Question

A conducting rod of length L is falling with velocity v perpendicular to a uniform horizontal magnetic field B. The potential difference between its two ends will be

• A. 2BLv
• B. BLv
• C. $\frac{1}{2}$BLv
• D. (BLv)${}^2$

Answer 1

The correct option is B BLv

Force on a charge q in the rod = $qvB$

electric field inside the rod due to displacements of charges due to force by relative motion in magnetic field $=\frac{emf}{l}$

As the rod moves in constant velocity, net force of constituent charge q in the rod $=0$
Therefore,

$q\frac{emf}{l}=qvB$
$\Rightarrow emf=Blv$