Two point charges of magnitudes +3μC and −12μC are fixed on a straight line and kept 60cm apart in air. Take the origin at the position of the +3μC charge and the positive x-axis directed towards the −12μC charge.
(i) Prove that there exists at least one point on the x-axis where a +1μC test charge would experience zero net electrostatic force.
(ii) Obtain the coordinate(s) of such point(s) with respect to the origin.
(iii) Assuming the test charge is displaced slightly towards either fixed charge and released, state with reasons whether the equilibrium at the point found in part (ii) is stable, unstable, or neutral.