# Homework Help: Coulomb's Law in 1D

1. Jun 10, 2010

### Mitchtwitchita

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

Three charges lie along the x-axis. The positive charge q1 = 10.0 x 10^-6 C is at x = 1.00 m, and the negative charge q2 = -2.00 x 10^-6 C is at the origin. Where must a positive charge q3 be placed on the x-axis so that the resultant force on it is zero?

2. Relevant equations

F=kq1q2/r^2

3. The attempt at a solution

F23 = -F13

F23 = k(-2.00 x 10^-6 C)q3/-x^2
F13 = -k(10.0 x 10^-6 C)q3/(1.0 m - x)^2

[k(-2.00 x 10^-6 C)q3/-x^2] - [k(10.0 x 10^-6 C)q3/(1.0 - x)^2] = 0
(-2.00 x 10^-6 C)/-x^2 = (10.0 x 10^-6 C)/(1.0 -x)^2
2/x^2 = 10/(1- x)^2
2 - 4x + 2x^2 = 10x^2
-8x^2 - 4x +2 = 0

My quadratic equation doesn't work out so I'm assuming there was a terrible malfunction earlier on. Can somebody please help me out with this one?

2. Jun 10, 2010

### Staff: Mentor

Hint: First figure out what region the positive charge q3 must be in. ( x < 0; 0 < x < 1; x > 1) The field from each charge may have a different sign in different regions, which affects how you'd write the equation.

3. Jun 10, 2010

### Mitchtwitchita

It's going to be left of the origin (-x). How would this affect my initial signs?

4. Jun 10, 2010

### Staff: Mentor

Actually your equations are fine. (I just saw the double negative.) Why do you think your quadratic doesn't work out?

5. Jun 10, 2010

### Mitchtwitchita

Because I end up with 4 +/- sqr.[(-4_^2) - (4)(-8)(2)]/2 x 2
= (4 - 80)/4
= -19 which is much too high.

6. Jun 10, 2010

### Mitchtwitchita

Er, I meant low in the last reply.

7. Jun 10, 2010

### Staff: Mentor

I assume you are trying to use the quadratic formula. Try again; you're making an error somewhere.

Edit: You forgot to take the square root.

8. Jun 10, 2010

### Mitchtwitchita

Is my error in the use of the quadratic formula or in the work leading up to it?

9. Jun 10, 2010

### Staff: Mentor

Your work is fine. You just forgot to take the square root. (See my last post.)

10. Jun 10, 2010

### Mitchtwitchita

Oooooooooh...duh. Thanks!!!