A point charge of -1.0 µC is located at the origin. A second point charge of 16 µC is at x = 1 m, y = 0.5 m. Find the x and y coordinates of the position at which an electron would be in equilibrium.
The Attempt at a Solution
I have gotten pretty far with the problem, but I have reached a block. I used the equation F=k((q1q2)/r^2) for both the point at the origin(F1) and the point at (1,0.5) (F2).
I have come up with the equations:
Then I set them equal to each other:
I know from here I should find a way to substitute r_2 to put it in terms of r_1 but I'm not sure how to go about it. I drew out where the points would be graphically, and I put the first point at the origin and the second point at (1,0.5), is that where I went wrong? Any help would be appreciated.