Question

A circular copper disc $10\, cm$ 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 $0.2\, T$ 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

Here $B=0.2\, T$ radius of the circular disc, $r=10\, cm =0.1\, m$ 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
$e=\frac{1}{2} B \omega r^{2}=\frac{1}{2} \times 0.2 \times 20 \pi \times(0.1)^{2}$
$=0.0628\, V$
Induced current $I=\frac{e}{R}=\frac{0.0628}{2}=0.0314\, A$