Chapter 22, Problem 72P

An electron is constrained to the central axis of the ring of charge of radius R in Fig. 22-11, with z R. Show that the electrostatic force on the electron can cause it to oscillate through the ring center with an angular frequency

$\omega =\sqrt{\frac{eq}{4\pi {\epsilon }_{0}m{R}^3}},$

where q is the ring’s charge and m is the electron's mass.