why do the electric field lines enter or leave the surface of the conductor perpendicularly? why is this assumed only at equilibrium?pl. explain with 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.