Question

A conducting cycle wheel, with each spoke of length $l$, is rotating about its geometrical axis, with uniform angular velocity $\omega$, in a uniform magnetic field as shown in the figure. If the number of spokes are $N$, then calculate the induced emf between the center and the rim of the wheel.

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

Answer 1

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

Since, all metal spokes are rotating inside the magnetic field with same angular velocity, therefore, same rotational emf will be induced across ends of each of them.

Emf generated in a single spoke is,

$E=\frac{1}{2}B\omega l^2$

All the spokes are connected in parallel across the center and the rim.

Therefore, the net emf of their combination is,

$E_{\text{net}}=\frac{1}{2}B\omega l^2$

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

Why this question? Note: The net emf does not depend on the number of spokes $\left(N\right)$ in the wheel.