# Gauss's Law explanation

1. Feb 12, 2005

### thisisfudd

Hi all,

Can someone give me a better explanation of precisely what Gauss's law and the term "electric flux" mean (better, that is, than Giancoli 6th edition, where they never really define it :grumpy: ). I just want to get a handle on the concept in general.

Thanks ~

2. Feb 12, 2005

### dextercioby

A highly intuitive and rather mathematically unrigurous approach would be defining the flux of a vector field (i hopeu know what a vector field is) through a closed surface S as the # of field lines which cross the surface S which encloses some volume.It's intuitive as it allows the interpretation of Gauss' law for magnetostatics as the fact that the vector field B has no sources,since the # of field lines must be zero...
I would still reccomend you to get a grip on Griffiths' book ("Introduction to electrodynamics",irrelevant which edition) and read from there...

Daniel.

3. Feb 12, 2005

### FulhamFan3

flux is vectors per unit area. In this case it would be electric field per unit area.

if you take an area element dA near a charge it has a high flux because of more field lines. Further away the flux would be lower because there are less field lines.

Gauss's law pretty much says that when you have an enclosed area the flux is directly proportional to the charge enclosed no matter what shape you have your area.

4. Feb 12, 2005

### dextercioby

Flux is vector TIMES AREA.So it's the other way around:vector field is the flux per unit area...

Daniel.

5. Feb 12, 2005

### mathwonk

consider the case of a plane, and an incompressible fluid flowing across the plane in various directions. then the law says the rather obvious fact that if we consider for any period of time, the total flow across the boundary of a circle say, then the samke amount of fluid flows outward across the circle as flows inward across it.

More generally, the differnce between the outward flow, and the inward flow, is equal to the amount of lquid generated from sources inside the circle.

This measured mathematically by arrows giving the magnitude and velocity of the flow at each point, called vector fields. There is an associated concept now called divergence, to measure the total fluid flowing out. Hence the theorem in mathematics is also called the divergence theorem.

This result appears in the introductory mathematical chapter of Maxwell's famous book on electricity and magnetism, where because he uses quaternions instead of vectors, the concept measure flow inward, and hence is called there "convergence".