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Question

A circular coil of 16 turns and radius 10 cm carrying a current of 0.75A rests with its plane normal to an external field of magnitude 5.0×102T. The coil is free to turn about an axis in its plane perpendicular to the filed direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 2.0/s. What is the moment of inertia of the coil about its axis of rotation?

A
1.2×104gcm2
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B
3×104kgm2
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C
0.3×104kgm2
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D
1.2×104kgm2
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Solution

The correct option is D 1.2×104kgm2
Given that,
Number of turns in the circular coil, N=16
Radius of the coil, r=10 cm =0.1m
Current in the coil, I=0.75A
Magnetic field strength, B=5.0×102T
Frequency of oscillations of the coil, v=2.0s1
Magnetic moment, M=NIA
M=NIπr2=(16)(0.75)π(0.1)2=0.3768JT1
The frequency is given by,
ν=12πMBI
I=MB4π2ν2
I=(0.3768)(5×102)4π222
I=1.19×104=1.2×104Kgm2

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