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Q.

A metal rod of length l cuts across a uniform magnetic field B with a velocity v. If the resistance of the circuit of which the rod forms a part is r, then the force required to move the rod is

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a

$\frac{B l v}{r}$

b

$\frac{B^{2} l^{2} v}{r}$

c

$\frac{B^{2} l^{2} v^{2}}{r}$

d

$\frac{B^{2} l v}{r}$

answer is A.

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Detailed Solution

$\begin{array}{rcl} Induced current & = & \frac{Bvl}{r} \\ Force & = & ilB = \frac{B^{2} {vl}^{2}}{r} \end{array}$

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