My prof in my intro to electrodynamics class briefly mentioned that the linearity of Maxwell's equations is related to the superposition of electric fields by point charges, but I don't see how. Would someone please elaborate on this?
It's a good question (and relevant also to quantum mechanics since the Schrödinger equation is linear too, albeit in the wavefunction rather than the fields).
Basically the linearity of the Maxwell equations means that if I know the solution to the equations for a single point charge then
- The solution to the equations for the fields for $N$ point charges is just the sum of the solutions for the fields of the $N$ individual charges.
Note that this is not generally the case in classical mechanics; usually the sum of two independent solutions of the classical equations of motion is not itself a solution of the equations of motion!