I'm trying to get a sense of how widely applicable Maxwell's equations really are. I've read that electrodynamics becomes non-linear in the Schwinger limit where electric field strengths get high enough, but are there other situations where Maxwell's equations are insufficiently accurate? What about in the low electric field limit or the high frequency limit? What about something like nano-engineering where the length scales are small and quantum effects have to be taken into account? Would a nano-engineer ever have to use quantum electrodynamics, or would they normally just use some sort of mixture between Maxwell's equations and Schrodinger (e.g. use Maxwell to find the hamiltonian and then solve the Schrodinger equation)?