>Hi my name is Hugo Ayala I'm 16.
>I was wondering about if you could give me an example of the gauss law?
>
**NOTE: I PASSED THIS QUESTION TO MY LABORATORY ASSISTANT**
Heya Hugo!
I have been asked to assist Nez in answering your question. I'll try my best to help you as well as she has to her readers.
Gauss' Law basically states that given a closed surface, say a ball, and some charge enclosed within it, that the total electric flux through the surface of the ball will be equal to the amount of charge contained inside of it divided by a 'e' ('e's is just a constant number representing the nature of space. 8.85*10^-12 F/m to be exact). Since I do not know your current background in physics, I'll assume nothing and explain the terms.
Vocab:
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Electric flux is product of the field strength perpendicular to a surface and the area of the surface. So if you were given an area of 4 m^2 and an electric field of 10 N/C passing through all points of the surface, you can then say that the flux through the area is 4*10 or 40 N*m^2/C.
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Although that previous example used only simple math, the situation that Gauss proposed is very different. He pictured a closed surface of any shape (like a cube, football, cylinder, blob) and a charge somewhere within it.
Since the field created by a charge changes by the distance away from the charge, you're stuck with a surface with a field that has different strengths across the surface. You can no longer just multiply the area and the field strength since the field strength changes depending on which part of the surface you're looking at and the area is not flat and not easy to find. To find the flux through the surface in this case would require complicated triple integrals and a whole lot of time. However, Gauss realized that you don't have to do that. For ANY closed shape and a charge ANYWHERE inside the shape, the total flux through the surface will equal the charge divided by 'e'.
With that, I'll give you a quick example of how to apply Gauss' Law.
Example 1:
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Q:Let's say you have a beanbag chair and within the bag, it contains a point charge of 10 coulumbs. What is the total flux through the surface of the bag?
A:This is a straightforward question. According to Gauss' Law, the total flux through the bag will be 10/'e'. We didn't even have to tell you the total area of the bag, where the charge was inside the bag, or what the shape of the bag was. It all doesn't matter according the Gauss.
It may seem as if this law is only good for textbook problems, but it has some very important applications on more real situations. This law helped clarify Maxwell's Displacement Current which claims that there will be a new type of current flowing through a capacitor. (a capacitor is a physical break in a circuit with plates on either side of the break. With a break in a circuit, one might think that there can not be any current flowing from one side to the other). Both of these can be easily proven using Gauss' Law but for me to tell you how without any pictures would be too hard.
I hope that I've been helpful and if you have any questions or want me to show a more complicated use of Gauss' Law, I'll be more than happy to help. Ciao!
-Dave-
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