Q. A particle of mass $M$ and moving with velocity $v$ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$ . the work done by the field when the particle completes one full circle is

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A

$\frac{\text{Mv}^{2}}{\text{R}}$

B

Zero

C

$\frac{\text{2Mv}^{2}}{\text{R}}$

D

$Mv^{2}R$

Solution:

When particle describes circular path in a magnetic field, its velocity is always perpendicular to the magnetic force.
Power, $\text{P} = \text{F.V} = \text{FV} cos \left(\theta \right)$
Here $\theta = 9 0$
P = 0
But $\text{P} = \frac{\text{W}}{\text{t}}$
$⇒ \, \, \, \text{W} = \text{P.t}$
Hence, work done
W = 0 (Everywhere)

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