Question

A conducting disc of radius $0.6\text{m}$ is in pure rolling motion. A magnetic field of $1\text{T}$ exists in the region along the axis of the disc. If the velocity of the center of the disc is $5\text{m/s}$, calculate the potential difference between the center and a point on its periphery.

• A. $2.5\text{V}$
• B. $1.5\text{V}$
• C. $3.5\text{V}$
• D. $9.5\text{V}$

Answer 1

The correct option is B $1.5\text{V}$

Since, the disc is in pure rolling motion, the angular velocity of the disc about its center is,

$\omega =\frac{v}{r}=\frac{5}{0.6}=\frac{25}{3}\text{rad/s}$

The potential difference between the center of the disc and a point on its periphery is,

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

$=\frac{1\times \frac{25}{3}\times {0.6}^2}{2}=1.5\text{V}$

Hence, option $\left(B\right)$ is the correct answer.