Two known charges, -12MC and 45 MC, and a third unknown charge are located on the x-axis. The charge -12 MC is at the origin, and the charge 45.0 MC is at x= 0.15 cm. The unknown charge is to be placed so that each charge is in equilibrium under the action of the electric forces exerted by the other two charges. Is this possible? Find the required location, magnitude and sign of the unknown charge.
The Attempt at a Solution
What I did first was to assume that the unknown charge is to the right of the -12 MC charge and when I set the forces of each of the known charges with the unknown charge equal to each other, I got a distance of 0.0160 m to the left of the -12 MC (though I'm not sure if it's right)...but then I think that the charge could be both positive and negative at the same location which I think makes sense. The trouble is how to find the magnitude after that...I tried finding the Electric field on the unknown charge by the two other known charges but that didn't really work...this is really frustrating!!