How Do You Calculate the Force Between Charges in Electrostatics?

[xwhyy]

Hi,
I have a problem with this basic question since it's been a while with my last time with physics :)

Homework Statement

I'm given 2 charges q1=-e and q2=e, attracting each other with force F12 within a distance r12What would be the force F13 between q1 and q3 = 2e on the distance r13 = 2*r12

Homework Equations

basically, the whole thing looks like that:
(q1) r12 (q2) r12 (q3)
I guess i need to calculate F13 in terms of F12

The Attempt at a Solution

Since

F12 = [K*(-e)*e]/[(r12)^2]
and
F13 = [K*(-e)*e*2]/[(r12)^2*2^2]

I think the proper answer should be
F13 = 2/4 F12

But my feeling is that it looks too simple. Did I forgot about something?
If something is not clear in my question, please let me know.
Thank you in advance!

 

[Angry Citizen]

Looks good to me, but I'd simplify the fraction.

 

[kuruman]

You are correct and it is that simple. I assume that F13 is the force exerted on charge 3 by charge 1 only and not the net force on charge 3. If that's the case, basically you are doubling the distance and doubling the charge at the same time. Doubling the distance reduces the the force by a factor of 4; doubling the charge increases the force by a factor of 2. Therefore, the overall effect is to multiply the force by a factor of 2/4 as you have shown.

 

[xwhyy]

I assume that F13 is the force exerted on charge 3 by charge 1 only and not the net force on charge 3.

yes, that's the case.
Thank you guys! :)