Electric Potential Energy of Point Charge Systems

[flyonthewall]

Homework Statement

Two point charges of opposite sign, - Qo and +Qo, are fixed in place a distance D apart from each other, as shown in the figure, while a third point charge with positive charge + Q3 is initially located a long distance away on the line joining
- Qo and + Qo. An external force moves point charge +Q3 along the line until it is in its final position a distance D to the right of +Qo. Which of the following claims is true during the time that point charge + Q 3 is being moved from its initial position to its final position?

A) The work done by point charge +Qo on point charge +Q3 is positive.
B) The work done by the external force on point charge +Q3 is zero.
C) The electric potential energy of the (-Qo) (+Q3) system becomes higher.
D) The electric potential energy of the (-Qo)(+Q3) system becomes lower.

Relevant Equations

Ue = (kq1q2) / r

Here is my line of thinking:
I know A and B aren't correct since the work done would be negative since the electric force and displacement are in opposite directions. When calculating the electric potential energies to consider options C and D, I thought the initial electric potential energy of the system was -(kQ^2)/D and the final electric potential energy was the sum of the three pairs of electric potential energy so it would be -(kQ^2)/d + (kQ^2)/d - (kQ^2)/2D which simplifies to -(kQ^2) / 2D. Since the final electric potential energy would be a smaller negative, I chose option C, that the electric potential of the system would increase (which also seemed to make sense to me intuitively since the two positive charges are brought closer together which they don't "like" so there potential energy would increase). The correct answer is D though and I can't quite understand what I'm messing up on because the problem itself doesn't seem that challenging. Thank you in advance!

 

[TSny]

Hello and welcome to PF!

Note that part (C) is referring to the potential energy of the system consisting of only the two charges (-Qo) and (+Q3). It is not referring to the potential energy of the system of all three charges.

 

[haruspex]

as shown in the figure,

The written description seems reasonably clear, but the diagram might be useful.

while a third point charge with positive charge + Q3 is initially located a long distance away on the line joining - Qo and + Qo. An external force moves point charge +Q3 along the line until it is in its final position a distance D to the right of +Qo.

And so presumably 2D to the right of -Qo.

Which of the following claims is true during the time that point charge + Q 3 is being moved from its initial position to its final position?

A) The work done by point charge +Qo on point charge +Q3 is positive.
B) The work done by the external force on point charge +Q3 is zero.
C) The electric potential energy of the (-Qo) (+Q3) system becomes higher.
D) The electric potential energy of the (-Qo)(+Q3) system becomes lower.
Relevant Equations: Ue = (kq1q2) / r

Here is my line of thinking:
I know A and B aren't correct since the work done would be negative since the electric force and displacement are in opposite directions.

For both A and B? B is not necessarily an electric force.

When calculating the electric potential energies to consider options C and D, I thought the initial electric potential energy of the system was -(kQ^2)/D and the final electric potential energy was the sum of the three pairs of electric potential energy so it would be -(kQ^2)/d + (kQ^2)/d - (kQ^2)/2D which simplifies to -(kQ^2) / 2D.

You seem to be assuming all charges have magnitude Q. I read it that the third charge can have a different magnitude. But your main error is misreading the question. C and D refer to only -Qo and +Q3, not the three charge system.