# Point Charges and Electric Potential Energy with Work Done

## Homework Statement

A point charge q1 is held stationary at the origin. A second charge q2 is placed at point a, and the electric potential energy of the pair of charges is + 5.4 x10^-8 J. When the second charge is moved to point b, the electric force on the charge does - 1.9x10^-8 J of work.

A) What is the electric potential energy of the pair of charges when the second charge is at point b?

U = kq1q2/r
W = -ΔU

## The Attempt at a Solution

I'm having a little difficulty understanding the concept of electric potential energy. This is what I think I understand.

A search on Google told me that U = 5.4x10^-8 J is the potential energy of the two charges, but the question seems to suggest to me that this value could be ΔU, how do I know it is not ΔU?

Also, would I be correct in saying that

W = -ΔU

therefore this would mean that:

-1.9x10^-8 J = -ΔU

As such the ΔU = 1.9x10^8 J

Additionally, because the work done is negative does this mean that q2 is being pushed away from q1 as there is work being done on q2 by q1?

Assuming my thought process has been somewhat accurate so far, would it then be reasonable to say that the electric potential energy has increased and that the electric potential energy of the charges when q2 is at point b would be:

5.4x10^-8J + 1.9x10^-8 J = 7.3x10^-8J

7.3x10^-8 J is the correct answer, but I want to know if my thought process is correct. I'm feeling a bit scatterbrained on this topic.

Any extra input would be appreciated.