Find frequency of oscillating electron in electric field

gacky27

1. The problem statement, all variables and given/known data
An electron is released from rest in an electric field (see picture attachment, it should explain everything). Upon release, it will oscillate due to the positive electric field. Find the frequency with which it oscillates.


2. Relevant equations
Coulomb's Law
Equation of an electrostatic field


3. The attempt at a solution
First, I found the electric field. I then used Coulomb's Law to find the force exerted by the field on the electron. I'm a little stuck from this point on.

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Redbelly98

Welcome to Physics Forums.

Please show your results so far! What is the force on the electron that you derived?

Once you have the force, use the assumption z«a,b to get an approximate, simpler expression.

gacky27

I've actually tried that. It turns out to be zero when I do that, which can't be right. My result for E was:

-(σ/2εo)[(z/b)-(z/a)]

If I plug in z<<a,b I just get zero

My initial train of thought was to find E, use F=qE, then go from there.

Perhaps the value for E i found is wrong? I'll have to go back and redo it I guess.

Redbelly98

That looks good so far.

Can you rewrite your expression for E, so that it is

E = something × z

Eventually, you want to come up with a force for the electron in the form:

F = - k z

where k is a constant expression involving σ, ε_o, etc.