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 xx10^(-2)T` Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 100, 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

Flux through each turn of the loop `=pi r^2 B cos (omegat)`
`epsi =-N omega pi r^2 B sin (omegat)`
`epsi_("max")=-Nomega pi r^2 B`
`=20 xx 50 xx pi xx 64 xx 10^(-4) xx 3.0 xx 10^(-2) = 0.603 V`
`epsi_("avg") ` is zero over a cycle
`I_("max") = 0.0603 A`
`P_("average") = 1/2 epsi_("max") I_("max") = 0.018 W`
The induced current causes a torque opposing the rotation of the coil. An external agent (rotor) must supply torque (and do work) to counter this torque in order to keep the coil rotating uniformly. Thus, the source of the power dissipated as heat in the coil is the external rotor.