# Maxwell's Equations

Could someone point me in the direction of the derviation of each of Maxwell's equations? I'm working on a presentation and can't find a good one that starts with primitive assumptions (i.e. to help explain to a non physics audience).

jtbell
Mentor
As far as I know, in classical electrodynamics, Maxwell's equations are ultimately "derived" from experimental evidence, not from more fundamental assumptions. Gauss's Law comes from studies of electric forces by Coulomb and others. Faraday's Law comes from experiments on magnetic induction, most notably by Faraday himself.

The one exception would be the part of Ampere's Law that was added by Maxwell in order to make the complete set of equations mathematically consistent (the "displacement current" term).

In modern quantum theory, one can derive electrodynamics (including Maxwell's equations) by requiring that the theory be invariant under local U(1) gauge transformations of the particle fields. See for example the last section of

http://www.upscale.utoronto.ca/GeneralInterest/DBailey/SubAtomic/Lectures/LectF13/Lect13.htm

I wouldn't want to try to explain this to a lay audience though.

Last edited:
Mapes