WHAT IS GAUSS'S LAW?

[elevated]

I'm a senior in high school, and I have a physics research paper due on Thursday. The problem is, I don't know what Gauss's Law is.

So I googled it.
In physics, Gauss's law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface.

I still don't know what it is.

Can someone explain in laymen's terms please?

Thanks
Ed

 

[Toastedlightly]

cross posting isn't allowed.

 

[CycloWizard]

The first hit on Google does a pretty good explanation...

The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.

The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field. Gauss's Law is a general law applying to any closed surface. It is an important tool since it permits the assessment of the amount of enclosed charge by mapping the field on a surface outside the charge distribution. For geometries of sufficient symmetry, it simplifies the calculation of the electric field.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html

Of course, I'm guessing your problem is understanding what flux is exactly, in which case this doesn't mean a whole lot. Flux is nothing but the rate at which something passes through a surface. More technically, flux is the amount of something passing through a unit area in one unit of time.

So, specifically, Gauss' law tells you how much electrical energy is leaving an object by considering the amount of charge held within the object and the material's permittivity (just some measured property).

edit: If you're just having a hard time grasping the concept because it's based on electricity, there are several analagous 'laws' for describing other fluxes for momentum, heat, and mass transfer. Newton's law of viscosity, Fourier's law of heat conduction, and Fick's law of binary mass diffusion. Some of those might be easier to get a handle on.

 

[elevated]

i can understand that, but how does this apply to real-world situations? we're supposed to talk for 5 to 10 minutes about this topic, and my physics teacher suggested this one because he says there's a lot to talk about.

it doesn't seem like describing the amount of electrons flowing out of an object at a certain point takes a long time to describe.

thanks CycloWizard

 

[CycloWizard]

Well, that's also a very good question. I'm not an electrical engineer, so I probably can't help much with the applications - I just figured that out by Googling and comparing to the other three analogies that I pointed out above - I'm much more familiar with those.

This image appears on many pages when I look for 'Gauss Law Applications', so that would be a good place to start. Also,

Gauss's law can be used to demonstrate that there is no electric field inside a Quick Facts about: Faraday cage
Quick Summary not found for this subjectFaraday cage without electric charges. Gauss's law is the electrostatic equivalent of Quick Facts about: Amp?res law
Quick Summary not found for this subjectAmp?re's law, which deals with magnetism. Both equations were later integrated into Quick Facts about: Maxwells equations
Quick Summary not found for this subjectMaxwell's equations.

 

[dmens]

not much to talk about gauss' law with "real world scenarios"... you can look at it as a general relation between field strength per unit surface area when wrapped around a source.

maybe you can talk about energy distribution from the sun on the earth or something. thats energy flux of sorts.

 

[f95toli]

Originally posted by: elevated
i can understand that, but how does this apply to real-world situations? we're supposed to talk for 5 to 10 minutes about this topic, and my physics teacher suggested this one because he says there's a lot to talk about.

it doesn't seem like describing the amount of electrons flowing out of an object at a certain point takes a long time to describe.

thanks CycloWizard

The electrons are not flowing out of the object, Gauss law is all about the electrid FIELD, the charges do not need to move.

Real-world situations: Gauss law is used all the time when we solve electromagnetic problems. Faradays cage is perhaps the most "direct" (and easiest) example but there are many others.
Asking for applications of Gauss law is a bit like asking for applications of Pythagoras theorem; it is a very general "tool".

 

[jmcoreymv]

Gauss also has a law for a magnetic field which is that the closed integral of magnetic flux density field dotted with the differential surface, over the entire surface, is 0. Using these two laws and Amperes law and Faradays law, you could derive the wave equation to show how electric and magnetic fields propagate through free space. This is important in antenna design and signal transmission.

 

[bobsmith1492]

I think we used it mostly (in Physics class) to calculate stuff in torroidal coils and solenoids. I think.... .might have been a different law.

 

[f95toli]

Gauss's law in physics is exactly what was written in the first posts.
However, there is also a theorem in math known as the "divergence theorem" which is sometimes refered to as "Gauss's theorem"; it gives the relation between the volume integral of the divergence over V and the surface integral over the boundary of V.
This theorem is used all the time in electromagnetic field theory but it is NOT what is normaly meant by Gauss's law.