Why would induced EMF be zero?

Question

If a rectangle loop would move inside a magnetic field, would the induced ϵ be zero?

Why would it? Is it due to the induced ϵ canceling out? Being in series and in opposition?

If it we're a single wire it would have an induced ϵ = −vBL.

Answer 1

Yes, it would be zero. According to Faraday's Law the induced EMF would be zero because by moving the loop in that way the magnetic flux would not change.

For an EMF to be induced the magnetic flux must change. This could happen if you spinned the loop so that the angle between \$ \vec{B} \$ and the normal to the loop would change.

But if the magnetic field itself was nonuniform then by moving the loop through areas with different intensities you could induce an EMF.

Edit:

A single wire moving in a magnetic field could have a current, which is explained by Lorentz force: because the wire is being moved so are its charges with velocity \$ \vec{v} \$, and so a force is applied on those charges, hence the current.

The same principle applies to the loop in the picture. Since \$ \vec{v} \$ is to the left and \$ \vec{B} \$ points out of the screen, \$ \vec{v}\times\vec{B} \$ will point down. Thus the current should have that direction (the electrons move in the opposite direction, i.e. up). But now notice both the wire on the left and on the right have currents that cancel out (they have the same absolute value but point opposite ways). So the resulting current is null.