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Question

A hollow conducting sphere of radius R and total charge q rotates about its diametrical axis with constant angular speed ω. The magnitude of magnetic moment of the sphere is :

A
23qR2ω
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B
25qR2ω
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C
15qR2ω
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D
13qR2ω
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Solution

The correct option is D 13qR2ω
The ratio of magnetic moment and angular momentum for a rotating charged body is given by,

ML=q2m

M=qL2m

The angular momentum of a sphere about a diametric axis is given as,

L=Iω

Where I=23mR2

M=q(Iω)2m

M=q2m×(23mR2ω)

M=13qR2ω

Hence, option (A) is the correct answer.
Why this question?
Note: The ratio of magnetic moment and angular momentum for a rotating charged body is given by,
ML=q2m

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