In reality I have much more complex physical system to solve, that is multiferroic BiFeO3 domain wall structure (here is the information: https://pubs.acs.org/doi/full/10.1021/acs.nanolett.9b03484). There were some activities on generating THz radiation charging and then shortening ultimate...
You say, Ez varies much slower than E_y and E_x, because the change of E_z is caused by slow movement of charges, while E_y and E_z are changing due to wave propagation. Do I understand correctly? It would simplify the problem but one has to be sure that the propagation of electromagnetic waves...
The entire problem is to have two sheets of charges (one positive and one negative), i.e. capacitor and then one shortens those two sheets. Of course, some electromagnetic waves will propagate inside the capacitor, but those waves are transverse, not changing z component of electric field. My...
Ok, I have a source, but from the symmetry reasoning still there is no dependence on x and y variables in free space (it is supposed that the charge is removed uniformly from any part of the sheet). thus, we still have the equation dEz/dz=0 and the homogeneous electric field along z at any time.
Consider infinite charged sheet in xy plane and suppose that charge is gradually and uniformly removed from the sheet. Electric field outside the sheet obviously do not depend on x and y variables, thus the Maxwell equation divE=0 reduces to the simpler form ∂Ez/∂z=0, this means that z component...