Investigating the 1d Equation: Charges & Field Disparity

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    1d Charges Field
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Discussion Overview

The discussion revolves around the application of a one-dimensional equation related to electric fields and charge densities. Participants explore the implications of integrating charge density and the resulting electric field configurations in different scenarios, specifically comparing two figures representing these concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the application of the 1D equation to two figures, suggesting that there should be a field present between the charge densities.
  • Another participant asserts that the intuition is incorrect, explaining that the electric fields point in opposite directions and that a negative constant of integration leads to zero electric field between the charges.
  • A participant acknowledges a misunderstanding and seeks clarification on the application of the 1D equation.
  • Further clarification is provided that the constant of integration must be determined from boundary conditions, indicating that the first graph needs adjustment to resemble the second graph.

Areas of Agreement / Disagreement

There is disagreement regarding the initial intuition about the electric field configuration. While some participants provide corrections and clarifications, the overall application of the 1D equation and the implications of the constant of integration remain points of discussion without a clear consensus.

Contextual Notes

Participants discuss the need for boundary conditions in determining the constant of integration, which may not have been fully established in the initial claims. The implications of these conditions on the electric field configurations are not resolved.

Noki Lee
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Can we apply the 1d equation (dE/dx = labmda/epsilon0)dEdx=λϵ0 to the first and the second figures?
1.PNG

But, in the 2nd case,
2.png


if we integrate the charge density, some field exists between the two charge densities. Intuitively, it should be like the last figure.
What's wrong with this?
 
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Your intuition is wrong. The E-field on the left and right point in opposite directions. This is what you get in your case (1) if you add a (negative) constant of integration so E is zero between the two charges.
 
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phyzguy said:
Your intuition is wrong. The E-field on the left and right point in opposite directions. This is what you get in your case (1) if you add a (negative) constant of integration so E is zero between the two charges.
3.png

I mistook the intuition, did you mean this figure?

But why we can't apply the above 1D equation?
 
Yes, I mean that figure. You can use the above 1D equation, but when you do the integration, you always have a constant of integration that you have to determine from the boundary conditions. So your graph (1) needs to have a negative constant added to it so it looks like the graph (2) in post #3. Do you understand?
 
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phyzguy said:
Yes, I mean that figure. You can use the above 1D equation, but when you do the integration, you always have a constant of integration that you have to determine from the boundary conditions. So your graph (1) needs to have a negative constant added to it so it looks like the graph (2) in post #3. Do you understand?
I got it, thank you.
 

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