I was under the assumption that a magnetic field acts similar to that of the normal force in mechanics; both affect the path of the object, but do no work. So now suppose that we have a rectangular circuit with the left side in an uniform magnetic field that is pointing towards the computer screen and the right side being moved at a velocity $v$ Since the whole circuit is moving with a velocity $v$ there is a magnetic force perpendicular to $v$, but still in the direction of the wire. Therefore the magnetic field pushes the charges along. If we assume the charges to be that of protons and electrons, the magnetic field will separate electrons from protons and cause current to flow. My confusion is on the very fact that the magnetic field is causing the current to flow. I simply thought the magnetic field would change the direction of current flow. How can this be?
Without the magnetic field the velocity of electrons is v. When the magnetic field is on, the velocity of electrons is v + u.
Velocity and kinetic energy of electrons increases when the wire enters magnetic field. The source of that energy is the force that pushes the electrons to the direction of the velocity vector v.
Electrons in a magnetic field would move around in a circle whose center is at rest relative to to the magnet. But in this case electrons are trapped in a tube that keeps moving on. That tube pushes the electrons in addition to the magnetic field that pushes the electrons to direction perpendicular to vector v + u .