Question

A conducting wheel rim in which there we three conducting rods of each of length $l$ is rotating with constant angular velocity $\omega$ in a uniform magnetic field $B$as show in figure. The induced potential difference between its centre and rim will be :

• A. $B\omega l^2$
• B. $\frac{3}{2}B\omega l^2$
• C. $0$
• D. $\frac{B\omega l^2}{2}$

Answer 1

The correct option is D $\frac{B\omega l^2}{2}$

Key Points Applying induced emf is equal to change of flux with respect to time.
According to question,
Induced emf $=\frac{\text{Change in flux}}{Time}=\frac{B\cdot A}{T}$
$ϵ=\frac{B\times \pi l^2}{T}[AreaA=\pi l^2]$
Frequency $v=\frac{1}{T}=\frac{\omega }{2\pi }$
So, $ϵ=\frac{B\times \pi l^2\times \omega }{2\pi }$
$=\frac{B\omega l^2}{2}$