A metal wire of mass m slides without friction on two rails spaced at a distance d apart. The track lies in a vertical uniform magnetic field B. A constant current I flows along one rail, across the wire and back down the other rail. If the wire is initially at rest, the time taken by it to move through a distance x along the track is

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$t = \sqrt{\frac{BId}{2 xm}}$

$t = \sqrt{\frac{2 xm}{BId}}$

$t = \sqrt{\frac{BIdm}{2 x}}$

$t = \sqrt{\frac{2 dm}{BIx}}$

answer is B.

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Detailed Solution

Force acting on the wire is
F = IdB a = IdB/m
$x = \frac{1}{2} {at}^{2}$
$t = \sqrt{\frac{2 x}{a}} = \sqrt{\frac{2 xm}{IdB}}$

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