A thin uniform rod of negligible mass and length l is attached to the floor by a frictionless hinge as shown. A horizontal spring with force constant k connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field B directed into the plane of the figure. There is a current i in the rod as shown and at equilibrium rod makes 53° angle with the floor. The energy stored by the spring in equilibrium is
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a
516i2B2l2k
b
33128i2B2l2k
c
25128i2B2l2k
d
716i2B2l2k
answer is C.
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Detailed Solution
Balancing torque about hingeiBl22=kxlsin53°⇒x=58iBlk \ Energy stored =12kx2=25128i2B2l2k