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Question

A non-conducting disc of radius 2 m is rotated about its axis of symmetry perpendicular to plane of disc with uniform angular speed ω. The disc carries a charge whose density is given as σ=ABr, where A and B are positive constants and r is distance from centre of the disc. The value of AB for which the magnetic field at the centre of the disc will be zero is

A
1
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B
2
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C
23
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D
43
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Solution

The correct option is A 1

dI=dq2πω=ω2π(σ2πrdr)=ω(ABr)rdr
(dq=σ.2πrdr=(ABr)2πrdr)

For a circular current carrying loop,
magnetic field at center of loop will be
dB=μ02rdI
=μ0ω(ABr)rdrB=μ0ω220(ABr)dr=μ0ω2(2A2B)B=0 for AB=1

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