A line charge I per unit length is pasted uniformly onto the rim of a wheel of mass m and radius R. The wheel has light non-conducting spokes and is free to rotate about a
vertical axis as shown in figure. A uniform magnetic field B exists as shown in figure. What is the angular velocity of the wheel when the field is suddenly switched off?

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.