Week 1: Discrete Charge and the Electrostatic Field 59
Problem 9.
−q+qE−q+qEtop viewside viewθSuppose you have a “dumbbell” consisting of two identical (pointlike)massesmattached to the
ends of a thin (massless) rod of lengthathat is pivoted at its center so that it can swing freely in
a plane. The masses carry a charge of +qand−q, and the system is located in an uniform electric
fieldE~.
Show that for small values of of the angleθbetween the direction of the dipole and the electric
field, the system displayssimple harmonic motion, and obtain an expression for the period of that
motion. (If you look back at the concepts section, I remind you of theformof the simple harmonic
oscillator equation – the idea is to transform the equation of motion into this form, at which point
youknow the solution and all about the associated motionfrom having solved it repeatedly in the
first part of the course.)