@vanhees71. Thank you so many for your explannations, without which the expression ##\rho(x,y,z) = \sigma(x,y)\delta(z)## would have seem so weird to me. You have dealt precisely with the dimensional issue : I think this is a model of answer, about a topic that is hardly found in classical books...
This is not what I meant. You assume that the e-field is discontinuous, say Heaviside-shaped. Then its derivative along z is Dirac. So far so good. But where are Maxwell equations in all of this ? How do you find the magnitude of the field near the surface, or more precisely, its orthogonal...
@DaleSpam. Thank you for your answers. I don't want to make you vasting time, in particular because I'm not sure this problem is of interest for you. You seem to say that you have guessed the form of the solution, and checked that it works. This is this "checking" that would have been...
@Nugatory. I don't see how the symetric derivative can be of any help to give a sense to the divergence in this case. Can you be more precise and show me equations, so I'll be able to grasp it ?
@DaleSpam. More or less, I would say you the same. Can you show me how you introduce the Dirac...
@DaleSpam. I was previously satisfied with your answer. Nevertheless, I have now one more question. Let ##x,y,z## be an orthogonal system of axes whose origin is at some point of the surface of the conductor, and such that ##x,y## is parallel to the surface and ##z## is orthogonal to the...
Your remark is interesting, and illustrates the fact that sufficient litterature about Faraday cages is lacking. I'm not sure that an electrically fed wire can be assimilated to a Faraday cage: it is more a circuit fed with a power supply. Anyway, I think it is well known that a Faraday cage...
I would like to point out that @coquelicot, which is one of my friends, has not claimed that a conductor violates Maxwell law (at least not in this thread), but on the contrary has stated that this is wrong and tried to undertand what seemed to him a paradox (presenting things as an apparent...