Figure shows a circuit having a coil of resistance `R = 2.5 Omega` and inductance `L` connected to a conducting rod of radius `10 cm` with its center at `P`.

Assume that friction and gravity are absent and a constant uniform magnatic 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^(-1)`. Find the magnitude of this torque (in `mNm`) 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) = (B omegal^(2))/(2R)`
Torque about the hinge `P` is
`tau = underset(0) overset(l) int i(dx)Bx rArr tau = (1)/(2) iBl^(2)`
Putting `i= i_(0)//2`, we get: `tau = (B^(2)Omega l^(4))/(8R) = 5mNm`