A straight conducting rod of length $0.40\text{m}$ slides on smooth horizontal rails with a constant speed $v=5{\text{m s}}^{-1}$ perpendicular to a uniform magnetic field $B=0.20\text{T}$ directed into the page. Find the magnitude of the induced emf across the ends of the rod.

Step-by-step solution

1. Write the formula for motional emf: $\epsilon =Blv$ because $\vec{v}\perp \vec{B}$.
2. Substitute the given values: $\epsilon =(0.20\text{T})(0.40\text{m})(5{\text{m s}}^{-1})$.
3. Calculate: $0.20\times 0.40=0.08$, then $0.08\times 5=0.40$.
4. Hence the induced emf is $0.40\text{V}$.

Concept tested: Motional emf in a moving conductor

Published 14 September 2026 · How this solution was prepared and checked