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(A) The magnetic moment $\mu$ is defined as the product of the current $I$ and the area $A$ of the loop,i.e.,$\mu = IA$.The current $I$ generated by a

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$\frac{1}{2} q \omega r^2$

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(A) The magnetic moment $\mu$ is defined as the product of the current $I$ and the area $A$ of the loop,i.e.,$\mu = IA$.The current $I$ generated by a rotating charge $q$ with frequency $f$ is $I = qf$.Since the angular velocity is $\omega$,the frequency $f = \frac{\omega}{2\pi}$.Thus,the current is $I = q \left( \frac{\omega}{2\pi} \right)$.The area of the loop is $A = \pi r^2$.Substituting these into the formula for magnetic moment:$\mu = \left( \frac{q \omega}{2\pi} \right) (\pi r^2)$.Simplifying the expression,we get:$\mu = \frac{1}{2} q \omega r^2$.

$A$ charge $q$ is spread uniformly over an insulated loop of radius $r$. If it is rotated with an angular velocity $\omega$ with respect to the normal axis,then the magnetic moment of the loop is:

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