Question

State Faraday's law of electromagnetic induction. Apply the law to obtain an expression for the induced emf in a conducting rod of length $a$ rotating about its one end with angular velocity $\omega$ in uniform magnetic field B.

Answer 1

According to Faraday's law of electromagnetic induction the magnitude of induced EMF is equal to the rate of change of magnetic flux linked with the closed circuit or coil. Mathematically

$E=-N\frac{d{\varphi }_B}{dt}$

where N is the number of terms in the circuit and

${\varphi }_B$ is the magnetic flux linked with each turn.

Supposed a conducting rod completes one revolution in time t then :

$\begin{array}{c}Changeinflux=B\times Area=B\times \pi l^2\\ InducedEmf=\frac{Changeinflux}{Time}\\ \epsilon =\frac{B\times \pi l^2}{T}\\ T=\frac{2\pi }{\omega }\\ \therefore \epsilon =\frac{B\times \pi l^2}{\frac{2\pi }{\omega }}=\frac{1}{2}B{l}^2\omega \end{array}$