Question

A +6.00 μC point charge and -8.00 μC point charge are placed along the x-axis at x = 0.000 cm and x = 40.0 cm, respectively. Where must a third charge, q, be placed along the x-axis so that it does not experience any net electric force due to the other two charges?

Answer 1

Here is the analysis.  We choose the negative answer out of the two, since the setup requires the test charge be on the left of the two charges.  That is the only place where the forces can cancel (point in opposite directions), rather than add (double) to result in a force in the same direction.  You can plug the result into the simplified equations at the center of the page and see the result is equal there.  Let me know if you have any questions