What is the concept of Gauss' physical law?

[galipop]

Can someone put into plain english the following points:

1. What is the concept of Gauss' physical law.

2. Why is the rotation of an electric field zero.

Cheers

 

[chroot]

1. Gauss' law simply says that the flux of the electric field through a surface is proportional to charge in the volume enclosed by that surface.

2. The curl (rotation) of the electric field around a loop is zero unless there is some magnetic flux through the loop. This is Faraday's law. You can also think of it this way: you don't have to use vectors to describe a static electric field. You can instead just consider the electrical potential at each point in space -- a scalar field. Any vector field that can be described this way must be curl-free via a simple theorem from vector calculus. The magnetic field, on the other hand, is never curl-free, and can never be described with "magnetic potentials."

- Warren

 

[Gza]

1. What is the concept of Gauss' physical law.

Thinking about it in terms of the water faucet and sinks analogy has always helped me visualize what's happening. The electric field (the water) only flows out of faucets (concentrations of positive charge); while the water flows into sinks (concentrations of negative charge). The mathematical statement of Gauss's Law which Chroot detailed for you,

Gauss' law simply says that the flux of the electric field through a surface is proportional to charge in the volume enclosed by that surface.

is relating the sink or faucet, to what happens on a surface outside the sink or faucet. Let's make this abstract "surface" outside the sink or faucet a balloon with holes in it. Now stick a balloon with holes in it over a faucet that is turned on, and we all know what will happen. Water will "flux" (latin for flow) out of the balloon. Using some common sense, it should be obvious that you will be able to determine the rate water comes out of the tap from knowing the rate water comes out of the holes in the balloon. Remember from the analogy that the rate water comes out of the faucet is the representation of the amount of positive charge. The same thinking works for "sinks" as well (water flows through the balloon into the sink.) That is the relation between electric flux and charge (aka Gauss's Law.)