To illustrate how magnets can be used to induce electric current into a copper wire, we can start by imagining a copper wire connected to an ammeter to measure current.
If we place this wire at rest on top of the north or south pole of a magnet, nothing happens. There is no measurable effect if nothing moves.
However, if either the magnet or the wire is moved in such a way that the copper wire cuts into the stream of polarized photons coming out of the magnet, then we will register a current.
This can be explained entirely in terms of polarized zero-point photons interacting with electrons in the wire.
Moving the wire into the magnetic field, as illustrated above, makes the positive orbs of the spinning photons hook into the side of electrons in the wire. The electrons move to the left. A current towards the right is thus induced into the wire.
The current moves in the direction dictated by the spin of the negative orbs.
Move the wire in the opposite direction and the spinning photons hook into the electrons from the opposite side. The current moves the other way.
Flipping the magnet around so that it points down will likewise send the current in the opposite direction.
The relationship between motion of a wire, magnetic field, and current induced is always the same.
This is the right hand rule of electromagnetism, which states that an open right hand with thumb perpendicular to fingers can be used to determine the direction of induced current.
Let the thumb be the direction of motion of a positive charge, let the fingers be the direction of the magnetic field lines. Then the palm of the hand becomes the direction of the induced force.
In the case of electric induction, the wire is the charge in motion and the induced force is the current.
In the case of an electric motor, the current is the charge in motion and the induced force is the generated mechanical motion.