Two point charges lie on the x-axis. If one point charge is 8.4 microcoulombs and lies at the origin and the other is -3.4 microcoulombs and lies at 19.4 cm, at what position must a third charge be placed to be in equilibrium?

Question

anonymous · Answer

So, I know I set the force of Q1 on Q3 = to Q2 on Q3, but my equation gets screwed up when I try to set the coordinates for for the radius (e.g. .0194 - x or some variation).   I end up with a quadratic and a determinant that gives me imaginary numbers.

Also, for future reference, I know that k and Q3 are canceled in the equation, but can I cancel out microcoulombs?  So the equation would just be (-3.4)/r^2 = (8.4)/r^2

anonymous · Answer

try using x for the radius of separation between Q2 and Q3, and .0194+x as the radius of the other. because the charges are opposite, the equilibrium point will be beyond the second point charge.

anonymous · Answer

|dw:1337237950248:dw|$$8.4/z^2=3.4/(19.4-z)^2$$
Rearrange it, you get a quadratic, and from this you find z.
It probably didn't work for you because you used -3.4, whereas it's actually |-3.4|.