Ideal Conductors:

Gauss's Law shows that at Equilibrium (when the charges are at rest):
a. any excess charge resides only on the surface of the conductor.
b. the Electric Field at every point inside a conductor is always Zero.
c. the Electric Field always emerges from (or enters into) a conductor perpendicular to the surface.
d. the magnitude of the Electric Field near the surface at a point where the Surface Charge Distribution at that point is s, is equal to

E = s/eo
e. The surface of a conductor is an equipotential surface, i.e. the electric potential is the same at every point of the surface.

Ideal Conductor
A metal Conductor is simulate with an excess of positive charge. An external charge magnitude can be varied to observe the behavior of the charge on the surface of the conductor.

Verbal discussion of the above points:

a. Any excess charges have the same sign and thus repel each other. The charges arrange themselves on the surface so that they have the maximum separation between them.
b. If the electric field inside a conductor were not zero then any free charges would move. Alternately, if the excess charges are on the surface of the conductor, then any Gaussian surface inside the conductor would have no charge in it. Thus Gauss's law shows that E must be zero everywhere inside the conductor.

It is useful to envision that the excess charges arrange themselves in such ways that the vector sum of their combined electric fields inside the conductor always adds up to zero. This means that the surface charge density becomes larger in regions where there is a larger surface curvature, i.e. the greater the curvature of the surface, the larger the concentration of charges.

c. If the electric field were not perpendicular to the surface of the conductor, then there would be some component of the E-field parallel to the surface. The excess charges would move along the surface until the arrange themselves so the their parallel E-fields cancel out and the come to rest.
d. If you get infinitesimally close to the surface of a conductor, then it will look like a very large flat plate with a surface charge density of s at that location. Applying Gauss's Law to a cylinder near the surface we get,
e. Equipotential surfaces are always at right angles to the electric field. Thus the surface of a conductor is an equipotential surface since the field line are always perpendicular to the surface of a conductor. Excess positive charges on the surface of a conductor move towards regions of lower potential. As the charges move they change the overall potential. Each charge keeps moving about in this shifting potential seeking out a region of lower potential. When the charges stop jockeying about, they all find themselves at the same potential on the surface of the conductor, an equipotential surface.
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