User:Bibliomancy

Maxwell's Equations
The following table provides the meaning of each symbol and the SI unit of measure:

Although SI units are given here for the various symbols, Maxwell's equations are unchanged in many systems of units (and require only minor modifications in all others). The most commonly used systems of units are SI, used for engineering, electronics and most practical physics experiments, and Planck units (also known as "natural units"), used in theoretical physics, quantum physics and cosmology. An older system of units, the cgs system, is also used.

In order to complete the theory of electromagnetism we need to add another equation to Heaviside's group of four 'Maxwell's Equations'. The force exerted upon a charged particle by the electric field and magnetic field is given by the Lorentz force equation:


 * $$\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}),$$

where $$ q \ $$ is the charge on the particle and $$ \mathbf{v} \ $$ is the particle velocity. This is slightly different when expressed in the cgs system of units below.

This extra equation appeared in cartesian format as equation (D) of the original eight 'Maxwell's Equations'.

Maxwell's equations are generally applied to macroscopic averages of the fields, which vary wildly on a microscopic scale in the vicinity of individual atoms (where they undergo quantum mechanical effects as well). It is only in this averaged sense that one can define quantities such as the permittivity and permeability of a material. Below the microscopic, Maxwell's equations, ignoring quantum effects, are simply those of a vacuum &mdash; but one must include all atomic charges and so on, which is generally an intractable problem.