Carl Friedrich
Gauss was a brilliant
mathematician,
physicist and
astronomer. His
mathematical works included many theories and papers in the
realm of pure
math, such as
Number Theory. In the
physics world, he is most remembered for his law regarding
electric fields.
All Electric charge exact forces upon each other, which is regulated by Coulomb's Law
F = k * q1 * q2 / r * r, where constant k = 8.9*10^9).
Electric fields make everything simpler by graphically showing the strength of attraction or repulsion by one particular charge (it doesn't emit a field, it is imaginary). The strength of the field is based on the strength of the charge. The field would then exert a force upon any charge in its vincinity (technically infinite, but at very long distances it is practically zero). On a positive test charge, the strength of the force would be
F = E * q
Where E is the strength of the field in newtons per coulomb and q is charge of the test charge.
This all builds up to the concept of electric flux. Flux is the a measurement of the amount of electric field passing through an area. The formula is given by:
Flux = (Integral) E dA, A is area, E is field strength
What has it to do with Gauss then? Well he made some obsevations regarding flux of enclosed surfaces (also known as Gaussian surfaces). For an charge enclosed in a space, no matter how you move the space around, warp it, stretch it, or whatever, as long as the charge is still inside, the flux remains constant. Here is an analogy. You get a box and put a positive charge inside. If you increase the dimensions of the box by a factor of 2, then at the stretched surface of the Gaussian space, the stregth of the field is decreased. However, the area of which the weakened field is going through increases by the same factor. Gauss came out with three conclusions:
Whether there is a net outward or inward electric flux through a closed surface depends on the sign of the enclosed charge
Charges outside the surface do not giv a net electric flux through the surface
The net electric flux is directly proportional to the net amount of charge enclosed within the surface but is otherwise independent of the size of the closed surface
Simplified, Gauss' Law is an alternative way to express the relationship between electric charge and electric field (the other way is Coulomb's Law). It states:
The total electric flux through any closed surface (a surface enclosing a definite volume) is proportional to the total net electric charge inside the surface.
The equation is:
Flux = (Intergral) E dA = Qenclosed / e , where Q is the algebraic sum of the charge inside the enclosed space, e is 8.854 X 10^-12
Hence electric flux passing through a closed surface is really just dependent on charge.