Position of proton and electron to create electric field

[cherry_cat]

Homework Statement

The electric field at a location C points north, and the magnitude is 1*10^6 N/C. Where should you place a proton and an electron, at equal distances from C, to produce this field? Give a numerical answer and a direction for each particle (North, South, East or West).

Homework Equations

E=k q/r^2
E=k q1 q2/r^2

The Attempt at a Solution

Because the distances are equal, I set two sets of the equation equal to each other (one for the electron and one for the proton)
k q1 q2/r^2=k q1 q2/r^2
q2/r^2=q2/r^2
1.6e-19/r^2=-1.6e-19/r^2
Taking square root of each side
√1.6e-19/r=√-1.6e-19/r
r√1.6e-19=r√-1.6e-19

Here I realized that this wasn't going to work, because I would be dividing r by r and also taking the square root of a negative number.
I thought the best way to do this would be by setting the two equations equal to each other as the distance must be the same, but the way I went about solving this problem didn't work.

 

[ap123]

The first thing you have to do is to decide where the particles are going to be located. Think about the direction of the electric fields produced by the particles in each of the possible locations and see which one will produce a total electric field North.

Then work out the magnitude of the field produced by each of the particles and relate this to the total field given.

 

[cherry_cat]

Thanks so much, the diagram really helped me visualise where they should be located. I realized I was looking at the problem in completely the wrong way.