# Distance between point charges in equilibrium (simple)

1. Jan 5, 2013

### Mitocarta

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

Two fixed charges, +1.07 uC and -3.28 uC, are 61.8 cm apart. Where may a third charge be located so that no net force acts on it?

2. Relevant equations

Coulombs law

3. The attempt at a solution

q1 = 1.07 uC
q2 = -3.28 uC
q3 = q

q1 ----- q2 ----- q

q1 and q2 are separated by 0.618 m and q2 and q are separated by x

Since the charges are in equilibrium,

0 = k (1.07E-6)(q) / (0.618+x)^2 + k(1.07E-6)(q) / (x)^2

factoring out and eliminating k and q,

(1.07E-6)/(0.618+x)^2 + (3.28E-6)/(x)^2 = 0

Solving for x gives me an imaginary distance. I feel like this is a very simple problem but I can't spot my error. What am I doing incorrectly? Thank you for your time.

2. Jan 5, 2013

### TSny

Hello Mitocarta, welcome to PF!

You've placed q closer to the larger magnitude charge. Is that going to work?

3. Jan 5, 2013

### Mitocarta

Thank you for replying. When I switch the charges,

(3.28E-6)/(0.618+x)^2 + (1.07E-6)/(x)^2 = 0

I still get an imaginary answer.

Edit: Is there a way to input math in an easier to read format on this forum?

4. Jan 5, 2013

### TSny

The two forces act in opposite directions on q. The net force will be zero if the magnitudes of the forces are equal to each other.

5. Jan 5, 2013

### Mitocarta

Oh I was overlooking that! Thank you so much, got the correct answer.