A circular coil having 20 turns, each of radius 8 cm, is rotating about its vertical diameter with an angular speed of 50 `rad//s` in a uniform horizontal magnetic field of 30 mT. Obtain the maximum, average and rms value of e.m.f. induced in the coil. If the coil forms a closed loop of resistance 10 ohm, how much power is dissipated as heat

Explanation

Here, `N = 20, r = 8 cm = 8 xx 10^(-2) m`, ltbgt `omega = 50 rad//s, B = 30 mT = 30 xx 10^(-3) T`,
`A = pi r^(2) = pi (8 xx 10^(-2))^(2) m^(2)`
`e_(0) = NA B omega`
`= 20 xx pi (8 xx 10^(-2))^(2) xx 30 xx 10^(-3) xx 50`
`= 0.603 V`
The average value of e.m.f.
`e_(av) =Zero`
`e_(rms) = e_(upsilon) = (e_(0))/(sqrt2) = (0.603)/(1.414) = 0.4265 W`
`R = 10 ohm`
power dissipated as heat
`= I_(upsilon)^(2) R = ((e_(upsilon))/(R ))^(2) R = (e_(upsilon)^(2))/(R) = ((0.4265)^(2))/(10) = 0.0182 W`