Relativity.

All particle interactions are explained as being mediated through bosons. The virtual photon is the electromagnetic interaction’s boson.

It is easy to deduce Coulomb’s Law if you assume that a charge emits virtual photos isotropically at an equal rate to its charge.

Where field intensity is proportional with photon density.

Start moving the charge.

What happens when the charge moves?

(Thanks to Giordan Stark, for this image.

It causes the field to be distorted. The field is limited in its ability to respond at the speed light. Therefore, moving the charge forward does not change the speed in any direction. As a result, the field will be stretched behind and compressed ahead of the charge’s movement.

Maxwell’s equations assume the electric field doesn’t change with movement of the charge. Instead, they invoke a magnetic field which occurs with the charge.

(The entire mathematical derivation of this is in the book I don’t currently have access to).

It is fascinating to note that the magnetic field can be represented by the cross product between the motion-induced changes in the virtual photon fields and the field that would exist if there was no relativistic distortion.

You can also use the magnetic fields to calculate the magnetic force on a moving charge. The Lorentz-prescribed Cross Product is used again to compute the force on the other moving charge. This produces a force result that is equivalent to using just the relativity-shifted virtual particle field.

Permanent magnets can be described using the same model but with angular momentum. Instead of using a point-charge, take a charge that has finite volume but is close to zero, and give it some angular momentum. The magnetic field equivalent distortions are caused by the smaller charges at a finite distance from the center.

You can describe magnetism using only electricity and relativity.