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Electrical engineering's development began with Faraday and Henry who, independently, discovered the principles of magnetically induced electromotive force and methods for converting mechanical into electrical energy directly.

Force on a Charge in a Wire in a Magnetic Field Illustration

The illustration at right shows a wire of length l in a magnetic field B that is into the page (the x's stand for into the page; · stand for out of the page). If you move the wire with a velocity v to the right, the magnetic field will interact with the charges q in the wire. If you are thinking of positive charges, you would use your right hand, with your thumb pointing in the direction of the velocity and your four other fingers pointing into the page. The force that the positive charges experience would be toward point a. If you are thinking of negative charges, you would use your left hand, and the force that the charges experience would be toward point b. The force that the charges experience is equal to F = qv × B.

Induced Current in a Rectangular Loop with a Moving Wire Illustration

Because you have moving charges, you create a change in potential difference. This potential difference is said to be the induced electromotive force (EMF). Now let's say we have a moving conductor on a stationary U-shaped conductor as illustrated at left. When the moving conductor has a length of l and moves across the U-shaped conductor with a velocity v. The portion that is moving now creates a potential difference, just as if you had a battery connecting the ends of the U-shaped conductor. Since it takes work to move this wire (there is a force that opposes the movement of the wire, which will be explained in a later section of this page), you are essential changing mechanical energy into electrical energy.

Now let's get into the mathematics of the situation. The work that you do to move the wire is the force times the length:
W = Fl = vBql
The EMF (x) that is induced is just the work per charge, so:

If you use your right hand rule, you will find that the current induced by the EMF goes counterclockwise, moving from point a to b to c to d. It is just if you placed a battery with a voltage of vBl with a positive terminal connected to point a and the negative terminal connected to point b.

More generally, you can define the EMF as the following, which considers the shape and orientation angle of the moving conductor with the field:

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