Question

A charge ‘q’ is given to a solid conducting sphere of mass ‘m’ and is rotating about it’s diameter with angular velocity ω. Then ratio of it’s magnetic moment to its angular momentum is
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Answer 1

Ratio of magnetic moment M to angular moment = (1/5)qR²ω

Explanation:

Let R be the radius of a solid conducting sphere, m its mass and ω its angular velocity.

Then the ratio of its magnetic moment M and angular momentum L will be:

M/ L = q / 2m where q is the charge.

M = (q/2m)L

     = (q/2m)(Iω)

     = (q/2m) (2/5. mR²ω)

     = 1/5. qR²ω

Magnetic moment M = 1/5. qR²ω

Angular Moment L = Iω

Ratio = M/L = 1/5. qR²ω