W9_parallel_resonance.eps

62 Week 2: Continuous Charge and Gauss’s Law

Advanced Problem 12.

+Q

−q,m

L

x

A small bead of massmand carrying a negative charge−qis constrained to move along a long,
thin, frictionless rod. A distanceLfrom the center of this rod is a positive chargeQ. Show that if
the bead is displaced a distancexfrom the center (wherex≪L) and released, it will exhibit simple
harmonic motion. Obtain an expression for the period of this motion interms of the parametersL,
Q,q, andm.

You will need to use expansions to solve this problem.