Question

A hollow sphere of radius $r=20\text{cm}$ and mass $m=1\text{kg}$ has a charge of $Q=1\text{C}$ distributed uniformly over its surface. If the sphere is rotated about a diameter with an angular speed $\omega =30\text{rad/s}$ then its magnetic moment is measured to be $10x{\text{Am}}^2$. Find $x$



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Answer 1

Magnetic moment of the uniformly distributed hollow sphere rotating about its diameter is given by $$\mu =\frac{Q\omega r^2}{3}$$ From the data given in the question,

$\mu =\frac{1\times 30\times (0.2{)}^2}{3}=0.4{\text{Am}}^2$

Comparing with the data given in the question, $10x=0.4\Rightarrow x=0.04$

Accepted answer : $0.04$