[UPSC CSE 2026] Electrostatics and Magnetostatics (Q4, 15M)

A wire of length 2\text{ m} is perpendicular to the X\text{--}Y plane. It is moved with velocity \vec{V} = 2\hat{i} + 3\hat{j} + \hat{k}\text{ m/s} through a region of uniform magnetic induction \vec{B} = \hat{i} + 2\hat{j}\text{ Wb/m}^2. Compute the potential difference induced between the ends of the wire.