Question

A metal disc of radius R rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. The induced electromotive force between the rim and the axis of the disc is:

• A. $-B\pi R^2$
• B. $-\frac{2B{\pi }^2{R}^2}{\omega }$
• C. $-B\pi R^2\omega$
• D. $\frac{B{R}^2\omega }{2}$

Answer 1

The correct option is D $\frac{B{R}^2\omega }{2}$

$\begin{array}{c}A=\pi R^2\\ \frac{dA}{dt}=\frac{\pi R^2}{\frac{2\pi }{W}}=\frac{W{R}^2}{2}\\ emf\in =-B\times \frac{dA}{dt}=\frac{BW{R}^2}{2}\end{array}$