Faraday's Law of Electromagnetic Induction

Practice Questions:

Question 1: moderate

A square loop of side 5 cm enters a magnetic field with 1 cms–1. The front edge enters the
magnetic field at t = 0 then which graph best depicts emf ?

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Question 2: moderate

In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency ω in a magnetic field B. The maximum value of emf generated in the coil is :

1. N.A.B.R.

2. N.A.B.ω

3. N.A.B.R.ω

4. N.A.B.

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Question 3: 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 4: 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 5: 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 :

1. \[\frac{\sqrt{3}}{4}\frac{l^{2}}{R}\]

2. \[\frac{4}{\sqrt{3}}\frac{l^{2}}{R}\]

3. \[\frac{\sqrt{3}}{4}\frac{R}{l^{2}}\]

4. \[\frac{4}{\sqrt{3}}\frac{R}{l^{2}}\]

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