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

In summary, the time period of oscillation for a negative point charge released from rest at a distance d from an infinite charged plane with charge density σ is 4t, calculated using the equation d=1/2at² and assuming that the charge can freely move through the plane without disturbing the charge density.
  • #1
Saptarshi Sarkar
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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.
 
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  • #2
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?
 
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  • #3
rude man said:
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.
 
  • #4
Saptarshi Sarkar said:
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]
Saptarshi Sarkar said:
Thanks, got it. It should be 4t.
Yes. Good going.
 
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FAQ: Time period of oscillation of charge in front of infinite charged plane

1. What is the formula for calculating the time period of oscillation of charge in front of an infinite charged plane?

The formula for calculating the time period of oscillation of charge in front of an infinite charged plane is T = 2π√(m/k), where T represents the time period, m represents the mass of the charge, and k represents the force constant.

2. How does the distance between the charge and the plane affect the time period of oscillation?

The time period of oscillation is directly proportional to the square root of the distance between the charge and the plane. This means that as the distance increases, the time period also increases.

3. Does the charge of the plane have an effect on the time period of oscillation?

Yes, the charge of the plane does have an effect on the time period of oscillation. The force between the charge and the plane is directly proportional to the charge of the plane, which in turn affects the force constant and the time period.

4. What is the significance of the time period of oscillation in this scenario?

The time period of oscillation is an important factor in understanding the behavior of the charge in front of an infinite charged plane. It helps determine the frequency and amplitude of the oscillation, which can provide valuable information about the system.

5. Can the time period of oscillation be affected by external factors?

Yes, the time period of oscillation can be affected by external factors such as external forces or changes in the environment. This can alter the force constant and therefore change the time period of oscillation.

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