1. 3. Basic Principles of Electrostatics
Electrostatics is concerned with three functions, (x), E(x), and V(x). To proceed to the next few chapters one must comprehend the six relations among these three functions. For each pair of functions there is an integral formula and a partial differential equation.
(In the integrals for E and V, r is the distance from the source point x’ to the field point x, and dV’= d3x’ is the elemental volume at the source point.)
G L Pollack and D R Stump Electromagnetism

2. Use of Gauss’s Theorem (Figure 3.8)
By Gauss’s theorem, the flux of E through a closed surface S is equal to Q/0 where Q is the charge enclosed. For a charge distribution with spherical, cylindrical or planar symmetry, E(x) can be determined.
For spherical symmetry, apply Gauss’s theorem to a spherical surface around the center of symmetry; the flux of E is Er(r)4 r2.
For cylindrical symmetry use a cylindrical gaussian surface around the line of symmetry; the flux of E is Er(R)2 Rh.
For planar symmetry use a cylindrical gaussian surface with the end-caps at equal distances above and below the plane of symmetry; the flux of E is 2Ez(z) A.
G L Pollack and D R Stump Electromagnetism