Finding an electric field vector

[Timebomb3750]

Finding an electric field vector...

Homework Statement

A cube of side s has a point charge at each corner. Explain how you would find the electric field vector at a point a distance A from the center of any face along a normal to the face through the center of the face. If all the charges were identical, discuss how you would take advantage of the symmetry of the problem to solve it.

Homework Equations

E=F/q=kq/r^(2)

The Attempt at a Solution

What's throwing me off is the wording of this problem. It doesn't tell me the kind of charge these eight point charges have.(Does it even matter in this case?)Am I supposed to draw out multiple vectors representing how they act upon the test charge, or am I just looking for one vector? I'm really lost.

So, I drew a 3D cube with black dots at each corner. Then, I drew a test charge above the top face of the cube, lined up with the face's center too.

After that, I'm really confused as to how to move on. Any sort of help that would get me in the right direction would be greatly appreciated.

 

[Tomer]

I think they meant an identical charge in each corner, otherwise there is no symmetry.

You're not expected to do any calculations but to explain how you'd use the symmetry simply.

Well, let's think of a point above the center of the bottom face of the cube (not nescessarily in the middle). let's think of the 4 identical charges located at each of this points' directions, that are placed on the closest face - the bottom one. Notice they all have the same distance to the point. Think of which components might cancel each other and which add to each other.
Then do the same process with the charges in the face further away, the upper one.

Hint: In order to calculate the field , you need to do merely two calculations.

 

[Timebomb3750]

Okay, so are we saying all the points charges and test charge have the same sign?

 

[Tomer]

There is no test charge, you need to find the field.
And yeah, I would assume all the charges have the same sign and size, otherwise, like I said, there is no symmetry.