Electrodynamics/Faraday's Law

How Generators Work

Faraday's law states that the Electromotive Force (EMF) produced in a coil is the negative derivative of the Flux:

$V=-\frac{\partial \mathrm{\Phi }}{\partial t}$

What this is saying is that if there is a change in how much magnetic field passes through a coil (flux) then a Potential Difference will be establish in the coil proportionally to that change. This could be done by changing the strength of the field, or, as is used mostly, changing the dimensions or orientation of the coil with respect to the magnet.

If a coil has n turns. Then we can multiply the amount of potential by that number of turns.

$V=-N\frac{\partial \mathrm{\Phi }}{\partial t}$

Real Generators

Real generators generally spin a large magnet inside a Coil, in Australia we use three phase generators, meaning that there are in fact three coils, at 120 degree spacings. These generators produce voltages in the thousands. They are powered by sources such as coal, oil, and hydoelectric. In some countries Nuclear Fission is used to produce steam which turns turbines.

More on Faraday's Law

Faraday's Law is considered one of Maxwell's Equations. When it is used as such it is expressed as

$\mathrm{\nabla }\times 𝐄=-\frac{\partial 𝐁}{\partial t}$,

or in its integral form,

${\oint }_{\partial S}𝐄\cdot d𝐥=-\frac{d\mathrm{\Phi }}{dt}$,

where

$\mathrm{\Phi }=\underset{S}{\int }𝐁\cdot d𝐬$.

Here, $d𝐥$ and $d𝐬$ stand for the (vector-valued) line element and surface element respectively. One should be aware that surface $S$ is not allowed to change in time in the above integral form of the law.