How do I calculate the acceleration of a particle in a parallel plate capacitor?

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Homework Help Overview

The discussion revolves around calculating the acceleration of a particle in a parallel plate capacitor, specifically focusing on the forces acting on an oil droplet within an electric field. Participants explore the relationship between electric fields, forces, and motion in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use kinematic equations to find acceleration but is questioned on the validity of this approach due to the nature of the forces involved. Some participants suggest using the relationship between charge, electric field, and mass to find acceleration. Questions arise regarding the calculation of the electric field and the forces acting on the droplet.

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on the use of free body diagrams to analyze forces. There is a recognition of the need to consider varying forces rather than assuming constant acceleration. Multiple interpretations of the forces acting on the droplet are being explored, indicating a productive discussion.

Contextual Notes

Participants note the lack of information regarding the charge of the plates and the implications this has on calculating the electric field. The discussion also touches on the effects of air friction and gravity on the droplet's motion.

temaire
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Homework Statement


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The Attempt at a Solution


All I need to know is the acceleration acting on the particle after the potential is applied.

v_f^2 = v_i^2 + 2ad
(1*10^{-5})^2 = -(1*10^{-5})^2 + 2a(1*10^{-3})
a = 1*10^{-7} m/s2

Is this the correct approach to finding acceleration?
 
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I don't think so because your acceleration is actually not going to me constant. Recall that the equation you used only applies for a constant acceleration.

I think you should go along the lines of qE = ma to find this.

You're given enough info to find the electric field between the plates, you are given the net charge of the droplet, and density multiplied by volume will give you the mass of your droplet.
 
How do I find the electric field between the plates? I don't have the charge of the plates.
 
Draw a free body diagram for the oil droplet for both of the given cases. What forces are acting? Can you draw any conclusions about the magnitude of the force due to air friction when the droplet is moving at speed vt?
 
By drawing a FBD for the first case, I was able to determine the force due to air friction is equal to force due to gravity. For the second FBD, I was able to determine that the force due to the electric field is equal to the sum of the forces due to air friction and gravity. Therefore, the force due to the electric field is equal to twice the force due to gravity. Is this correct?
 
temaire said:
By drawing a FBD for the first case, I was able to determine the force due to air friction is equal to force due to gravity. For the second FBD, I was able to determine that the force due to the electric field is equal to the sum of the forces due to air friction and gravity. Therefore, the force due to the electric field is equal to twice the force due to gravity. Is this correct?

Sounds good!

What does that tell you about the magnitude of the electric field between the plates (when the plates are given a potential difference)? Can you write an expression?
 
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E = \frac{2mg}{q}

Thanks for the help.
 

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