Question

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

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

Answer 1

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

According to Faraday's law of electromagnetic induction, the induced emf is equal to the rate of change of magnetic flux.

We know that induced emf in a conducting rod rotating in a uniform magnetic field is given by

$E=\frac{B\omega l^2}{2}$

Since, all four rods are connected between center and the rim behaves like a cell, and they are all connected in parallel, so the induced potential difference between its centre and rim will be equal to induced emf across each rod.

$\therefore E_{wheel}=\frac{B\omega l^2}{2}$

Hence, option $\left(\text{D}\right)$ is correct.