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 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 exist as shown in Fig.

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.

Answer

5

Explanation

Induced emf = `1/2 B omega l^(2)`
Maximum current : `i_(0) =(Bomegal^(2))/(2R)`
Torque about the hinge P is
`tau=int_()^(1) i(dx)Bxd implies tau = 1/2 iBl^(2)`
put `i=i_(0)//2`, we get , `tau = (B^(2)omegal^(4))/(8R)=5 mMm`.