Question

A circular coil, of radius a, (having N turns) is made to rotate about its vertical diameter with an angular speed ω. The coil is present in a region where a uniform horizontal magnetic field B is present. If the coil has a resistance R, the rms value of the induced current and the resulting power loss, in it, are given, respectively, by

(1) \(\frac{N\pi a^2 ωB}{R}\) and \(\frac{(N\pi a^2)^2ωB} {R}\)

(2) \(\frac{N\pi a^2 ωB}{\sqrt{2}R}\) and \(\frac{2(N^2 \pi a^2 ωB)}{R}\)

(3) \(\frac{N\pi a^2 ωB}{\sqrt{2}R}\) and \(\frac{2(N^2 \pi a^2 ωB)}{2R}\)

(4) \(\frac{N\pi a^2 ωB}{\sqrt{2}R}\) and \(\frac{(N\pi a^2 ωB)}{\sqrt{2}R}\)

Answer 1

(2) \(\frac{N\pi a^2 ωB}{\sqrt{2}R}\) and \(\frac{2(N^2 \pi a^2 ωB)}{R}\)

The instantaneous flux, linked with the coil; is

ϕ = Nπa²Bcos(ωt)

∴ Instantaneous induced emf is