# Electrostatic Potential Energy

1. ### quebecois22

23
1. The problem statement, all variables and given/known data

How much work is required to exchange the positions of q2 and q3?

q2 q3

q1

q1 and q2 are separated by a distance of 4.00 cm and q2 and q3 are separated by a distance of 2.00cm

The charge on q1 is 5.00nC, q2 is -5.00nC and q3 is 10.0nC

2. Relevant equations

U=(K(q2)(q3))/(r23) (#1)
U=qV (#2)

3. The attempt at a solution

Since the energy required to hold these charges at their positions is equation 1, my guess to simply found the energy holding the charges and that would be the energy required to move them... Guess I'm wrong...

Any help is appreciated...

2. ### CanIExplore

100
Can you help us picture the charge configuration? I'm guessing they're all lying on the same line but can you clarify this for me. How are they oriented with respect to eachother?

3. ### nickjer

675
Work is just the change in potential energy. So just find the difference in the final and initial total potential energies.

So write down the initial total potential energy and the final total potential energy.

4. ### quebecois22

23
@CanIExplore:

They're positioned just like in my first post: q2 directly over q1 and q3 directly across q2.

@nickjer: Aren't both potential energies equal? I mean at the end the only difference is that they switched places...

5. ### Saraphim

47
If the concept of moving the charges around in an existing field is confusing you, try moving them to infinity and then back into their new positions and consider the work you're doing.

6. ### nickjer

675
quebecois22 the distance between charges q1 and q2 will change, as well as q1 and q3. So the total potential energy will change.

7. ### quebecois22

23
I am completely lost...

I don't know how to take q1 into account... how does it behave on the two charges?

8. ### nickjer

675
The total potential energy of 3 particles is just $U_{12} + U_{23} + U_{13}$. You can probably find that in your book.

9. ### quebecois22

23
Ah so the final and initial potential energies will vary according to the distances between them...
So delta U is the energy required to shift q2 & q3 places?

10. ### nickjer

675
You want to find the different in total potential energy when you switch q2 and q3. It shouldn't be 0, unless q2=q3 or the distance between q1 and q2 is the same as between q1 and q3.

11. ### quebecois22

23
Yeah it's not so the difference won't yield zero...
So this difference in potential energies is the energy required to shift those two charges?

12. ### nickjer

675
Yes, since this is a conservative force.