A rectangular conducting loop of width $0.08\text{m}$ and length $0.12\text{m}$ moves with a constant speed $v=3{\text{m s}}^{-1}$ into a region of uniform magnetic field $B=0.04\text{T}$ directed into the page. The plane of the loop remains parallel to the field direction. Find the magnitude of the induced emf while the loop is partially inside the field.

Step-by-step solution

1. Identify the part of the loop that is entering the field: the length $l=0.08\text{m}$ (the side perpendicular to the motion) sweeps out area at rate $v\times l$.
2. Use Faraday’s law for a moving conductor: $\epsilon =Blv$ because the flux change per unit time is $\Delta \Phi /\Delta t=B(lv)$.
3. Substitute the numbers: $\epsilon =0.04\text{T}\times 0.08\text{m}\times 3{\text{m s}}^{-1}=9.6\times 10^{-3}\text{V}$.
4. State the magnitude as required.

Concept tested: induced emf in moving conductor

Published 6 September 2026 · How this solution was prepared and checked