Table of contents |

2 The Electric Field E 3 Electromagnetic waves |

The electromagnetic field exerts the following force (often called the Lorentz force) on charged particles:

This description of the force between charged particles, unlike Coulomb's force law, does not break down under relativity and in fact, the magnetic force is seen as part of the relativistic interaction of fast moving charges that Coulomb's law neglects.

The electric field **E** is defined such that, on a stationary charge:

The above definition seems a little bit circular, but in electrostatics, where charges are not moving, Coulomb's law works fine. So what we end up with is:

Note: the above is just Coulomb's law, divided by q_{1}, added up more multiple charges.

Changing the summation to an integral yields the following:

Both of the above equations are cumbersome, especially if one wants to calculate **E** as a function of position. There is, however, a scalar function called the electrical potential that can help. Electric potential, also called voltage (the units for which are the volt), which is defined thus:

Unfortunately, this definition has a caveat. In order for a potential to exist must be zero. Whenever the charges are stationary, however, this condition will be met, and finding the field of a moving charge simply requires a relativistic transform of the electric field.

From the definition of charge, it is trivial to show that the electric potential of a point charge as a function of position is:

Note well that φ is a scalar, which means that it will add to other potential fields as a scalar. This makes it relatively easy to break complex problems down in to simple parts and add their potentials. Getting the electric field from the potential is just a matter of taking the definition of φ backwards:

A changing electromagnetic field propagates away from its origin in the form of a wave. These waves travel in vacuum at the speed of light and exist in a wide spectrum of wavelengths. Examples of the dynamic fields of electromagnetic radiation (in order of increasing frequency): radio waves, microwaves, light (infrared, visible light and ultraviolet), x-rays and gamma rays. In the field of particle physics this electromagnetic radiation is the manifestation of the electromagnetic interaction between charged particles.