# How is a current induced in this translating wire?

I am familiar with the principles of electromagnetic induction, but I am stuck on the scenario below: a long straight wire is translating in a uniform magnetic field. According to my book, this causes an EMF to be induced across it, and subsequently a current.

I'm struggling to understand why, since the wire is just translating. Applying Faraday's law $$V = -\frac{\partial \Phi }{\partial t} = -\frac{\partial BA }{\partial t}%$$ there needs to be a change in flux cutting the conductor somewhere. The flux density is uniform so this is not the cause. I also don't see how the wire's reference area could be changing since it is simply a long cylinder (not a wire loop or something where the angle could be varied).

• Consider the Lorentz force: $\vec{F} = q \vec{v} \times \vec{B}$. – ytlu Feb 20 at 16:44