# Gauss's Law

Discussion in 'MCAT Study Question Q&A' started by twoinone, May 29, 2008.

1. ### twoinone

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So I was going through the topic list by AAMC and much to my surprise discovered that Gauss's law is tested on the exam. Can someone please explain what it is and if possible work out a sample problem. We did not cover this in our physics class and none of the review books seem to mention it. Thanks!

3. ### physics junkie

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I'm pretty sure Gauss' Law is not tested on the MCAT because it requires integral calculus. Here is my best shot at an explanation though.

Gauss realized that if you have a charged particle and draw a surface around it then the flux of charge through the surface would tell you about how much charge is inside that surface. Flux can be thought of as counting the number of electric field lines coming out of the charge. Sounds like a mouthful but it's really not.

The equation looks something like this:

E*Area=Q/e

E is electric field. A is the area of the surface that you have drawn around the charge. Q is the total amount of charge inside. e is the permittivity constant.

So let's say we have a charge and draw a sphere around it.

so E(4*pi*r^2) = Q/e

Rearrange this and you get:

E = q/(4*pi*e*r^2)

This tells us the field produced by a point charge is q/4*pi*e*r^2...just like you learned in class.

This is commonly taught as Coulomb's law but it is really just a special case of Gauss' law. Gauss' law is actually more general.

With Gauss' law you can calculate the electric field produced by a point charge or a group of charges(such as a line of charges) by choosing the appropriate surface to draw around the charges. So if you had a line of charge you would want to draw a cylinder around it. If you had a sheet of charge you would want to draw a box around it. There are plenty of examples of this online. Unfortunately Gauss' law is a bit much to grasp unless you do a few problems related to it. I bet they just meant you need to know Coulomb's law as a specific form of Gauss' law.

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