Investigating the 1d Equation: Charges & Field Disparity

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SUMMARY

The discussion centers on the application of the 1D equation (dE/dx = λ/ε0) in analyzing electric fields between charge densities. It is established that when integrating charge density, a constant of integration must be added to account for boundary conditions, which can result in an electric field of zero between two charges. The participants clarify that the direction of the electric field on either side of the charges opposes each other, and this must be reflected in the graphical representation of the field. Misinterpretations of the equation's application are addressed, emphasizing the importance of correctly applying boundary conditions.

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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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