Question

A circular copper disc $10cm$ in radius rotates at $20\pi rad{s}^{-1}$ about an axis through its centre and perpendicular to the disc. A uniform magnetic field of $0.2T$ acts perpendicular to the disc. What is the induced current (in A), if the resistance of $2\Omega$ is connected in between axis and rim of the disc.

Answer 1

Answer: 0.0314

Here $B=0.2T$ radius of the circular disc, $r=10cm=0.1m$ resistance of the disc, $R=2\Omega$ angular speed of rotation of the disc, $\omega =20\pi rad{s}^{-1}$
If $e$ is the induced emf produced between the axis of the disc and its rim, then
$e=\frac{1}{2}B\omega r^2=\frac{1}{2}\times 0.2\times 20\pi \times (0.1{)}^2$
$=0.0628V$
Induced current $I=\frac{e}{R}=\frac{0.0628}{2}=0.0314A$