A physicist works in a laboratory where the magnetic field is 2 T. She wears a necklace enclosing area 0.01 m² in such a way that the plane of the necklace is normal to the field and is having a resistance R = 0.01$\mathrm{\Omega }$. Because of power failure, the field decays to 1 T in time 10^–3 seconds. Then what is the total heat produced in her necklace ? (T = Tesla)

The diagram shows a circuit having a coil of resistance $R=2.5\Omega$ 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.