Electrostatics: Two charged balls with attraction

[thebe39]

Hi, I have an exam coming up soon. But I thought I would clear my doubts ahead of time.

1. A fixed conducting ball has charge q1= 3X10^-6C. An identical ball with charge q2 is held at a distance x away from q1. The two balls attract each other with a force of 13.5N. The balls are then connected by a conducting wire. After the wire is removed, the balls repel each other with a force of 0.9N.

a) what was the charge of q2 of the second ball?
b) What is the separation x between the balls?

2. At what position between particles 1 and 2 will particle 3 experience no net force?
q1= 2x10-9 q2=3x10-9 q3= -2x10-9. The distance between particle 1 and 2 is 0.04.


Thanks

 

[LowlyPion]

Welcome to PF.

Where did you get stuck on the first problem?

 

[thebe39]

well I know that in the beginning the q2 should have a - charge since it is attracted to the q1 and then after the wire it should become -. I'm not really sure how to isolate for
q2 from the equation.

 

[LowlyPion]

well I know that in the beginning the q2 should have a - charge since it is attracted to the q1 and then after the wire it should become -. I'm not really sure how to isolate for
q2 from the equation.

If the charge from both is the same it will be repulsive.

That means in the first you a force made up of the given charge times the unknown. The second force is derived from the average of the 2 charges squared.

F = kq1*q2/r²

After

F = k(q1 + q2)²/(4*r²)

Where (q1 + q2) / 2 is the average that gets squared.

 

[thebe39]

how did you get F=Kq(q1+q2)/(4*r^2) ? where does the extra q come from?

 

[thebe39]

btw the answer to this problem is apparently
a) -5x10-6 C
b) 0.10m

But I really just want to understand what I'm doing with the steps.

 

[LowlyPion]

how did you get F=Kq(q1+q2)/(4*r^2) ? where does the extra q come from?

Sorry, there is no extra q. I noticed the typo and edited it apparently after you picked up the post.
Note that the correct formula is

F = k(q1 + q2)²/(4*r²)

 

[thebe39]

So I'm going to let r^2 equal each other

kq1q2/F = k(q1 +q2)^2/F(4)

So I isolate for q2 right?

or do I say that kq1q2/F = k(q1 +q2 divide by 2)^2/F(4)

 

[ideasrule]

So I'm going to let r^2 equal each other

kq1q2/F = k(q1 +q2)^2/F(4)

So I isolate for q2 right?

or do I say that kq1q2/F = k(q1 +q2 divide by 2)^2/F(4)

The factor of 4 came from q=q1+q2 divide 2, so your first equation is correct, but not your second. Note that the two "F"'s are different: in kq1q2/F, F=-13.5 N, but in k(q1+q2)^2/4F, F=0.9 N.

Otherwise, you're on the right track. Cancel out the k, expand the right side, and you'll get a quadratic equation. It should be easy from there. Remember that q1, F, and the other F are all given.