A metal rod of length $l=1\text{ m}$ rotates about one end with an angular velocity $\omega =20\text{ rad/s}$ in a uniform magnetic field $B=0.5\text{ T}$ directed perpendicular to the plane of rotation. What is the induced electromotive force $\epsilon$ between the ends of the rod?

Solution

1. Given: length $l=1\text{ m}$, angular velocity $\omega =20\text{ rad/s}$, and magnetic field $B=0.5\text{ T}$.
2. The induced EMF $\epsilon$ for a rod rotating about one end is given by the formula $\epsilon =\frac{1}{2}B\omega l^2$.
3. Substituting the given values, we get $\epsilon =\frac{1}{2}\times 0.5\times 20\times (1{)}^2$.
4. Calculating the result, $$\begin{array}{rl}\epsilon & =0.5\times 10\\ & =5\text{ V}\end{array}$$.
5. Hence the answer is (A).