Is the Electric Field Always Conservative or Can it be Non-Conservative?

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Discussion Overview

The discussion centers on whether the electric field is always conservative or if there are conditions under which it can be non-conservative. It involves theoretical considerations related to electrostatics and changing electric fields, as well as implications for circuit analysis.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants note that the integral of the electric field over a closed path is zero in electrostatics, indicating a conservative field.
  • Others point out that in the presence of changing magnetic fields, the integral of the electric field is equal to the negative rate of change of magnetic flux, suggesting non-conservative behavior.
  • One participant highlights that textbooks may incorrectly present the conservative nature of the electric field without acknowledging the conditions under which this holds true, particularly in the context of AC circuits involving inductors.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which the electric field can be considered conservative, with some agreeing on the special case for electrostatics while others emphasize the importance of changing fields and their implications.

Contextual Notes

Limitations include the dependence on specific conditions such as the presence of changing magnetic fields and the potential misrepresentation in educational materials regarding the applicability of conservative field concepts.

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In some books I have seen:

[tex]\oint \mathbf{E} \cdot d\mathbf{s}=0[/tex]

Since the Electric Field is meant to be conservative.


Elsewhere, however, I have also seen:

[tex]\oint \mathbf{E} \cdot d\mathbf{s} = -\frac{d\Phi_B}{dt}[/tex]


What's going on here?

Thanks
 
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The first case is for electro-statics (no changing fields) and hence is true for the special case when [tex]\frac{d\Phi_B}{dt}=0[/tex]
 
Ah, thanks Matterwave
 
Matterwave said:
The first case is for electro-statics (no changing fields) and hence is true for the special case when [tex]\frac{d\Phi_B}{dt}=0[/tex]

This is true, of course.

What is amazing is that circuit or physics textbooks often quote the special case erroneously. They sometimes even call it a version of Kirchoff's Voltage Law, which is not correct. Any AC circuit that includes an inductor violates the quoted special case. Students should keep an eye out for this, and make sure the special case is really valid.
 

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