A straight wire of length 2 m is perpendicular to the xy-plane. It moves with velocity v⃗=(2î+3ĵ+k̂) m/s in magnetic field B⃗=(î+2ĵ) Wb/m². Find the potential difference between its ends in volts.
Physics · Electromagnetic Induction
JEE Mains

Question

A straight wire of length 2 m is perpendicular to the xy-plane. It moves with velocity v⃗=(2î+3ĵ+k̂) m/s in magnetic field B⃗=(î+2ĵ) Wb/m². Find the potential difference between its ends in volts.

Physics · Electromagnetic Induction

G1 Physics · Accepted Answer

ε=(v⃗×B⃗)·ℓ⃗. Here v⃗×B⃗ has z-component 1, and the wire length along z is 2 m. Therefore ε=2 V.