Two charges of same magnitude move in two circles of radii $R_1=R$ and $R_2=2 R$ in a region of constant uniform magnetic field $B _0$. The work $W_1$ and $W_2$ done by the magnetic field in the two cases respectively, are such that
KVPY 2009, Medium
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(a)
Force on a charged particle moving in region of magnetic field is
$F =q( v \times B )$
Clearly, $F$ is perpendicular to both $v$ and $B$.
As, magnetic force is perpendicular to velocity of moving charged particle. So, work done in time $\Delta t$ is
$W=( F \cdot v ) \Delta t=0$
$\text { Hence, } W_1=W_2=0$
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