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- Summary
- I want to know if the time derivative of the electric and or magnetic field jumps over a material interface.

So I just wanted to see if anyone could offer some suggestions. So in my mind this seems impossible, in the case of electric field a jump in time derivative of that field would indicated in my mind that electric charge was either introduced or removed from the system instantaneously which would violate conversation of electric charge. If you prescribe to the quantum mechanic perspective that magnetic charge exists, the same argument would hold the magnetic field, since magnetic charge would also have to be conserved. If you just assume gausses law of magnetism holds, then again, this would mean a magnetic monopole would be introduced to the system, which is also problematic.

I'm not sure if there is a rigorous mathematical argument for this though - or if this is just true based on empirical observation (similarly how gausses law of magnetism is derived)

I would very much appreciate some comments on this subject.

I'm not sure if there is a rigorous mathematical argument for this though - or if this is just true based on empirical observation (similarly how gausses law of magnetism is derived)

I would very much appreciate some comments on this subject.