Two equal positive charges Q are on the x axis at x = L and x

Two equal positive charges Q are on the x axis at x = ½ L and x = ½ L.

(a) Obtain an expression for the electric field as a function of y on the y axis.

(b) A ring of mass m, which carries a charge q, moves on a thin frictionless rod along the y axis. Find the force that acts on the charge q as a function of y; determine the sign of q such that this force always points toward y = 0.

(c) Show that for small values of y the ring exhibits simple harmonic motion.

(d) If Q = 5 μC, |q| = 2 μC, L = 24 cm, and m = 0.03 kg, what is the frequency of the oscillation for small amplitudes?