A circular coil of radius 8.0 cm and 20 turns rotates about its vertical diameter with an angular speed of 50 `s^(-1)` in a uniform horizontal magnetic field of magnitude `3 xx 10^(-2) T`. Obtain the maximum and average e.m.f. induced in the coil . If the coil forms a closed loop of resistance `10 Omega`, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from ?

Explanation

Here, `r = 8.0 cm = 8 xx 10^(-2) m, N = 20, omega = 50 s^(-1), B = 3 xx 10^(-2) T, e_(0) = ?, e_(av) = ?, R = 10 Omega, P = ?`
As `e_(0) = NAB omega = N (pi r^(2)) B omega :. E_(0) = 20 xx (22)/(7) (8 xx 10^(-2))^(2) xx 3 xx 10^(-2) xx 50 = 0.603` volt
Average value of emf induced over a full cycle, `e_(av) = 0`
`I_(0) = (e_(0))/(R ) = (0.603)/(10) = 0.0603 A`
Power dissipated `= (e_(0) I_(0))/(2) = (0.603 xx 0.603)/(2) = 0.018 W`
The induced curren causes a torque opposing the rotation of the coil. An external agent (rotor) must supply torqe (and to work) to counter this torqe in order to keep the coil rotating uniformally. Thus, the source of power dissipated as heat in the coil is the external rotor.