Chapter 21, Problem 21P

(III) Two positive charges +Q are affixed rigidly to the x axis, one at x = +d and the other at x = −d. A third charge +q of mass m, which is constrained to move only along the x axis, is displaced from the origin by a small distance s << d and then released from rest. (a) Show that (to a good approximation) +q will execute simple harmonic motion and determine an expression for its oscillation period T. (b) If these three charges are each singly ionized sodium atoms (q = Q = +e) at the equilibrium spacing d = 3 × 10⁻¹⁰ m typical of the atomic spacing in a solid, find Τ in picoseconds.