A conducting wire of length l , positioned perpendicular to a...

The motional electromotive force (EMF) induced in a straight conducting wire of length $l$ moving with velocity $v$ perpendicular to a uniform magnetic field $B$ is given by:

$E = (\vec{v} \times \vec{B}) \cdot \vec{l}$

Since the velocity $\vec{v}$, magnetic field $\vec{B}$, and the length of the wire $\vec{l}$ are mutually perpendicular, the magnitude of the induced EMF is:

$E = vBl$

This induced EMF is equal to the potential difference established across the ends of the wire.

Therefore, the potential difference is $lBv$.