Week 1: Discrete Charge and the Electrostatic Field 61
Advanced Problem 11.
+Q
+q,m
A small (point) massm, which carries a chargeq, is constrained to move vertically inside a
narrow, frictionless cylinder. At the bottom of the cylinder is a pointmass of chargeQhaving the
same sign asq.
a) Show that the massmwill be in equilibrium at a height:
y 0 =
√
kqQ
mg
.
b) Show that if the massmis displaced by a small amount ∆yfrom its equilibrium position and
released, it will exhibit simple harmonic motion with angular frequency:
ω= (2g/y 0 )^1 /^2
.
You will need to use expansions to solve this problem.