Two positive point charges of magnitudes +6μC (at point A) and +2μC (at point B) are fixed 30cm apart on a straight line in vacuum. A third point charge q is to be placed at a point C on the line AB such that all three charges remain in equilibrium under their mutual electrostatic forces.
a. (i) Derive the condition that relates q with the given charges so that the net force on each charge is zero.
b. (ii) Calculate the magnitude, sign, and position (distance from A) of q that satisfy the condition obtained in part (i).
c. (iii) State, with reasoning, whether the equilibrium of the charge q so obtained is stable or unstable against a small displacement along the line.