A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad `s^(-1)` in a uniform horizontal magnetic field of magnitude `3.0 xx 10^(-2)` T. Obtain the maximum and average emf 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

Maximum induced emf is given by formula,
`epsilon_0=NABomega`
`=N(pir^2)Bomega`
`=(20)(3.14)(0.08)^2 (3xx10^(-2))(50)`
`therefore epsilon_0`=0.6029 V
Instantaneous power,
`P=epsilon^2/R=(epsilon_0^2 sin^2 (omegat))/R " " [because epsilon=epsilon_0 sin (omegat)]`
`therefore` Average power
`lt P gt =epsilon_0^2/R lt sin^2 (omegat)gt`
`therefore lt P gt = epsilon_0^2/R xx 1/2`
`=(0.6029)^2/10xx1/2`
`therefore lt P gt` = 0.01817 W