Find frequency of oscillating electron in electric field

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.
Attached Thumbnails

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 Mentor Blog Entries: 10 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.
 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<

Mentor
Blog Entries: 10

Find frequency of oscillating electron in electric field

 Quote by 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<
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, εo, etc.

 Tags coulomb's law, electric field, electric potential, frequency

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