Electric Forcs and Work (Algebra based physics)

[Seikon85]

Charges q1=+7.15 x 10-05 C and q2=-7.80 x 10-04 C are placed at rest 71.5 cm apart. How much work must be done by an outside agent to move these charges slowly and steadily until they are 31.0 cm apart?

Ok so I tried a few things on my own, and got stuck. So I referred to a previous post from this morning for guidance:

http://answerboard.cramster.com/physics-topic-5-199660-0.aspx

however, I am still getting the wrong answer.


I am using F = kq/r initially. The r value i am using was obtained by figuring out the distance one charge moved. (.715-.31)/2. Then subtracting that distance from .715. So my r = .513m here.

I get F = 968J.

W = F*d = 968J * (.31m) = 300J.


Am I missing something obvious. Any insight?

Thanks.

 

[Shooting Star]

Have you learned about potential energy between two charges?

 

[Moetasim]

First of all, great job on attempting to solve the problem on your own and seeking guidance when you got stuck. It's always important to utilize all available resources in order to fully understand a concept.
Now, let's take a look at the problem. You are correct in using the formula F = kq/r initially. However, the distance between the charges is not simply the difference between their initial and final positions. In this case, the distance between the charges changes as they are moved closer together. Therefore, you need to use the formula for electric potential energy, which is U = kq1q2/r. This takes into account the changing distance between the charges.
Now, to find the work done by an outside agent, we can use the formula W = Uf - Ui, where Uf is the final potential energy and Ui is the initial potential energy.
Using this formula, we get:
W = (kq1q2)/rf - (kq1q2)/ri
= (9x10^9)(+7.15x10^-5)(-7.80x10^-4)/(.31) - (9x10^9)(+7.15x10^-5)(-7.80x10^-4)/(.715)
= -1.98 J
Therefore, the work done by an outside agent to move the charges slowly and steadily until they are 31.0 cm apart is -1.98 J.
I hope this helps clarify the problem for you. Keep up the good work!