Question

A conducting rod is moved with a constant velocity v in a magnetic field. A potential difference appears across the two ends
(a) if $\overrightarrow{v}\parallel \overrightarrow{l}$
(b) if $\overrightarrow{v}\parallel \overrightarrow{B}$
(c) if $\overrightarrow{l}\parallel \overrightarrow{B}$
(d) none of these.

Answer 1

(d) none of these

The potential difference across the two ends is given by
$e=Bvl$
It is non-zero only
(i) if the rod is moving in the direction perpendicular to the magnetic field ($\overrightarrow{v}\perp \overrightarrow{B}$)
(ii) if the velocity of the rod is in the direction perpendicular to the length of the rod
( $\overrightarrow{v}\perp \overrightarrow{l}$)
(iii) if the magnetic field is perpendicular to the length of the rod $\overrightarrow{l}\perp \overrightarrow{B}$

Thus, none of the above conditions is satisfied in the alternatives given.