In the derivation of the boundary conditions we apply the integral form of maxwell's equations, but once we take a very small volume we find that some terms disappear like the displacement current aswell as the time derivative of the magnetic field. Why do these terms disappear? For reference...
disappearing terms in electrodynamics boundary conditions
disappearing terms in electrodynamics boundary conditions
disappearing terms in electrodynamics boundary conditions
disappearing terms in electrodynamics boundary conditions
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