Can a Gaussian Surface Confirm Zero Electric Field Between Two Charges?

[Gamezwn]

1. We have two positive point charges (+q) at a distance from each other
2. Goal is to Find electric field at point A halfway between the point charges
3.By logic and summation of fields we should get ZERO
4. But how would I use a gaussian surface (sphere i assume ) to prove at point A E=0 n/c
5. Personally, I'm attempting a spherical surface around one of the points with radius of :(half distance between charges)
https://drive.google.com/file/d/0B0TaDjU5g_GAVm9hUjliTHhSM1BSbXoyRVp3dXd6MDR4TzE4/view?usp=sharing

 

[Avatrin]

I think you are making it harder than it really is. There is a formula for the electric field created by a point charge. Use that together with symmetry arguments since an electric field is a vector field.

 

[Gamezwn]

I think you are making it harder than it really is. There is a formula for the electric field created by a point charge. Use that together with symmetry arguments since an electric field is a vector field.

Yeah I know It is E= kQ/r^2 ...i just want to understand the effect of external charges on a gaussian surface...like in my book they said that external charges don't affect the gaussian surface because all the external field lines come in and come out...no idea what that means tbh

 

[Avatrin]

Okay, I understand. The idea is that, for a gaussian surface, the same amount of field lines will be pointing into the surface as will be pointing out.

Lets take a very simple example; Think of a perfect sphere in an electric field that is constant everywhere. You are looking directly at the sphere, and let's say the field vectors are pointing towards your right. Using symmetry, it should be easy to see that the net electric flux through the sphere is zero (as much is "coming in" as is "leaving"). Gauss's law says that is true in general; If the electric field is generated by something outside the gaussian surface, the electric flux due to that thing through the surface will be zero.

So, the external charges do affect individual portions of the surface. However, they do not affect the flux through the entire surface. That will remain zero.