Three charged particles, A, B, and C, are placed in a line. Particles A and B are fixed in place. Particle C (we'll refer to it as the test charge) is free to move if an electric force is exerted on it, but remains stationary when placed at some location to the left of the other two charged particles, A and B. The distance from particle A to the test particle (C) is half of the distance separating A and B, as shown below. Particle C is known to be positively charged, but we are not told the signs of the charges on A and B. G+ B (a) As always, draw a diagram of the situation described in the problem statement. information you can deduce immediately from the problem statement. Add any (b) Is the information provided in the problem statement sufficient to infer the sign of the charge on A? On B? If yes, what are the signs? If not, why not, and can we at least say whether A and B must carry charges of the same or opposite signs? Explain. (c) Find the ratio, qA/qB, of the magnitude of the charge on A to the magnitude of the charge on B. (d) Is charge C in a stable or unstable equilibrium? Explain. Note that the answer may depend on the sign of the charges A and B. ("Stable equilibrium" means that if we move a away from the equilibrium position, there will be a net force that pushes the charge back toward the equilibrium position. Think of a marble at the bottom of a well. "Unstable," on the other hand, means that such a shift results in a net force pulling the charge even further from the equilibrium position. Think of a marble balanced on the tip of a needle.) (e) Check your answer to part c by considering how it depends on the separation of charges A and B, and how it depends on the distance between the test charge and A. If the distance between the A and B remains the same, and the test charge C moves farther away, we expect the ratio 9A/9B to get closer and closer to 1. Check that this is indeed the case for your solution, and explain why we would make that prediction. Now consider the other check: how should the ratio behave if we move charge B farther away and leave C where it is? Why? Is your answer mathematically consistent with your physics prediction?