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L is a smooth conducting loop of radius ...

L is a smooth conducting loop of radius l=1.0 m & fixed in a horizontal plane. A conducting rod of mass m=1.0 kg and length slightly greater than l hinged at the centre of the loop can rotate in the horizontal plane such that the free end slide on the rim of the loop. There is a uniform magnetic field of strength B=1.0 T directed vertically downward. The rod is rotated with angular velocity `omega_(0)=1.0 rad//s` and left. The fixed end of the rod and the rim of the loop are connected through a battery of emf . E, a resistor of resistance R`=1.0 Omega`, and intially uncharged capacitor of capacitance C=1.0 F in series. Find :
(i) the time dependence of emf . E such that the current `I_(0)=1.0A` in the circuit is constant.
(ii) energy supplied by the battery by the time rod stops.

Text Solution

Verified by Experts

The correct Answer is:
(i) `(1)/(2)+(7t)/(4)` (ii) `(13)/(18)J`
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