Calculating Vector Force Between Charged Particles

[Minihoudini]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

I know that they are both positive particles, so I am assuming both are +1.60x10^-19c.
Also I believe we use F= (K q1 q2/r^2). I've tried inserting different things into the formula but none of it gives me the answer I am looking for which is 1.57microNewtons

 

[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.

 

[Redbelly98]

... I am assuming both are +1.60x10^-19c.

I wouldn't make that assumption ... I see nothing in the problem statement that would allow this.

Also I believe we use F= (K q1 q2/r^2).

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?

 

[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 I am stuck on, I'll be able to get the rest but I don't know what to do with both unknowns.

 

[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!

 

[Redbelly98]

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

Uh, wait, that should be

r^2 x F/k = q1 q2​

 

[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.