The diagram shows a circuit having a coil of resistance $$R=2.5$$Ω and inductance L connected to a conducting rod PQ which can slide on a perfectly conducting circular ring of radius $$10$$ cm with its centre at 'P'. Assume that friction and gravity are absent and a constant uniform magnetic field of $$5$$ T exists as shown in figure.At t $$=$$ $$0$$, the circuit is switched on and simultaneously a time varying external torque is applied on the rod so that it rotates about P with a constant angular velocity $$40$$ $$rad/s$$. Find magnitude of this torque (in$$ milli $$Nm) when current reaches half of its maximum value. Neglect the $$self-inductance$$ of the loop formed by the circuit.

Question

The diagram shows a circuit having a coil of resistance $$R=2.5$$Ω and inductance L connected to a conducting rod PQ which can slide on a perfectly conducting circular ring of radius $$10$$ cm with its centre at 'P'. Assume that friction and gravity are absent and a constant uniform magnetic field of $$5$$ T exists as shown in figure.At t $$=$$ $$0$$, the circuit is switched on and simultaneously a time varying external torque is applied on the rod so that it rotates about P with a constant angular velocity $$40$$ $$rad/s$$. Find magnitude of this torque (in$$ milli $$Nm) when current reaches half of its maximum value. Neglect the $$self-inductance$$ of the loop formed by the circuit.

Infinity Learn · Accepted Answer

Induced emf $$=12B$$ω$$l2Maximum$$ current: $$i0=B$$ω$$l22RTorque$$ about the hinge P isτ$$=$$∫$$0li(dx)Bxd$$⇒τ$$=12iBl2Put$$ i $$=$$ $$i0/2$$, we get : τ$$=B2$$ω$$l48R=5$$ mNm

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