Faraday's Law

This was discovered independently by Joseph Henry, also. It is the principle behind the generator and many other important toys.

Here's how it works: the line below represents a conductor of length d moving straight down the page in a magnetic field (the x's) directed into the page. Electrons are free to move in a conductor, so immediately a bunch of them will pile up on the left end, making the left negative and the right positive. An equilibrium will be established between the magnetic force to the left on an electron in the middle of the wire and the electric force to the right. The electric force is qE and the magnetic force is qvB. Equate them, cancel q, use V = Ed, and then it is a simple matter to obtain the equation for the voltage between the ends of the conductor, and it turns out to be equal to the rate at which the magnetic flux is swept through. (Flux f is B times ^ area, and flux "swept " per time is B times d times y / t, but y/t is velocity…)

V_induced = D f /D t.

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x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

From this derivation it may not be clear how general it really is, and I will not dwell on the connection between the above and the other kinds of applications below.

The usual Faraday's law applications involve coils. This enhances the effect. The voltage induced between the ends of a coil is the sum of the voltages induced in the loops, and this in turn is the sum of the rates of change of flux through them. If all N loops of a coil have the same flux through them,
then V_induced = ND f /D t. This effect can be used as a source of electric power, so the voltage is referred to as an emf (electromotive force, which is not a force, but the name stuck).

The equation is usually written
e = - ND f /D t, with the minus sign (a convention) because the direction is opposite to a right-hand rule.

Move a coil toward or away from a magnet (or move the magnet) in such a way that the flux through the coil increases or decreases, or spin the coil or magnet. Or send alternating current through one coil and it will induce an AC voltage in a neighboring coil. A pair of coils designed for this is called a transformer, and they are generally wound on a common iron core.

You will now be induced back into fluids&heat&E&M.

Or my other main physics pages:
Mechanics

Vibrations and waves
Quantum
alphabetical quickies in index

Comments, questions: fredrick.gram@tri-c.edu