Self Induction

Question 1:
The self inductance of a toroid is :-

\[\frac{\mu_{0}N^{2}r^{2}}{2R_{m}}\]

\[\frac{\mu_{0}N^{2}\pi r}{2R_{m}}\]

\[\frac{\mu_{0}N^{2}r}{2R_{m}}\]

\[\frac{\mu_{0}N^{2}r\pi}{2R_{m}}\]

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Question 2:
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 :-

5 H

10 H

11 H

12 H

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Question 3:
How much length of a very thin wire is required to obtain a solenoid of length l0 and inductance L.

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

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

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

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

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Question 4:
What is the mutual inductance of a two-loop system as shown with centre separation l ?

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

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

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

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

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Question 5:
A coil resistance 20 Ω and inductance 5 H is connected with a 100 V battery. Energy stored in
the coil will be :-

41.5 J

62.50 J

125 J

250 J

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