Two point loads Q1 and Q3 are fixed at a distance and we can move another load Q2 to place it in an equilibrium position which is between the two, at a distance a/3 of Q1. Loads Q2 and Q3 are then set at a distance and Q1 is free to be moved to the equilibrium position, which is at a distance 2a/3 to the right of Q2, as shown in the figure.

a) (0.5 points) Without any calculation, show that the three loads must have the same sign.

b) (1 point) Find the relationship between the three loads. (Answer: Q1 : Q2 : Q3 = 1 : 16 : 4)

Q3 Q2 2a/3 QI a/3 Q3 Q1 a/3 Q2 2a/3