A ring of thin wire with active resistance R and inductance L rotates with constant angular velocity w in the external uniform magnetic field perpendicular to the rotation axis. In the process, the flux of magnetic induction of external field across the ring varies with time as Ф = Ф cos wt. Demonstrate that (a) The inductive current in the ring varies with time as I = I m sin (wt – φ), where I m = wФo /√R2 + w2L2 with tan φ = wL/R;
(b) The mean mechanical power developed by external forces to maintain rotation is defined by the formula P = ½ w2Ф2R/(R2 + w2L2).