Question

A conducting wheel in which there are four rods of length $l=20\text{cm}$ as shown in the figure, is rotating with angular velocity $10\text{rad/s}$ in a uniform magnetic field of $2.5\text{T}$ perpendicular to the plane of wheel. The induced potential difference between its center and rim will be -

• A. $0.4\text{V}$
• B. $0.2\text{V}$
• C. $0.1\text{V}$
• D. $0.5\text{V}$

Answer 1

The correct option is D $0.5\text{V}$

Since, all the rods are rotating in the same magnetic field with the same angular velocity, equal emf will be generated across them.

EMF generated across a single rod is,

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

$=\frac{2.5\times 10\times {0.2}^2}{2}=0.5\text{V}$

The equivalent circuit diagram can be drawn as shown below.



As the cells are connected in parallel, their equivalent EMF will be $E$.

Therefore, the induced potential difference between its center and rim is

$V=E=0.5\text{V}$

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