Question

A rod of length l rotates with a small but uniform angular velocity $\omega$ about its perpendicular bisector. A uniform magnetic field B exists parallel to the axis of rotation.The potential difference between the and an ends is

Answer 1

REF.Image

The rotates an follows :-

Note that an EMF always generated

along the direction of $(\overrightarrow{V}\times \overrightarrow{B})$

For circular motion, $\overrightarrow{V}=\overrightarrow{R}\omega$ hence

$\epsilon \equiv \omega (\overrightarrow{R}\times \overrightarrow{B})\to \left(1\right)$

now, halves $OA=OB$ thus $\left|\overrightarrow{R_1}\right|=\left|\overrightarrow{R_2}\right|$, but $\overrightarrow{R_1}=-\overrightarrow{R_2}$ on OA and

OB exists in opposite direction at any instant of time.

Thus two emfs ${\epsilon }_1$ and ${\epsilon }_2$ are generated in equal and opposite

direction, wading to a net ZERO potential difference across

the ends.