Time period of oscillation of charge in front of infinite charged plane

[Saptarshi Sarkar]

Homework Statement

A negetive point charge -q with mass m is held at rest at a distance d from an infinite charged plane with charge density σ and released. Find time period of oscillation (assuming that charge can freely move through plane without disturbing the charge density).

Relevant Equations

F = -qσ/2ε
a = -σq/2εm

I tried to calculate the time the charged particle will take to reach the plane using the a and using d=1/2at² and found the t to be equal to root(4εmd/σq).

I guess the time period of oscillation will be double of t (by symmetry), i.e. 2root(4εmd/σq). I don't know if this is correct.

 

[rude man]

I should have looked at your work more closely. You have the picture quite correct.
Only small thing - if t is the time to fall to the plane, is the period really 2t?

 

[Saptarshi Sarkar]

I should have looked at your work more closely. You have the picture quite correct.
Only small thing - if t is the time to fall to the plane, is the period really 2t?

Thanks, got it. It should be 4t.

 

[rude man]

Homework Statement:: A negetive point charge -q with mass m is held at rest at a distance d from an infinite charged plane with charge density σ and released. Find time period of oscillation (assuming that charge can freely move through plane without disturbing the charge density).
Homework Equations:: F = -qσ/2ε

OK

a = -σq/2εm

I tried to calculate the time the charged particle will take to reach the plane using the a and using d=1/2at² and found the t to be equal to root(4εmd/σq).

I guess the time period of oscillation will be double of t (by symmetry), i.e. 2root(4εmd/σq). I don't know if this is correct.
[/QUOTE]

Thanks, got it. It should be 4t.

Yes. Good going.