An elliptical loop having resistance R , of semi major axis a , and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x -axis with angular frequency ω , the average power loss in the loop due to Joule heating is :

Step-by-step solution

The expression for induced EMF in the rotating loop in uniform magnetic field is given by ε = NAB ω   cos ω t The average power loss P = < ε 2 R > = < A 2 B 2 ω 2 cos 2 ω t R > < cos 2 θ > = 1 2 < P > = A 2 B 2 ω 2 R 1 2 ⇒   < P > = π 2 a 2 b 2 B 2 2 R ω 2