What is the physical explanation of the fact, that the electric field is zero inside a conductor?
In a conductor, say a metal wire, the charge carriers (electrons) are able to move under the influence of even a tiny electric field. If this field is steady (i.e. does not vary in time) then after a long enough time ~ 10^ - 9 seconds an isolated conductor will macroscopically have zero net electric field in it's interior.
As the electrons are free to move they do so until they find positions where they feel no net force. When they come to rest the interior of the conductor must have zero electric field. This means
1) The macroscopic charge density inside a conductor is zero.
2) The net charge on a conductor only exists on the surface. (at least to good approximation as the electric field will penetrate slightly into the conductor).
3) External electrostatic fields are always perpendicular to the conductors surface. Otherwise this would produce a force on the charge carriers inside the conductor and so the field would not be static as we assume.
4) The electrostatic field at the conductor's surface is proportional to the surface charge, i.e. does not depend on the charge carriers inside the conductor.
Andrew James Bruce, Physics grad student, UK
Charges have maximum freedom of movement within a conductor, and this gives way to there being no electric field within the conductor.
This is a very intuitive negative-feedback process within the conductor. At any point when there is an electric field within the conductor, positive charges (or lack of negative charges) that are entirely free to move will move in the direction of the electric field, and negative charges are entirely free to move opposite the direction of the electric field. However, these charges are surrounded by their own electric field. The charges that just moved with the influence of the internal electric field will thus create a field that will counter the effect of the original field.
Perhaps it will be clearer with a more specific example.
Imagine an electric field going from left to right through a metal conductor. The electrons in the conduction band of this metal have no restrictions in their movement. Thus, the electrons in the metal are going to move toward the left (because field lines are drawn in the direction of positive charges). This will leave an absence of electrons on the right and a surplus of them on the left. This charge separation is like a little battery -- it creates an electric field from right to left. It creates an electric field from the absence of electrons to the surplus of electrons. This electric field completely counters the original left-to-right field.
This is also the explanation for why electric fields must ALWAYS be PERPENDICULAR to the surface of conductors. At the surface, the electrons are NOT free to move in all directions. They may then build up on the surface. If there is any field lines that are slanted, the tangential components (the components parallel to the surface) will cause lateral motion of the charges until the resulting secondary displacement field will counter the original field. So the only electric fields at the surface of a conductor will be perpendicular to the surface.
So again, it's due to the dynamics of the free charges within the conductor. It creates a negative feedback effect so that the static equilibrium will have no internal electric field. Thus, those materials that are not conductors that force a particular organization of the electrons will not be free to counter external electric fields, and they will then have those same fields within them (or fields with interesting modifications -- consider materials that DO allow some movement but only along particular axes).
Ted Pavlic, B.S., Electrical Engineering Grad Student, Ohio State U.
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'