Coulumbs Force question

1. Feb 14, 2009

Minihoudini

1. The problem statement, all variables and given/known data
A charged particle A exerts a force of 2.62microNewtons to the right on a charged particle B when the particles are 13.7 mm apart. Particle B moves straight away from A to make the distance between them 17.7mm. What vector force does it then exert on A?

2. Relevant equations
I know its easy, very, but for the love of god I can't figure this out.

3. The attempt at a solution
I know that they are both positive particles, so im assuming both are +1.60x10^-19c.
Also I believe we use F= (K q1 q2/r^2). Ive tried inserting different things in to the formula but none of it gives me the answer im looking for which is 1.57micronewtons

2. Feb 14, 2009

Delphi51

Yes, use use F= (K q1 q2/r^2).
No need to assume a charge. Put in the force and distance for the first position, and calculate the value of K q1 q2. This will carry over to the new distance.
Knowing that and the new distance, you can calculate the new force.

3. Feb 14, 2009

Redbelly98

Staff Emeritus
I wouldn't make that assumption ... I see nothing in the problem statement that would allow this.
Yes, that is the equation for this problem.
Here's a question: what must the product (q1 q2) be equal to, so that the force is 2.62 μN when r=13.7mm?

EDIT: Delphi gave even better advice. What is (K q1 q2) when the force is 2.62 μN and r=13.7mm?

4. Feb 14, 2009

Minihoudini

alright, well K=8.99 x 10^9

so the formula should look like this now. r x [square root of F/k] = q1 q2
inputting everything it looks like this
(0.0137m) times square root of (2.62 x 10^-7 N )/(8.99 x 10^9) = 7.39 x 10^-11
equaling that to q1 q2. this is one part im stuck on, I'll be able to get the rest but I don't know what to do with both unknowns.

5. Feb 14, 2009

Delphi51

If q1 q2 is bothering you, make this change in the formula: C = q1 q2.
Then you will have only the one unknown!
The important thing is that C is a constant in this problem.
Even better: let C = kq1 q2. Saves wear on the calculator!

6. Feb 14, 2009

Redbelly98

Staff Emeritus
Uh, wait, that should be
r^2 x F/k = q1 q2​

7. Feb 14, 2009

Minihoudini

there we go, again thanks everyone. that was what was screwing up my answer, I saw another equation like the one I put up for a similar question so I thought I could apply it here. I see now that I can't. again thanks.