So recently in our electrostatics course the lecturer keeps repeating a certain set of steps whenever he solves a problem, and I am not quite sure why these assessments are true.
- First, he makes the assumption that the conductor is ideal, and that hence all charge resides on the surface.
- We've been only doing spheres, planes and cables, but does that actually apply to every conductor? And why?
- Hence if we put a Gaussian surface inside the conductor, the surface encloses no charge. By Gauss's Law, that means there is no electric flux (and hence field) inside a conductor.
- This seems to me like the lecturer jumped a few steps there. From my understanding of Gauss's law, it says that the net electric field through the surface is zero, i.e. there could be electric field at any point on or within the surface, but in some places it points towards the inside of the surface, and towards the outside in others. Hence, when you integrate over the surface, the result will be zero, but the field at any given point is not necessarily zero.
- In fact, when I tried calculating electric field inside an infinitely long wire with charge uniformly distributed on it's surface by using Coulomb's Law, it seemed rather obvious that the field does not equal to zero anywhere except for the centre of the wire.
Is there something I am missing here? Some additional implied assumptions? Or is the lecturer overgeneralising?