I Investigating the 1d Equation: Charges & Field Disparity

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The discussion focuses on the application of the 1D equation (dE/dx = λ/ε0) to analyze electric fields between charge densities. It highlights a misunderstanding regarding the behavior of the electric field, which points in opposite directions on either side of the charges, leading to a zero field between them. The necessity of incorporating a constant of integration based on boundary conditions is emphasized for accurate graph representation. The conversation clarifies that the initial intuition about the field's behavior was incorrect. Ultimately, the participants reach an understanding of how to correctly apply the equation and adjust the graph accordingly.
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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.
 
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?
 
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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