1. The problem statement, all variables and given/known data In the figure particle 1 of charge q1 (at origin) and particle 2 of charge q2 = 3q1, are held at separation L on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a)x and (b)y coordinates of particle 3? 2. Relevant equations E = k q1q2/r2 3. The attempt at a solution We know that the third particle will be held at equilibrium between the two particles (so y = 0), so the forces on it from q1 and q2 will cancel out. From this idea we get: E13 - E23 = 0 E13 = E23 We plug in our relevant equation: k q1q3/r2 = k q2q3/(L-r)2 Plug in and cancel like terms: k q1q3/r2 = k q2q3/(L-r)2 k q1q3/r2 = k 3q1q3/(L-r)2 k q1q3/r2 = k 3q1q3/(L-r)2 q1/r2 = 3q1/(L-r)2 1/r2 = 2q1/(L-r)2 Attempt to isolate for r: (L-r)/r = sqrt(2q1) And this is where I get stuck.