Coulomb's Law

1. Aug 27, 2009

exitwound

1. The problem statement, all variables and given/known data

2. Relevant equations

F=kQq/d^2

3. The attempt at a solution

I've tried working on this for two days and can't figure it out.

In (a), the cumulative force on A is the sum of the force from B and the force from C. or:

$$F=\frac{k Q_a Q_b}{d^2} + \frac{k Q_a Q_c}{d^2}$$

In (b), the same applies.

however, I can't figure out what to do with these equations in order to isolate Qb or Qc. If I use a negative d (-d) as a distance from A-->B in (b), then I get two equations that are identical, but shouldn't be. If I move the origin, it doesn't seem to matter either.

I don't know how to start this problem.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 27, 2009

Qc/Qb=1.328 (sorry)

Ok, so in the first scenario, both charges B and C exert forces to the left, on charge A, since all charges are positive. However, in figure b, charge b exerts a force to the right, while charge C exerts a force to the left, on charge a. Hence, in fig. a,
-2.03x10^-23==-kQAQB/r^2-kQAQC/r^2
while in fig b
-2.86x10^-24==-kQAQC/r^2+kQAQB/r^2

If you factor out k, QA, and r^2, keeping in mind that RB=RC (distance from a to b, and a to c are the same in both figures), and divide the two equations, you can get QC/QB which is 1.328

Hope this helps,

Last edited: Aug 27, 2009
3. Aug 27, 2009

Because of the direction of the force you know that Qc is bigger than Qb so write an equation like you did for part a but getting the directions right.Now divide one equation by the other and tidy it up.

4. Aug 27, 2009

You are correct, QC should be larger than Qb, but when I worked it out, I got QC/QB==1.328, I don't know why...

corrected, see above, I had a problem with the signs in my initial equation...

Last edited: Aug 27, 2009
5. Aug 27, 2009

exitwound

I'm still absolutely lost on this.

Faraday, I understand what you did taking into account the negative Force due to B in the second example. However, I don't know what to do with the equations at this point.

I end up with:

(a) F=(kQa/d^2)(Qb+Qc)

(b) F=(kQa/d^2)(Qc-Qb)

I don't understand where to go from here.

6. Aug 27, 2009

You can now divide the two equations above, so F1/F2==(QB+QC)/(QC-QB), hence, qc/qb is 1.328. (I had a problem with my signs in the initial solution.)

Last edited: Aug 27, 2009
7. Aug 27, 2009

exitwound

Why should I do that? I am not following the logic, I guess.

8. Aug 27, 2009

ideasrule

Both equations have "d", which you don't know but can eliminate by dividing the equations. After dividing, you have the ratio F1/F2, which you can calculate, as well as Qb and Qc. You'll have to rearrange to get an expression for the ratio Qb/Qc.

9. Aug 27, 2009

exitwound

Okay. 1.328 is right, and I did the simplification on paper here as well. Ends up looking like:

$$\frac{Q_c}{Q_b} = \frac {F_1+F_2}{F_1-F_2}$$

I don't know if I ever would have figured out to divide one by the other though.