Problem 11.

  A thin disk with a circular hole at its center has inner radius a nd outer radius . The disk has a uniform positive surgace charge density on its surface. The disk lies in the yz plane, with its center at the origin.

A point particle with mass m and negative charge -q is free to move along the x axis (but cannot move off the axis). The particle is originally placed at rest at x=0.01 and released. Find the frequency of oscillations.

Solution

From the previous problem we know the expression for electric field

At small x we have:

Then the force acting on a negative charge (-q) is

This force has a form for which the frequency is . Then the frequency is