A rectangular loop with a sliding connector of length l =1.0 m is situated in a uniform magnetic field B = 2T perpendicular to the plane of loop. Resistance of connector is r=2 $\Omega$. Two resistance of 6 $\Omega$ and 3 $\Omega$ are connected as shown in figure. The external force required to keep the connector moving with a constant velocity v = 2 m/s is

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.