Two charges a and B are placed on the smooth insulating plane in vacuum, with the distance r between them. The charges are QA = + 9q, QB = + Q respectively, and another point charge QC is placed Just so that the three spheres are in equilibrium only under the action of their mutual electrostatic force, what kind of charge should QC carry, where should it be placed, and what is the amount of charge

Two charges a and B are placed on the smooth insulating plane in vacuum, with the distance r between them. The charges are QA = + 9q, QB = + Q respectively, and another point charge QC is placed Just so that the three spheres are in equilibrium only under the action of their mutual electrostatic force, what kind of charge should QC carry, where should it be placed, and what is the amount of charge

Let QC = - Q, then the analysis of QC shows that the gravity of a is balanced with that of B, and FAC = fbck * 9q * q / Lac ^ 2 = k * Q * q / (r-lac) ^ 2, lac is the distance from charge C to a, and lac = 3 R / 4, that is, charge C should be placed on AB line