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).
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
Maxwell's equations are usually considered the most fundamental equations of classical electromagnetism, and therefore cannot be derived. They are accepted because they successfully predict the widest range of classical electromagnetic phenomena. However, if you there is a slightly different approach where you can start with electrostatics, and assume special relativity, and then you are force to invent magnetism, or something like that. I don't remember the details, and I don't know how fudge free this approach is, but you can look at Ohanian's EM text for details.