If the angular momentum of an electron of mass $m$ is $J$ then the magnitude of the magnetic moment will be

Question

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Answer 1

Magnetic moment, $M = I \times A . . . . . . . . . . . (1)$ where I is current and A is area

$I = \frac{e}{T} = \frac{e}{\frac{2 π r}{v}} = \frac{e v}{2 π r}$

$A = π r^{2}$

Angular Momentum $J = m v r . . . . . . . (2)$

Put values of $I$ and $A$ in equation (1)

$M = \frac{e v}{2 π r} π r^{2}$

$M = \frac{e v r}{2}$

$M = \frac{e J}{2 m} (∵ v r = \frac{J}{m})$

Answer 2

Magnetic moment, $M = I \times A . . . . . . . . . . . (1)$ where I is current and A is area

$I = \frac{e}{T} = \frac{e}{\frac{2 π r}{v}} = \frac{e v}{2 π r}$

$A = π r^{2}$

Angular Momentum $J = m v r . . . . . . . (2)$

Put values of $I$ and $A$ in equation (1)

$M = \frac{e v}{2 π r} π r^{2}$

$M = \frac{e v r}{2}$

$M = \frac{e J}{2 m} (∵ v r = \frac{J}{m})$