Work required to move capacitor plates

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Homework Help Overview

The discussion revolves around determining the work required to move the plates of an ideal parallel plate capacitor from a separation distance of D to an integer multiple of D, with the assumption that only one plate is moved. The problem involves concepts from electrostatics and energy stored in capacitors.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore various approaches, including the use of energy density in electric fields and potential energy equations. There is a mention of needing to evaluate an integral between the initial and final distances for a general solution. Some participants question the appropriateness of different methods and the consistency of results obtained from them.

Discussion Status

The discussion is active, with participants providing different perspectives on how to approach the problem. Some guidance has been offered regarding the use of energy equations and integrals, but there is no explicit consensus on the best method. Participants are also exploring the implications of whether the capacitor is charged and connected to a battery or not.

Contextual Notes

There is a consideration of how the capacitor's charge and voltage change based on its connection to a battery, which may affect the approach to calculating work. Participants express uncertainty about the integral approach and its validity in this context.

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Homework Statement



Determine the work required to move the plates of an ideal parallel plate capacitor from a separation distance of D to an integer multiple of D, (assume only one moves for simplicity). The each plate has an area A.

Homework Equations


F = q^2 /( 2 e_0 A) field strength between the plates
[tex]\Delta[/tex] V = U/q
[tex]\Delta[/tex]U = -W
[tex]\Delta[/tex]V= Qd/e_0 A



The Attempt at a Solution



moving the terms above around I came up with U = Qdq/e_0A
I know I need an integral here, probably evaluated between D and multiple of D(its a general solution that's needed)
Am I on the right track?
 
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Though it's a little cheap and probably not what your professor had in mind, you can use the equation for energy density(J/m^2) stored in an electric field to solve this problem. Do final energy stored minus initial energy stored to calculate what energy was added (or done) to the system.
 
I appreciate the reply. I thought about that, but I use that in another part of the problem, not that I can't use it again since its different variables, but I am fairly certain I'll be graded on the diversity of methods used.

Anyone know if that integral approach would work or am I grasping at fog?
 
Why not use the appropriate equation for energy stored in a capacitor?
 
well since you know the force between the two plates

Work is

W=Integral (Fdr)
 
Thats what I thought but I encounter a problem, when I compare the integral result to one obtained by use of potential energy, I am getting a different result depending on different terms. Considering that the work should be the same, I am stuck. Is there anyway Q^2= Vbat?
 
In the question has the capacitor been charged and disconnected from the battery?If so Q remains constant and V changes if the plate separation is changed.If the capacitor remains connected to the battery V remains constant and Q changes.
 
Also remember the potential energy of a system is (CV^2)/2
 

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