number of turns. Unit: weber (Wb).
Formula:
magnetic flux linkage = NΦ = BAN = or BANcosθ

Question 13

Questions related to topics above

Answer 13

Ref: pg 532

Question 14

Define Weber (Wb)

Answer 14

One weber (1 Wb) is the magnetic flux that passes perpendicularly through a cross-section of area 1m^2 when the magnetic flux density is 1 T. 1 Wb = 1 Tm2.

Question 15

Three ways in which an e.m.f. can be induced in a circuit

Answer 15

• changing the magnetic flux density B
• changing the cross-sectional area A of the circuit
• changing the angle θ

Question 16

Faraday’s law of electromagnetic induction

Answer 16

“The magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage”.
Formula: e.m.f E = Δ(NΦ) / Δt
♪ Note that it allows us to calculate the magnitude of the induced emf; its direction is given by Lenz’s law.

Question 17

Worked Example 2 - A straight wire of length 0.20 m moves at a steady speed of 3.0 m s−1 at right angles to a magnetic field of flux density 0.10 T. Use Faraday’s law to determine the magnitude of the induced e.m.f. across the ends of the wire.

Answer 17

Step 1 - With a single conductor, N = 1. To determine the induced e.m.f. E, we need to find the rate of change of magnetic flux; in other words, the change in magnetic flux per unit time.
Figure 26.17 shows that in a time t, the wire travels a distance 3.0t. Therefore:
change in magnetic flux = B × change in area
change in magnetic flux = 0.10 × (3.0t × 0.20)=0.060t
Step 2 - Use Faraday’s law to determine the magnitude of the induced e.m.f.
E = rate of change of magnetic flux linkage
E = Δ(NΦ) / Δt
ΔΦ = 0.060t, Δt = t and N = 1
E = 0.060t / t = 0.060 V
(The t cancels. You could have done this calculation for any time t, even 1.0 s. The results would still be the same.)
The magnitude of the induced e.m.f. across the ends of the wire is 60 mV.

Question 18

Worked Example 3 - This example illustrates one way in which the flux density of a magnetic field can be measured, shown in Figure 26.18. A search coil is a flat-coil with many turns of very thin insulated wire.
A search coil has 2500 turns and cross-sectional area 1.2 cm2. It is placed between the poles of a magnet so that the magnetic flux passes perpendicularly through the plane of the coil. The magnetic field between the poles has flux density 0.50 T. The coil is pulled rapidly out of the field in a time of 0.10 s.
Calculate the magnitude of the average induced e.m.f. across the ends of the coil.

Answer 18

Step 1 - Calculate the change in the magnetic flux linkage, Δ(NΦ).
When the coil is pulled out from the field, the final flux linking the coil will be zero. The cross-sectional area A needs to be in m2. Note: 1 cm2 = 10−4 m2.
Δ(NΦ) = Final NΦ − initial NΦ
Δ(NΦ) = 0 − [2500 × 1.2 × 10−4 × 0.50] = −0.15 Wb
Step 2 - Now calculate the induced e.m.f. using Faraday’s law of electromagnetic induction.
Δ(NΦ) = −0.15 Wb and Δt = 0.10 s
magnitude of e.m.f E = Δ(NΦ) / Δt = 0.15/0.10 = 1.5 V
(The negative sign is not required; you only need to know the size of the e.m.f.)
Note that, in this example, we have assumed that the flux linking the coil falls steadily to zero during the time interval of 0.10 s. The answer is, therefore, an average value of the induced e.m.f.

Question 19

Q10 (Self-a) - A conductor of length L moves at a steady speed v at right angles to a uniform magnetic field of flux density B. Show that the magnitude of the induced e.m.f. E across the ends of the conductor is given by the equation: E = BLv

Answer 19

let time be t,
change in area = L × vt
rate of change magnetic flux = BA/t = BLvt/t = BLv
Faraday’s law: magnitude of the induced e.m.f = rate of change of magnetic flux linkage, therefore, E = BLv

Question 20

Detail - The origin of electromagnetic induction
[A part of explanation leading to Lenz’s law]

Answer 20

Fleming’s right-hand rule gives the direction of a current caused by induced e.m.f. First, we will see how the motor effect and the generator effect are related to each other.
Figure 26.20 gives an explanation. A straight metal wire XY is being pushed downwards through a horizontal magnetic field of flux density B. Now, think about the free electrons in the wire. They are moving downwards, so they are, in effect, an electric current. Of course, because electrons are negatively charged, the conventional current is flowing upwards. We now have a current flowing across a magnetic field, and the motor effect will, therefore, come into play. Each electron experiences a force of magnitude Bev. Using Fleming’s left-hand rule, we can find the direction of the force on the electrons. The diagram shows that the electrons will be pushed in the direction from X to Y. So a current has been induced to flow in the wire; the direction of the conventional current is from Y to X.
Now, we can check that Fleming’s right-hand rule gives the correct directions for motion, field and current, which indeed it does. So, to summarise, there is a current caused by the induced e.m.f. current because the electrons are pushed by the motor effect. Electromagnetic induction is simply a consequence of the motor effect.
In Figure 26.20, electrons are found to accumulate at Y. This end of the wire is thus the negative end of the e.m.f. and X is positive. If the wire was connected to an external circuit, electrons would flow out of Y, round the circuit, and back into X. Figure 26.21 shows how the moving wire is equivalent to a cell (or any other source of e.m.f.).

Question 21

Detail - Forces and movement
[A part of explanation leading to Lenz’s law]

Answer 21

IMPT!
We turn a coil in a magnetic field, and the mechanical energy we put in is transferred to electrical energy. By thinking about these energy transfers, we can deduce the direction of the current.
Case 1:
Figure 26.22 shows one of the experiments from earlier in this chapter. The north pole of a magnet is being pushed towards a coil of wire. There is a current in the coil, but what is its direction? The diagram shows the two possibilities.
The current in the coil makes it into an electromagnet. One end becomes the north pole, the other the south pole. In Figure 26.22a, if the current is in this direction, the coil end nearest the approaching north pole of the magnet would be a south pole. These poles will attract one another, and you could gently let go of the magnet and it would be dragged into the coil. The magnet would accelerate into the coil, the current caused by induced e.m.f. would increase further, and the force of attraction between the two would also increase.
In this situation, we would be putting no (or very little at the start) energy into the system, but the magnet would be gaining kinetic energy, and the current would be gaining electrical energy. A nice trick if you could do it, but this would violate the principle of conservation of energy!
Figure 26.22b shows the correct situation. As the north pole of the magnet is pushed towards the coil, the current caused by the induced e.m.f. makes the end of the coil nearest the magnet become a north pole. The two poles repel one another, and you have to do work to push the magnet into the coil. The energy transferred by your work is transferred to electrical energy of the current. The principle of energy conservation is not violated in this situation.
Case 2:
Figure 26.23 shows how we can apply the same reasoning to a straight wire being moved in a downward direction through a magnetic field. There will be a current caused by induced e.m.f. in the wire, but in which direction? Since this is a case of a current across a magnetic field, a force will act on it (the motor effect), and we can use Fleming’s left-hand rule to deduce its direction [basically sab say pehlay current find karlo using generator rule (F.L.H.R) ‘cuz we are applying force on a conductor in Magnetic field. Once done then find the Force BQv due to motor effect (F.L.H.R)].
First, we will consider what happens if the current caused by the induced e.m.f. is in the wrong direction. This is shown in Figure 26.23a. The left-hand rule shows that the force that results would be downward–in the direction in which we are trying to move the wire. The wire would thus be accelerated, the current would increase and again we would be getting both kinetic and electrical energy for no energy input. The current must be as shown in Figure 26.23b. The force that acts on it due to the motor effect pushes against you as you try to move the wire through the field. You have to do work to move the wire, and hence to generate electrical energy. Once again, the principle of energy conservation is not violated.

Question 22

Define Lenz’s law

Answer 22

An induced e.m.f. is in a direction so as to produce effects which oppose the change producing it.

Question 23

A general law for induced e.m.f. [The Lenz’s law]

Answer 23

Lenz’s law summarises this general principle of energy conservation. The direction of a current caused by induced e.m.f. or e.m.f is such that it always produces a force that opposes the motion that is being used to produce it. If the direction of the e.m.f were opposite to this, we would be getting energy for nothing.
Here is a statement of Lenz’s law:
Any induced e.m.f. will be established in a direction so as to produce effects that oppose the change that is producing it.
This law can be shown to be correct in any experimental situation. For example, in Figure 26.3, a sensitive ammeter connected in the circuit shows the direction of the current as the magnet is moved in and out. If a battery is later connected to the coil to make a larger and constant current in the same direction, a compass will show what the poles are at the end of the solenoid. If a north pole is moved into the solenoid, then the solenoid itself will have a north pole at that end. If a north pole is moved out of the solenoid, then the solenoid will have a south pole at that end.
Faraday’s law of electromagnetic induction, and Lenz’s law, may be summarised using the equation:
E = − Δ(NΦ) / Δt
where E is the magnitude of the induced e.m.f. and the minus sign indicates that this induced e.m.f. causes effects to oppose the change producing it. The minus sign is there because of Lenz’s law – it is necessary to emphasise the principle of conservation of energy.

Question 25

Generators

Answer 25

We can generate electricity by spinning a coil in a magnetic field. This is equivalent to using an electric motor backwards. Figure 26.25 shows such a coil in three different orientations as it spins.
Notice that the rate of change of magnetic flux linkage is maximum when the coil is moving through the horizontal position. In this position, we get a large induced e.m.f. As the coil moves through the vertical position, the rate of change of magnetic flux is zero and the induced e.m.f. is zero.
Figure 26.26 (EXTREMELY IMPT!!) shows how the magnetic flux linkage varies with time for a rotating coil.
According to Faraday’s and Lenz’s laws, the induced e.m.f. is equal to minus the gradient of the flux linkage against time graph:
E = − Δ(NΦ) / Δt
When the flux linking the coil is:

» Maximum, the ‘rate of change of flux linkage’ is zero and hence the ‘induced e.m.f.’ is zero.
» Zero, the ‘rate of change of flux linkage’ is maximum (the graph is steepest) and hence the ‘induced e.m.f.’ is also maximum.
Hence, for a coil like this, we get a varying e.m.f. – this is how alternating current is generated.

Question 26

Transformers

Answer 26

A simple transformer has a primary coil and a secondary coil, both wrapped around a soft iron core (ring). An alternating current is supplied to the primary coil. This produces a varying magnetic flux in the soft iron core (see Figure 26.28). The secondary coil is linked by the same changing magnetic flux in the soft iron core, so an e.m.f. is induced at the ends of this coil. According to Faraday’s law, you can increase the induced e.m.f. at the secondary coil by increasing the number of turns of the secondary coil. Having fewer turns on the secondary will have the reverse effect. Transformers are used to transport electrical energy using overhead cables.

Question 27

Exam style Q 5 - Figure 28.26 shows the magnetic flux linkage and induced e.m.f. as a coil rotates. Explain why the induced e.m.f. is a maximum when there is no flux linkage and the induced e.m.f. is zero when the flux linkage is a maximum.

Answer 27

When there is no flux linkage, the flux is changing at the greatest rate and so the induced e.m.f. is a maximum.
When the flux linkage is a maximum, it is, instantaneously, not changing and thus there is no induced e.m.f.

Question 28

Exam style Q 2 - A student thinks that electrical current passes through the core in a transformer to the secondary coil. Describe how you might demonstrate that this is not true and explain how an electrical current is actually induced in the secondary coil. Use Faraday’s law in your explanation.

Answer 28

The most obvious demonstration is to show that the secondary coil is made of insulated wire, so no current can flow from the core to the secondary coil. (Alternatively, if you
arrange for a small gap in the core, perhaps a piece of paper, then there is still an induced e.m.f., even though paper is an insulator. The e.m.f. will be reduced because the amount of flux in the core is reduced if there is not a complete circuit of iron.)
An electrical current is induced because there is a change in the magnetic flux linking the secondary coil. This changing flux is caused by the changing current in the primary coil.

Question 29

Q20 (Self-a) - Explain why, if a transformer is connected to a steady (d.c.) supply, no e.m.f. is induced across the secondary coil.

Answer 29

For a d.c. supply, the magnetic flux linkage is constant. There is no change in the magnetic flux, and hence according to Faraday’s law, there is no induced e.m.f.