What is the electrical potential energy of a triangular charge configuration?

[stonecoldgen]

Homework Statement

Derive and simplify an expression for the electrical potential energy of the charge configuration. It's an equilateral triangle with charges +q, -q and +q.

Homework Equations

E_p=Kq²/r

The Attempt at a Solution

I know how to do this with squares (it's basically exploding the symmetry). For example in a square there are charges #s1,2,3 and 4. I do the equation with 1 respect to 2,3 and 4. Then with 2 respect to 3 and 4. Finally, 3 respect to 4. I see which terms cancel out, then it's all algebra.

I did this in this triangle, getting -kq²/r as the final expression, which for some reason doesn't convince me (perhaps because it's too simple? lol).

I don't know if in the square you are ''unconsciently'' multiplying by the sin90, therefore I should multiply by sin60 here. If so, is it just multiplying sin60 by each term?

I do know that electrical potential energy is a vector quantity and not a scalar quantity like voltage, right?


Thanks.

 

[stonecoldgen]

so would the expression be -kq2/r *sin60?

 

[ehild]

The potential energy is a scalar quantity. Show your work in detail, please.

ehild

 

[ehild]

Homework Statement

Derive and simplify an expression for the electrical potential energy of the charge configuration. It's an equilateral triangle with charges +q, -q and +q.


I did this in this triangle, getting -kq²/r as the final expression, which for some reason doesn't convince me (perhaps because it's too simple? lol).

It is correct if you mean the side of the triangle by "r".

ehild