Three parallel, infinite, uniformly charged planes are arranged as shown in Figure 24.32.(adsbygoogle = window.adsbygoogle || []).push({});

(it looks just like it's described. The middle plate is positive sigma, the outer plates are both negative sigma.)

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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?

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Periodic motion, electric charge

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