  After having identified all the possible relationships between the electric
field and the magnetic field in a given inertial reference frame we derive the
transformation equations for the components of these fields. Special relativity
is involved via the addition law of parallel speeds or via the Lorentz
transformations for the space-time coordinates of the same event. Electricity
and magnetism are involved via Gauss's and Ampere's laws. In this way we avoid
the transformation equations for the Lorenz force components which are used in
most derivations of the transformation equations for E and B fields.

General Physics