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Q.

A conducting solid sphere having uniform charge Q on it has radius R. It is rotating with an angular velocity $ω .$ If a uniform magnetic field B is present perpendicular to axis of rotation then the torque on sphere will be

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a

$\frac{q ω R^{2}}{8} B$

b

$\frac{q ω R^{2}}{3} B$

c

$\frac{q ω R^{2}}{5} B$

d

$\frac{q ω R^{2}}{2} B$

answer is B.

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Detailed Solution

Magnetic moment of sphere is M then

$\frac{M}{\frac{2}{3} {mR}^{2} ω} = \frac{q}{2 m}$

$\Rightarrow M = \frac{{qωR}^{2}}{3}$

$Torque = MBsin 90^{\circ} = \frac{q {ωR}^{2} B}{3}$

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A conducting solid sphere having uniform charge Q on it has radius R. It is rotating with an angular velocity ω. If a uniform magnetic field B is present perpendicular to axis of rotation then the torque on sphere will be