Conditions for a E field to be possible

  • Context: Undergrad 
  • Thread starter Thread starter cutesteph
  • Start date Start date
  • Tags Tags
    Conditions Field
Click For Summary

Discussion Overview

The discussion revolves around the conditions necessary for an electric field \( \vec{E} \) to exist in free space, specifically within the context of electrostatic systems. Participants explore the mathematical criteria that must be satisfied, focusing on the divergence and curl of the electric field.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests verifying the electric field by checking if \( \nabla \times \vec{E} = 0 \).
  • Another participant states that in free space, \( \nabla \cdot \vec{E} = 0 \) must always hold, while \( \nabla \times \vec{E} = 0 \) is only applicable in electrostatic systems.
  • A participant confirms that their system is indeed electrostatic.
  • Following the confirmation, it is reiterated that the electric field must be irrotational and divergence-free.

Areas of Agreement / Disagreement

Participants generally agree on the conditions that must be satisfied for an electric field in an electrostatic system, specifically the need for the field to be irrotational and divergence-free. However, the initial question regarding the verification process remains open to interpretation.

Contextual Notes

The discussion does not resolve the implications of the conditions in non-electrostatic scenarios, nor does it clarify the specific methods for verifying the electric field's properties beyond the stated mathematical conditions.

cutesteph
Messages
62
Reaction score
0
If I want to verify an electric field E is possible in free space, do I just need to check ∇xE =0?
 
Physics news on Phys.org
In free space what always has to hold is ##\vec{\nabla}\cdot \vec{E} = 0## whereas ##\vec{\nabla}\times \vec{E} = 0## only holds in electrostatic systems. Is your system electrostatic?
 
Yes, the system is electrostatic.
 
Then yes you have to check that the electric field is irrotational. You also have to check that it is divergence-free.
 

Similar threads

Undergrad E field in a wire
  • · Replies 3 ·
Replies
3
Views
914
Undergrad Electric Field of Uniformly Charged Infinite Plane
  • · Replies 6 ·
Replies
6
Views
591
Undergrad Gauss' law seems to imply instantaneous electric field propagation
  • · Replies 29 ·
Replies
29
Views
2K
High School Electric Fields inside Conductors & Gauss' Law
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Discontinuity of Electric field
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad How Do Time-Varying Currents in Conductors Generate EM Fields and Waves?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Boundary conditions and discontinuity of EM fields
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad Resonant cavity with non-resonant dielectric
  • · Replies 10 ·
Replies
10
Views
2K
High School Electric Field Created by 2 Infinite Plates
  • · Replies 1 ·
Replies
1
Views
2K
High School Electric Field Created by a Finite Plate
  • · Replies 2 ·
Replies
2
Views
2K