Statement of 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 mathematicaly 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. It will be equal to 0 so the factor cos q will equal 1 in all of our applications of Gauss's law.

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) = 8.85e-12. So Gauss's law also takes the form F = Q / e0 .


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