Capacitor with uniform space charge between them

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Homework Help Overview

The discussion revolves around a physics problem involving two large plates separated by a distance d, with a uniform space charge density p placed between them and a potential difference V applied across the plates. Participants are tasked with finding the electric field strength at a distance x from the positive plate.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of charge redistribution and the application of Gauss's law. There are attempts to derive expressions for the electric field under different assumptions about charge behavior, including fixed versus redistributing charges. Questions arise regarding the electric flux and the conditions under which the electric field contributions from the space charge would cancel out.

Discussion Status

The discussion is active, with participants providing insights and questioning each other's reasoning. Some guidance has been offered regarding the use of Gaussian surfaces and the implications of symmetry in the electric field. There is acknowledgment of the need to carefully consider the conditions under which the electric field contributions are evaluated.

Contextual Notes

Participants are grappling with the complexities of charge distribution and the effects of a uniform space charge, as well as the constraints imposed by the problem's setup. The discussion reflects uncertainty regarding how to mathematically formulate the electric field contributions accurately.

rohanlol7
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Homework Statement



2 large plates are separated by a distance d and a space charge of uniform charge density p is placed between them and a potential difference V is applied across the plates. Find the electric field stength at a distance x fromt the positive plate
The answer is -V/d +p(x-2d)/2e ( e = epsiolon0)

Homework Equations


gauss law

The Attempt at a Solution


using gauss law:
EA = Qenc/e, Qenc = A*g + charge inside my box, which i can't seem to find, since i have no idea how all the charge will redistribute, I'm guessing some will go onto the plates, or maybe they will redistrubute so as to create an opposing field of equal magnitude to the external field...
 
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rohanlol7 said:
... since i have no idea how all the charge will redistribute ...
Suppose the charges are fixed and do not redistribute. What would your answer be in that case?
 
kuruman said:
Suppose the charges are fixed and do not redistribute. What would your answer be in that case?
-V/d + px/e
 
rohanlol7 said:
px/e
How did you find this? DId you consider the electric flux through both sides of the Gaussian surface?
 
kuruman said:
Suppose the charges are fixed and do not redistribute. What would your answer be in that case?
kuruman said:
How did you find this? DId you consider the electric flux through both sides of the Gaussian surface?
no i didn't. So if i try and consider this, does is go like this ? the E field going from the positive plate will be -V/2d + px/e and through the left that should give -V/2d -p(d-x)/e and adding those two would give -V/d + pd/e ?
 
You have to be careful here. Suppose you only have the space charge. The electric field at a point equidistant from the two ends must be zero because you have as much charge on the left side as on the right. Therefore, whatever expression you find for the space charge electric field contribution alone must give zero at x = d/2. Do you agree?
 
kuruman said:
You have to be careful here. Suppose you only have the space charge. The electric field at a point equidistant from the two ends must be zero because you have as much charge on the left side as on the right. Therefore, whatever expression you find for the space charge electric field contribution alone must give zero at x = d/2. Do you agree?
yes i definitely do agree, i did realize that if its at a point x then a further distance of x on the other side will cancel that E field, however I'm not sure how to go around formulating that properly mathematically properly
 
Consider a Gaussian surface with one edge at d/2. Call that x = 0 (temporarily). The other edge of the surface is at x to its right. Use Gauss's law to find the field through the surface at x. Move the origin to the zero that the problem has defined by transforming x → x - d/2.
 

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