# Finding the neutral point of two charges

## Homework Statement

Two charges q1=+9c and q2+-1c are separated by 2m. Where is their neutral point?

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

## 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.

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SammyS
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Homework Helper
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## Homework Statement

Two charges q1=+9c and q2+-1c are separated by 2m. Where is their neutral point?

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

## 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.
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.

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.
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:
SammyS
Staff Emeritus
Homework Helper
Gold Member
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?
Show what you get when you put values for charge into the following and do a little simplifying.
k q1/(2+x)^2 = -(k q2/x^2)
Also,
What is the quadratic equation you get?

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?
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.