We know that different physical laws have their own domains of applicability. For example, Newton's law of Gravitation is valid when the gravitational field is weak and Einstein's theory takes over when the field is not weak. The latter is believed to be an overarching theory that is valid whether or not the field is weak (barring quantum).
In the same sense, is there a limited domain of applicability of Maxwell's equations i.e., do they ever break down? If so, what way? I mean what are the instances of it breaking down? One of the examples that I can think of, where classical electrodynamics break down (hence, Maxwell's equations are inadequate), is blackbody radiation. But is there a breakdown for strong fields?
Can Maxwell's equations be thought of as an approximation of some other overarching equations/theory which does not break down where Maxwell's equations do? Thanks.
