(A) The magnetic dipole moment $M$ is given by $M = i A$,where $i$ is the current and $A$ is the area of the ring.Since the charge $q$ is rotating wit

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(A) The magnetic dipole moment $M$ is given by $M = i A$,where $i$ is the current and $A$ is the area of the ring.Since the charge $q$ is rotating with angular velocity $\omega$,the time period of one revolution is $T = \frac{2 \pi}{\omega}$.The equivalent current $i$ is given by $i = \frac{q}{T} = \frac{q \omega}{2 \pi}$.The area of the ring is $A = \pi R^2$.Substituting these values into the formula for $M$:$M = \left( \frac{q \omega}{2 \pi} \right) (\pi R^2) = \frac{1}{2} q \omega R^2$.

Class 12 Physics Moving Charges and Magnetism Magnetic Moment of Current Carrying Coil

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$A$ charge $q$ is spread uniformly over an isolated ring of radius $R$. The ring is rotated about its natural axis with an angular velocity $\omega$. Magnetic dipole moment of the ring is

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A
$\frac{q \omega R^2}{2}$
B
$\frac{q \omega R}{2}$
C
$q \omega R^2$
D
$\frac{q \omega}{2R}$

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Moving Charges and Magnetism

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Magnetic Moment of Current Carrying Coil

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$A$ charge $q$ is spread uniformly over an isolated ring of radius $R$. The ring is rotated about its natural axis with an angular velocity $\omega$. Magnetic dipole moment of the ring is

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