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A conducting rod of length $2l$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field $B$ exists parallel to the axis of rotation. The e.m.f. induced between the two ends of the rod is:

1. $B\omega l^2$
2. $\dfrac{1}{2}l^2B\omega$
3. $\dfrac{1}{8}l^2B\omega$
4. Zero

Correct answer: Zero

Solution

The induced emf depends on the component of $\vec v\times\vec B$ along the rod. Here the rod rotates about an axis parallel to $\vec B$, so the magnetic force on charges is perpendicular to the plane of motion and does not drive charges from one end to the other. Hence the emf between the ends is zero.

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