Art wrote:
"Maxwell`s additive to the equations have the units of current such that
Newton`s laws are satisfied."

Many experimenters wrapped wire around magnets hoping current would be
produced in the wire. It never worked until Michael Faraday discovered
that moving a magnet with respect to the wire or connecting and
disonnecting a battery to a coil of wire induced a transient current in
an adjacent coil.

Maxwell was a brilliant mathematician and theoretical physicist. He
found he could formulate a set of equations which expressed all the
known electromagnetic phenomena at once from all the earlier laws.

Maxwell noted his equations were similar to those which expressed the
motion of waves on water. He was convinced that electromagnetic waves
could exist and was able to calculate the speed at which they would
travel.

To show that Maxwell`s equations actually represent wave equations, an
equation is written in a form so that the magnetic vector potential
varies in all three spatial directions and in addition, a source term
(current density) is included.

If the source does not exist, we get a homogeneous wave equation for the
magnetic vector potential.

Other potential functions or the various field variables themselves may
be used to obtain similar wave equations.

Best regards, Richard Harrison, KB5WZI