First slide

Magnetic flux and induced emf

Question

A circular copper disc 10 cm in radius rotates at $20 π {rads}^{- 1}$ 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 $Ω$ is connected in between axis and rim of the disc.

Moderate

Solution

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

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