A circular coil of radius 8 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`. Find the maximum and average value of the emf induced in the coil.

Explanation

Here r = 8 cm = 0.08 m, or area of coil `A = pir^(2) = pi xx (0.08)^(2) = 64pi xx 10^(-4)m^(2), N = 20, omega = 50s^(-1) = 50 x 2pi rad s^(-1) = 100pi rad s^(-1) and B = 3 xx 10^(-2) T`
`therefore` Induced emf `varepsilon = N B A omegasin omegat`
`therefore` Maximum value of induced emf
`varepsilon_(max) = NBAomega = 20 xx 3 xx 10^(-2) xx 64pi xx 10^(-4) xx 100pi = 3.79 V`
and average value of sinusoidal induced emf for the complete cycle = 0.