Q.

A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle 2θ.The earth's magnetic field component in the direction perpendicular to swing is, B. Maximum potential difference induced across the pendulum is

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a

2BLsin⁡θ2(gL)1/2

b

BLsin⁡θ2(gL)

c

BLsin⁡θ2(gL)3/2

d

BLsin⁡θ2(gL)2

answer is A.

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Detailed Solution

From figure,⇒ h=L(1−cos⁡θ)Maximum velocity at equilibrium is given by∴     v2=2gh=2gL(1−cos⁡θ)=2gL2sin2⁡θ2 ⇒ v=2gLsin⁡θ2Thus, maximum potential differenceVmax=BvL=B×2gLsin⁡θ2L=2BLsin⁡θ2(gL)1/2
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