Question

A circular coil is rotating with its vertical diameter In a uniform horizontal magnetic field . What is the average EMF induced in the coil ?

Answer 1

Dear Student,
Here in this case we know that in a coil of diameter D and radius r with N number of turns and magnetic field B is acting on it and it is rotating with a angular speed of $\omega$ then the induced emf , $e=NAB\omega \sin \omega t$
Therefore , the average emf induced in the coil is ,
$$\begin{gathered} e_{avg}=\frac{1}{T}{\int }_0^{2\pi }NAB\omega \sin \omega tdt \\ =\frac{1}{T}NAB\omega {\left[\frac{\cos \omega t}{\omega }\right]}_0^{2\pi } \\ =\frac{NAB}{T}\left[\cos 2\pi -\cos 0\right] \\ =\frac{NAB}{T}\left[1-1\right] \\ =0 \end{gathered}$$
Regards