Hans Christian Oersted discovered this over a century ago.

He placed a magnetic compass near a wire. When current flowed through the wire the compass needle deflected. This is shown at the Exploratorium Exhibit Circles of magnetism.

Soon Michael Faraday in England was studying the motion of wires when placed in a magnetic field. This is best shown in the exhibit and Snack of the same name, Motor Effect. The motion of the current carrying wire in a magnetic field is given by the right hand rule (or the left hand rule if you consider the current to be the motion of negative charges.)

The wire could be made to move in a circle using sliding electric contacts called brushes as part of commutators. The result was the electric motor.

A simple working motor is described in the snack "Stripped Down Motor."

In particular, if you have a coil of wire, if the magnetic field through the coil changes, a voltage called an EMF or electromotive force is produced which will drive a current around the coil.

Don Rathjen has created a new Snack titled Striped down Generator in which a stack of magnets moves back and forth through a coil of wire creating an electric current which will light an LED.

These last two laws result in the production of electromagnetic waves, like light.