Gauss's Law

Gauss´s law allows one to solve some problems involving charge distributions on conductors, and to calculate the electric field of several simple charge configurations. It is a mathematically equivalent form of Coulomb´s law.

Gauss´s law relates the flux F of electric field that "leaves" through a closed surface, to the total charge interior to that surface. The formula is

F = (E)(A)(cos q) = 4 p k Q

where E is the electric field, A is the surface area, and Q is the charge enclosed by the surface.

The angle q is the angle between E and the normal to the surface. In all of our applications of Gauss´s law, the electric field will be perpendicular to the surface, so q will be equal to 0 and therefore the factor cos q will simply be equal to 1.

We have to live with a perverse tradition that the constant k is frequently written as;

1/(4 p e0),

where e0 = 1/(4 p k) = S.35e-12.

So Gauss´s law also may be seen written in the form

F = Q/ε₀