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A particle of mass $M$ and charge $Q$ moving with velocity $\mathbf{v}$ 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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The correct answer is:
zero
When particle describes circular path in a magnetic field, its velocity is always perpendicular to the magnetic force?
Power
$\begin{aligned} P=\mathbf{F} \cdot \mathbf{v} & =F \vee \operatorname{co} \\ \theta & =90^{\circ} \\ P & =0
\end{aligned}$
Hence,But
$\begin{aligned}P=\mathbf{F} \cdot \mathbf{v} & =F \vee \cos \theta \\\theta & =90^{\circ} \\P & =0 \\P & =\frac{W}{t} \Rightarrow W=P \cdot t\end{aligned}$
Hence, work done $W=0$ (everywhere)
Power
$\begin{aligned} P=\mathbf{F} \cdot \mathbf{v} & =F \vee \operatorname{co} \\ \theta & =90^{\circ} \\ P & =0
\end{aligned}$
Hence,But
$\begin{aligned}P=\mathbf{F} \cdot \mathbf{v} & =F \vee \cos \theta \\\theta & =90^{\circ} \\P & =0 \\P & =\frac{W}{t} \Rightarrow W=P \cdot t\end{aligned}$
Hence, work done $W=0$ (everywhere)
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