Formulated by Karl Friedrich Gauss, arguably one of the greatest mathematicians in history, who provided significant contributions to many areas of both mathematics and theoretical physics. Gauss's Law expresses the relationship between electric charge and electric field and provides an alternative to Coulomb's Law. It states that total electric flux through a closed surface enclosing a definite volume is proportional to the net charge inside the surface.
It is not affected by the radius from the charge to the surface in any way. It can be expressed in its simplest form as:
Electric Flux = Charge enclosed / Epsilon Nought (the Permeability of free space, constant)
The surface involved can be imaginary, there need not be any material present at the location of the surface - such a closed surface can be referred to as a Gaussian Surface.
Gauss's Law can be used in calculating the electric fields caused by a variety of charge distributions, or in reverse to determine charge distribution from a known electric field pattern. Without a computer, such calculations are usually feasible when both the charge distribution and the Gaussian Surface under consideration have some symmetrical property. Most calculations involving this law involve some degree of integration, but this can be avoided in simple examples with careful algebraic manipulation.