I have decided not to include Gauss' Law in the curriculum
this year, because its applications are limited and its
mathematical basis is obscure at this level.
All of the problems that are traditionally solved using
Gauss' law in a course like this can be solved more simply
by elementary methods, as long as you remember the following
basic principles:
- When charge is spread uniformly over the surface of a
sphere, it produces no field inside the sphere; while outside
the sphere it produces a field that is just as if all of the
charge were at the center of the sphere.
- The electric field of a uniform sheet of charge is
2*pi*k*Q/A where A is the area of the sheet; and hence the
electric field between two parallel plates with charges Q and
-Q is 4*pi*k*Q/A.
- Electric fields obey the Principle of Superposition:
The electric field caused by several charges is found by
adding the vectors of the fields caused by each charge.
- The electric field within a (perfect) conductor is zero.