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
2BLsinθ2(gL)1/2
b
BLsinθ2(gL)
c
BLsinθ2(gL)3/2
d
BLsinθ2(gL)2
answer is A.
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Detailed Solution
From figure,⇒ h=L(1−cosθ)Maximum velocity at equilibrium is given by∴ v2=2gh=2gL(1−cosθ)=2gL2sin2θ2 ⇒ v=2gLsinθ2Thus, maximum potential differenceVmax=BvL=B×2gLsinθ2L=2BLsinθ2(gL)1/2