Change in energy between system of point charges

[z0k]

Homework Statement

The energy stored by any pair of positive charges is inversely proportional to the distance between them, and directly proportional to their charges. Three identical point charges start at the vertices of an equilateral triangle, and this configuration stores 15 Joules of energy. How much more energy, in Joules, would be stored if one of these charges was moved to the midpoint of the opposite side?

Homework Equations

The Attempt at a Solution

We determine our formula to be $$U = \frac{kq^2}{r}.$$ Then from the given data, for three point charges we have $$U = 3 \frac{kq^2}{r} = 15J.$$ To compute the new position:

$$
U' = k(\frac{q^2}{r/2} + \frac{q^2}{r/2} + \frac{q^2}{r}) \\
U' = 5 \frac{kq^2}{r} \\
U' = 25J \\

$$

So the difference is $$U' - U = 10J.$$

I'm not quite sure if I am going about this the right way.

 

[BruceW]

I think you have gone about it almost the right way. I think the problem is where you did 1/2 + 1/2 + 1 = 5 This is not right.

PS welcome to physicsforums! :)

EDIT: I am tired and didn't read your post through properly. Sorry. Your maths was 2 + 2 + 1 = 5 which is of course correct. I think your answer is all OK, why do you think it is wrong?

 

[z0k]

Sorry, I think my typesetting make the fractions look confusing. I'm still learning to use Tex properly.
I just wanted to make sure that my set up was correct.
Thank you for your help and for the welcome!

 

[BruceW]

yep, no worries :)

 

[Nickie]

I am assuming that the charges are positive, since it doesn't specify in the statement. If they were negative, the energy would decrease as they move closer together. Additionally, I am not sure if the given 15 Joules is the total energy or the energy per charge. If it is the total energy, then each charge would have 5 Joules of energy. In that case, the solution would be $$U' - U = 5J.$$ Overall, it is important to clarify any ambiguities in the given data to ensure an accurate and precise solution.