I Why are field lines parallel in a uniform field?

AI Thread Summary
In a uniform electric field created by charged plates, the individual atomic charges generate radial fields that typically do not exhibit parallel field lines. However, the vector sum of these radial fields results in a uniform field where lines appear parallel. This phenomenon can be likened to wave propagation, where adjacent sources create a linear wave front, as explained by Huygens' principle. The charges on the plates remain stationary, leading to fields that are perpendicular to the surface without tangential components. Thus, the parallel nature of the field lines in a uniform field arises from the cumulative effect of these radial fields.
jackiepollock
Messages
11
Reaction score
2
For a uniform field like this, I imagine the two plates that creates it are made of multiple atoms with charges, which are points sources that create radial fields. We know that radial fields don't have parallel fields lines, so how are parallel fields lines form when the field is made of various radial fields? Is it caused by the vector sums of these radial fields?

Screenshot 2021-08-03 at 20.51.09.png
 
Physics news on Phys.org
Hello,

Yes you have the right picture in mind. There is an analogy with waves: the summation of waves propagating in circles from adjacent sources generates a more or less linear wave front ( google huijgens principle ).

So on the edges of the plates the field lines will bulge outward a little bit## \ ##
 
  • Like
Likes jackiepollock
BvU said:
Hello,

Yes you have the right picture in mind. There is an analogy with waves: the summation of waves propagating in circles from adjacent sources generates a more or less linear wave front ( google huijgens principle ).

So on the edges of the plates the field lines will bulge outward a little bit## \ ##
Thank you!
 
jackiepollock said:
For a uniform field like this, I imagine the two plates that creates it are made of multiple atoms with charges, which are points sources that create radial fields. We know that radial fields don't have parallel fields lines, so how are parallel fields lines form when the field is made of various radial fields? Is it caused by the vector sums of these radial fields?

View attachment 287041
On the plate the charges are on the surface which can’t move because the field don’t have any tangential component along the surface. The vector sum of all the fields at all points are fields perpendicular to the surface.
 
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
Back
Top