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

basicly, 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! :)

 

[rwisz]

Hi there,

Thank you for your question. It seems like you are on the right track with your solution. The only thing I would suggest is to use the correct distance in your calculation for F13. Since the distance between q1 and q3 is 2 times the distance between q1 and q2, the correct equation would be:

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

= [K*(-2e^2)]/[4*(r12)^2]

= (-1/2)F12

So, the force between q1 and q3 is half the force between q1 and q2. This makes sense because q3 is twice as far away from q1 compared to q2, so the force would be weaker.

I hope this helps. Keep up the good work with your physics studies!