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PQRS is a horizontal board containing a small uniform inward magnetic field B. A copper rod of length = L is connected to a non conducting rigid wall of the board by means of a non conducting spring of force constant k. The spring is compressed by a length a and then released. The maximum emf induced in the rod is (the mass of the rod is m)

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BaL $\sqrt{\frac{k}{m}}$

BaL²

BaL

BaL $\sqrt{\frac{m}{k}}$

answer is A.

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Detailed Solution

When the rod crosses the mean position it will have maximum velocity and hence emf induced will be maximum
$\frac{1}{2} {ka}^{2} = \frac{1}{2} {mv}^{2} v_{max} = \sqrt{\frac{k}{m}} a E_{max} = {Bv}_{max} L = BaL \sqrt{\frac{k}{m}}$

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