Charged ring and electric field problem

1. Jan 13, 2008

Ertosthnes

The problem:
You are part of a design team assigned the task of making an electronic oscillator that will be the timing mechanism of a micro-machine. You start by trying to understand a simple model, which is an electron moving along an axis through the center and perpendicular to the plane of a thin positively charged ring. A team member suggested to determine how the frequency of the electron depends on the size and charge of the ring for displacements of the electron from the center of the ring which are small compared to the size of the ring. Follow through with this suggestion and determine if an expression for the oscillation frequency of the electron for small oscillations can be determined by such an approach. If so, provide the expression, and, for reasonable values for the size of the ring and its charge, estimate the frequency.

Relevant equations:
F = kqq/r^2
F = -kx
f = 1/(2pi)$$\sqrt{k/m}$$

Calculus is needed to determine the sum of the electric field.

For variables, I'm setting the ring on the xy plane with the electron above it on the z plane. The distance from the electron (charge e) to the ring (radius R) at any point is r = $$\sqrt{x^{2}+z^{2}$$.

For force, so far I have F = KzQe/R^3, but I'm not even sure that's right. Somehow, I need to put frequency in terms of R and e. Any help would be much appreciated!

Last edited: Jan 13, 2008