Electromagnetic Induction

Practice Questions:

Question 21: easy

A coil having 500 square loops each of side 10 cm is placed normal to a magnetic flux which increases at the rate of 1.0 Tesla/second. The induced e.m.f. in volts is :

1. 0.1

2. 0.5

3. 1

4. 5

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Question 22: moderate

A conducting circular loop is placed in a uniform magnetic field of inducting B tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate (dr/dt). Then the induced e.m.f. at the instant when the radius is r is :

1. \[\pi rB\left( \frac{dr}{dt} \right)\]

2. \[2\pi rB\left( \frac{dr}{dt} \right)\]

3. \[\pi r^{2}B\left( \frac{dr}{dt} \right)\]

4. \[\frac{\pi Br^{2}}{2}\left( \frac{dr}{dt} \right)\]

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Question 23: easy

The adjoining figure shows two bulbs B1 and B2 resistor R and an inductor L. When the switch S is turned off :

1. Both B1 and B2 die out promptly

2. Both B1 and B2 die out with some delay

3. B1 dies out promptly but B2 with some delay

4. B2 dies out promptly but B1 with some delay

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Question 24: moderate

A varying current in a coil changes from 10 amp to zero in 0.5 sec. If average EMF is induced in
the coil is 220 volts, the self inductance of coil is :

1. 5 H

2. 10 H

3. 11 H

4. 12 H

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Question 25: easy

A wire is bent to form the double loop shown in figure. There is a uniform magnetic field directed into the plane of the loop. If the magnitude of this field is decreasing, current will flow from :-

1. A to B and C to D

2. B to A and D to C

3. A to B and D to C

4. B to A and C to D

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Question 26: moderate

The figure shows four wire loops, with edge lengths of either L or 2L. All four loops will move
through a region of uniform magnetic field \[\overrightarrow{B}\] (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the e.m.f induced as they move through the field, greatest first :-

1. \[\left( e_{c}=e_{d} \right)<\left( e_{a}=e_{b} \right)\]

2. \[\left( e_{c}=e_{d} \right)>\left( e_{a}=e_{b} \right)\]

3. \[e_{c}>e_{d}>e_{b}>e_{a}\]

4. \[e_{c}<e_{d}<e_{b}<e_{a}\]

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Question 27: moderate

How much length of a very thin wire is required to obtain a solenoid of length l0 and inductance L.

1. \[\sqrt{\frac{2\pi Ll_{0}}{\mu_{0}}}\]

2. \[\sqrt{\frac{4\pi Ll_{0}}{\mu_{0}^{2}}}\]

3. \[\sqrt{\frac{4\pi Ll_{0}}{\mu_{0}}}\]

4. \[\sqrt{\frac{8\pi Ll_{0}}{\mu_{0}}}\]

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Question 28: difficult

What is the mutual inductance of a two-loop system as shown with centre separation l ?

1. \[\frac{\mu_{0}\pi a^{4}}{8l^{3}}\]

2. \[\frac{\mu_{0}\pi a^{4}}{4l^{3}}\]

3. \[\frac{\mu_{0}\pi a^{4}}{6l^{3}}\]

4. \[\frac{\mu_{0}\pi a^{4}}{2l^{3}}\]

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Question 29: moderate

An equilaterial triangular loop having a resistance R and length of each side ‘l’ is placed in a magnetic field which is varying at dB/dt =1 T/s. The induced current in the loop will be :