The magnetic moment of a circular orbit of ra | vedclass

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(B) The convection current $I$ is defined as the charge per unit time.Since the charge $q$ completes one revolution in time $T = \frac{2\pi r}{v}$,the

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$\frac{qvr}{2}$

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(B) The convection current $I$ is defined as the charge per unit time.Since the charge $q$ completes one revolution in time $T = \frac{2\pi r}{v}$,the current is:$I = \frac{q}{T} = \frac{q}{2\pi r / v} = \frac{qv}{2\pi r}$The magnetic moment $M$ of a current loop is given by the product of current $I$ and the area $A = \pi r^2$:$M = I 	imes A = \left( \frac{qv}{2\pi r} ight) 	imes (\pi r^2)$Simplifying the expression:$M = \frac{qv \pi r^2}{2\pi r} = \frac{qvr}{2}$

The magnetic moment of a circular orbit of radius $r$ carrying a charge $q$ and rotating with velocity $v$ is given by

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