Calculating Electric Fields on the Surface of a Charged Cube

[Violagirl]

Homework Statement

A cube of side a has a cube of side a/2 centered within it. The inner cube has a total charge Q that is uniformly distributed over its surface. A) For the surface of the outer cube, find:

∫_s E * dA

B) Is this sufficient information to find the electric fields at points on the surface of the outer cube? Explain.

Homework Equations

E = F/Q

(?)

Not sure with a cube otherwise.

The Attempt at a Solution

Not sure how to start it. Drew out diagram of situation. See attached document.

 

[Enigman]

Use Gauss's law! This one is tailor made for it!
http://en.wikipedia.org/wiki/Gauss's_law

 

[Violagirl]

Thanks for your response! Ok so looking at it again:

∫E * dA

Since E is a constant, it can be pulled out:

E ∫dA = (a) (a/2) = a²/2

If I'm doing this right, then I just need to find the integral of a²/2, right? So I would then get:

E * a²x/2

As for the second question, if the above is correct, I would say then you have enough information to find the electric field at points on other areas of the surface of the cube too then.

 

[Enigman]

Use the Gauss's law! It directly gives the required integral without any integration!
$\int E.dA=Q/ \epsilon$

I would say then you have enough information to find the electric field at points on other areas of the surface of the cube too then.

Note:-If all you have got is the electric flux through the surface you cannot find the electric field at all the points.
To do this you will have to integrate due to the lack of symmetry of the surface.

 

[Violagirl]

Ok, that makes more sense since the outer surface is not symmetric as you said. You have to integrate at along different points to find each electric field. Thanks for your help with this problem!