Building up some intuition with Gauss's LAw

[H2Bro]

I'm trying to build up some intuition with Gauss's law, calculating the flux through surfaces given certain charge configurations etc.

For example, for any number of different charges enclosed in a box or sphere, if I move far away can I consider the object as a point source having the sum of the enclosed charges?

Likewise, if I'm moving through the interior of a sphere with a constant charge per unit volume, and I'm some x distance from the center, can I conceive of the flux at this point as being the same as it would be if i was on the surface of a smaller sphere with radius x? i.e.,, would the concentric outer layers of the sphere cancel each other out.

Anyone willing to share their favorite conceptualizations with this kind of stuff is much appreciated.

 

[BOYLANATOR]

The further you move away the better the approximation that they are a point source of charge will work, but this is not Gauss' Law. Gauss' Law says that the total electric flux through a closed surface is proportional to the total charge enclosed within that volume, regardless of whether the charges are clumped together or spread out. The law is most useful when applied to symmetrical charge distributions.

You can imagine you are on the surface of a smaller sphere yes. The gravity of Earth works the same way.

 

[jfizzix]

Gauss's law is a theorem about all inverse square forces, and fields.

Something else that goes as the inverse square is the intensity of light from a point light source.

Let's say you had a white-hot one kilogram chunk of iron. Gauss's law says that the integrated flux of photons through any closed surface that encompasses that chunk will be the same.

This is because, for a constant solid angle, the area of the surface cut out by the solid angle grows as the square of the distance to the source, and the intensity of the light decreases as the inverse square of the distance to the source, perfectly cancelling out the effect of the larger area.

Gauss's law as it is exists because we live in a world with three spatial dimensions. If we lived in four spatial dimensions, we might see a similar form of Gauss's law but with inverse cube force laws.