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## Homework Statement

This question has already been started here:

https://www.physicsforums.com/showthread.php?t=449070

but they never got to part (b).

PART A

A -10.1 nC point charge and a +18.9 nC point charge are 13.8 cm apart on the x-axis. What is the electric potential at the point on the x-axis where the electric field is zero?

I was able to figure this much out.

PART B

b) What is the magnitude of the electric field at the two points on the x-axis where the electric potential is zero? (Input your answers in order of increasing distance from the negative point charge)

[tex]q_{1}=-10.1 \times 10^{-9} C[/tex]

[tex]q_{2}=18.9 \times 10^{-9} C[/tex]

[tex]d=0.138 m[/tex]

[tex]r_{2}=d-r_{1}[/tex]

[tex]r_{1}=r_{1}[/tex]

## Homework Equations

[tex]V_{net}=\frac{Kq_{1}}{r_{1}}+\frac{Kq_{2}}{r_{2}}[/tex]

## The Attempt at a Solution

Simplified down to...

[tex]r_{1}=\frac{q_{1}d}{q_{1}-q_{2}}[/tex]

but this only finds me ONE point where the electric potential is zero. I'm supposed to end up with two...

I can't think of any other way to look at it, or get a quadratic out of it.

Where did I go wrong?