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Q.

A non conducting disc of radius R is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity ‘ $ω$ ’, charge q is uniformly distributed over its surface. The magnetic moment of the disc is

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a

$\frac{1}{4} q ω R^{2}$

b

$\frac{1}{2} q ω R$

c

$q ω R$

d

$\frac{1}{2} q ω R^{2}$

answer is A.

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Detailed Solution

$\frac{Magnetic moment}{angular momentum} = \frac{q}{2 m}$

Magnetic moment = $(\frac{q}{2 m})$ angular moment

$M = \frac{q}{2 m} (I W) \Rightarrow M = \frac{q}{2 m} (\frac{m R^{2}}{2} ω)$ $∴ M = \frac{1}{4} q ω R^{2}$

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A non conducting disc of radius R is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity ‘ω ’, charge q is uniformly distributed over its surface. The magnetic moment of the disc is