Periodic motion, electric charge

[tony873004]

Three parallel, infinite, uniformly charged planes are arranged as shown in Figure 24.32.
(it looks just like it's described. The middle plate is positive sigma, the outer plates are both negative sigma.)

Homework Statement

A small hole passes through the middle plane. At t=0 an electron emerges from the hole moving perpendicular to the planes with speed v_o . Assuming v_o is small enough that the electron does not collide with the negative plate, show that its motion is periodic, and find the period.

Homework Equations

The Attempt at a Solution

It's obvious that it will be periodic since there is no force to pull it off the x-axis, and there is no friction to rob it of energy.

I have a feeling it's like a pendulum, where the amplitude does not affect the period. But we haven't had any examples of periodic motion yet in E&M.

From the pendulum, we have a small amplitude formula for period of T=2pi sqrt(L/g). I imagine charge is somewhat analogus to gravity, and perhaps distance between the plates is somewhat analgous to L (length of pendulum). Where do I begin?

Homework Equations

The Attempt at a Solution

 

[rl.bhat]

Using Gauss's theorem calculate the electric field between the plates. Then find force and acceleration of the electron. In SHM, acceleration = w^2.A, where A is the amplitude of SHM and that is the distance between the plates. From w you can find the period of the SHM.