Confusion with the divergence of E fields

AI Thread Summary
The discussion centers around the confusion regarding the divergence of electric fields and the resulting charge density. The initial electric field, represented as E = 3x i + 3y j, yields a charge density of 6ε₀, while altering the direction of one component results in a zero charge density. This highlights that despite geometric similarities, the fields are fundamentally different in terms of their physical implications. The conversation also touches on the differences in charge distribution in 2D versus 3D, emphasizing that a constant surface charge density generates distinct electric fields. Ultimately, the calculations confirm that the divergence and charge density are consistent with the properties of electric fields.
maNoFchangE
Messages
115
Reaction score
4
Suppose I have electric field of the form ##\mathbf{E} = 3x\mathbf{i} + 3y\mathbf{j}##. Calculating the charge density gives me ##\rho = \epsilon_0 \nabla\cdot\mathbf{E} = 6\epsilon_0##.
But now if I turn one of the components of the field in the opposite direction, for example ##\mathbf{E} = 3x\mathbf{i} - 3y\mathbf{j}##, then the charge density vanishes. I am confused with this because the only difference between the first and the second fields is just the direction, geometrically they are similar. Where do I go wrong?
 
Physics news on Phys.org
You are on a 2D world. What must be ##\rho## on 3D world to make a field like ##\mathbf{E} = 3x\hat{\mathbf{i}}+3y\hat{\mathbf{j}} + 0\hat{\mathbf{k}} ##?
 
Untitled-1.png
Untitled-2.png

Do these look "geometrically similar" to you?
 
  • Like
Likes Dale and maNoFchangE
theodoros.mihos said:
You are on a 2D world. What must be ##\rho## on 3D world to make a field like ##\mathbf{E} = 3x\hat{\mathbf{i}}+3y\hat{\mathbf{j}} + 0\hat{\mathbf{k}} ##?
The divergence of such a field is ##6\epsilon##, so this kind of charge distribution may generate that field.
@Fightfish ah I see so they are actually quite different.
 
A constant surface charge density ##\rho## make a field ##\mathbf{E} = c\mathbf{k}##, for infinity surface. Flux by point sources relates by ##1/r^2## for 3D, by ##1/r## for 2D and are constants for 1D. Just trust your calculation.
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
Back
Top