# Finding the neutral point of two charges

1. Sep 9, 2015

### kspabo

1. The problem statement, all variables and given/known data
Two charges q1=+9c and q2+-1c are separated by 2m. Where is their neutral point?

2. Relevant equations
E = E(+) + E(-)
E= k q/r^2

3. The attempt at a solution
k q1/(2+x)^2 = -(k q2/x^2)

When I solve for this equation I end up square rooting a negative number which would then give i and I don't know how to work with this.

2. Sep 9, 2015

### SammyS

Staff Emeritus
Doesn't the electric field vector point away from a positive charge and towards a negative charge?

If so, the sign you use for the field from each of your charges depends upon the position relative to the charges.

3. Sep 9, 2015

### kspabo

Correct. So the positive field flows right towards the negative which continues a field to the right. I'm looking for the neutral point nearest the negative charge. How can I use this info to solve this if q1 is at 0 and q2 is at x=2?

Last edited: Sep 9, 2015
4. Sep 9, 2015

### SammyS

Staff Emeritus
Show what you get when you put values for charge into the following and do a little simplifying.
Also,
What is the quadratic equation you get?

5. Sep 9, 2015

### kspabo

k q1/(2+x)^2 = -(k q2/x^2)
q1/(2+x)^2 = -(q2/x^2)
+9/(2+x)^2 = -(-1/x^2)
9/(2+x)^2 = 1/x^2
x^2/(2+x)^2 = 1/9
x/(2+x) = ± 1/3
(2+x)/x = ± 3
2/x + 1 = ± 3
2/x = -1 ± 3
So we have x=1 when -1 + 3

Ah, that makes sense and I believe is the correct answer.