Question

A copper disc of radius $0.1$ $m$ rotated about its centre with $10$ revolutions per second in a uniform magnetic field of $0.1$ tesla with it's plane perpendicular to the field. The e.m.f. induced across the radius of disc is:

• A. $\frac{\pi }{10}volt$
• B. $\frac{2\pi }{10}volt$
• C. $\pi \times {10}^{-2}volt$
• D. $2\pi \times {10}^{-2}volt$

Answer 1

The correct option is C $\pi \times {10}^{-2}volt$

Consider a small radial segment of $dx$ at a distance $x$ from the centre of the disc. Velocity of this segment is $\omega x$. Emf induced across this segment
$de=vBL=\omega xBdx$
Total emf induced across radius of disc $r$

$E=\frac{1}{2}B\omega r^2$

As $\omega =2\pi n$ where $n$ is number of revolutions per second

$B=0.1T,r=0.1m,\omega =10rev/s=20\pi rad/s$

$E=\frac{1}{2}\times 0.1\times 0.01\times 20\pi =\pi \times {10}^{-2}V$