Maxwell's equations for the electromagnetic field [ in units with ] are:

Defining the anti- symmetric tensor with components:

the electric and magnetic fields are given by

If we also define a current four- vector:

Maxwell's equations can be written as [ Assignment 4 ]

where . We have now expressed Maxwell's equations in tensor form as required by Special Relativity.

The first of these equations implies charge conservaton

By performing a Lorentz transformation to a frame moving with speed v in the x direction, one can calculate how the electric and magnetic fields change: