For the charge distribution in Problem 32, the electric field at the origin is zero. A test charge q0 placed at the origin will therefore be in equilibrium.

(a) Discuss the stability of the equilibrium for a positive test charge by considering small displacements from equilibrium along the x axis and small displacements along the y axis.

(b) Repeat part (a) for a negative test charge.

(c) Find the magnitude and sign of a charge q0 that when placed at the origin results in a net force of zero on each of the three charges.

(d) What will happen if any of the charges is displaced slightly from equilibrium?