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Q.

A thin uniform rod with negligible mass and length l is attached to the floor by a frictionless hinge at point P. A horizontal spring with force constant k connects the other end to wall. The rod is in a uniform magnetic field B directed into the plane of paper. What is the extension in spring in equilibrium when a current is passed through the rod ? Assuming spring to be in natural length initially and it remains perpendicular to wall always.

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a

5ilB4k

b

3ilB8k

c

5ilB6k

d

5ilB8k

answer is A.

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Detailed Solution

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Magnetic force, F = Bil .The spring is extended when current passes through the rod from the outer end towards the hinge .
Net torque about Pis zero.

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Fl2  =  kxl  sin  530    Bil2  =  kx×  45  x=5ilB8k

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