The magnetic field in a region is given by $\overrightarrow{B}=B_0\left(\frac{x}{a}\right)\widehat{k}.$   A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity   $\overrightarrow{v}=v_o\stackrel{\wedge }{i}$. The emf induced in the loop 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.