Question

A copper disc of radius $0.1\text{m}$ is rotated about its centre at $20$ revolutions per second in a uniform magnetic field of $0.1\text{T}$ with its plane perpendicular to the field. The emf induced across the radius of the disc is -

• A. $\frac{\pi }{20}\text{V}$
• B. $\frac{\pi }{10}\text{V}$
• C. $20\pi \text{mV}$
• D. $100\pi \text{mV}$

Answer 1

The correct option is C $20\pi \text{mV}$

Emf induced across rotating element (here, disc)
$\in =\frac{B\omega R^2}{2}$

Given, $B=0.1\text{T}$
$\omega =20\text{rps}=20\times 2\pi =40\pi \text{rad/s}$
& $r=0.1\text{m}$

$\Rightarrow \in =\frac{0.1\times \left(40\pi \right)(0.1{)}^2}{2}$
$=20\pi \times {10}^{-3}\text{V}=20\pi \text{mV}$