Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 2 / 16D / b / iii / Solution

Translation parallel to the wire leaves every point of the loop at the same distance from the wire, so its magnetic flux is constant. Equivalently, the line integrals of the motional field $\mathbf{u}\times \mathbf{B}$ cancel on opposite sides. Hence