Please Help! Electrical charge questions.
Assume the corners of a cube of side a are occupied each by a positive charge q.
a) What is the net force on each of the eight charges?
b) how much electrical energy was needed to bring all the charges to this configeration?
c) If one of the charges was free to move, it will accelerate away from the rest of the charges. What will be its final speed when it is very far away?

Question

Please Help!  Electrical charge questions.
Assume the corners of a cube of side a are occupied each by a positive charge q.
a) What is the net force on each of the eight charges?
b) how much electrical energy was needed to bring all the charges to this configeration?
c) If one of the charges was free to move, it will accelerate away from the rest of the charges. What will be its final speed when it is very far away?

anonymous · Answer

Tricky one : )

First, I recommend that you draw a diagram of the cube.
Then pick one charge and study it's relation to the other 7 charges.
(Clearly each charge will experience the same total force, by symmetry, so you only need to do the calculation for one.)

You should be able to see that one charge is furthest away from your chosen charge, by a distance equal to the body diagonal.
Then three other charges are equally close, with a separation from the main charge of just a, the cube side.
And finally three charges are one face diagonal away from the main charge.

I think from the symmetry again, that the resultant force will be directed along a body diagonal of the cube, so you only need to work out the components of the forces in that direction.
Figuring out the relevant angles will take a bit more work : )

anonymous · Answer

I mainly need help with b and c, they have me stumped as to where to start.

anonymous · Answer

So you have an answer for part a ? I'd be interested to see if you agree with my result.

anonymous · Answer

(29/6)(q^2/a^2)

anonymous · Answer

Thats not what I have : (

anonymous · Answer

Part b is easier than a, you just have to add up the mutual potential energy of the various pair interactions in the cube, without having to worry about vector directions and components.

anonymous · Answer

I see where you have got the 29/6 from - you have completely ignored the fact that the forces of interaction are vectors.
Only one of the forces on a charge acts fully along the body diagonal, all the others only have a component of the full force along the body diagonal, because they actually point in different directions. That's why i mentioned having to find some angles.

anonymous · Answer

Yeah, i did go back and change it, and got 3.something.

anonymous · Answer

Yes, I have 3.29

anonymous · Answer

That is what I ended up getting too