Point Charges and Electric Potential Energy with Work Done

[Northbysouth]

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?

Homework Equations

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.

 

[anathema]

Thank you for your question and for sharing your thought process. It seems like you are on the right track in understanding electric potential energy. Let me clarify a few points for you.

Firstly, the value of 5.4x10^-8 J is the electric potential energy of the pair of charges at point a, not the change in electric potential energy (ΔU). Remember that electric potential energy is a scalar quantity, so it does not have a direction. Therefore, it is not the same as work, which is a vector quantity and can be positive or negative depending on the direction of the force.

Secondly, you are correct in saying that the work done on q2 is negative because it is being pushed away from q1. This means that the electric potential energy of the pair of charges has increased, as you correctly calculated.

Lastly, I would like to clarify that the electric potential energy of the pair of charges at point b is not equal to the sum of the electric potential energies at points a and b. The electric potential energy at point b is simply the value of ΔU, which you correctly calculated to be 1.9x10^-8 J.

I hope this helps to clarify your understanding of electric potential energy. Keep up the good work!