Deriving Electromagnetic Theory

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Discussion Overview

The discussion centers on the modification of classical electromagnetism through the introduction of magnetic monopoles. Participants explore theoretical implications, mathematical formulations, and references to existing literature on the topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant proposes to modify classical electromagnetism by postulating the existence of magnetic monopoles and seeks guidance on where to begin.
  • Another participant explains that introducing magnetic monopoles can lead to symmetrical Maxwell's Equations, where the divergence of magnetic flux density corresponds to magnetic charge density, similar to electric charge density.
  • It is suggested that magnetic currents can be treated as the dual of electric currents, allowing for the excitation of electromagnetic waves through either type of current.
  • A reference is made to Weng Cho Chew's "Waves and Fields in Inhomogeneous Media" for further reading on duality in electromagnetism.
  • A participant recalls that the concept of duality was also discussed in Halliday and Resnick's physics textbook from decades ago, although it is unclear if current editions maintain this discussion.
  • Another participant advises on the convention for signing magnetic currents when using the Maxwell-Herz equations in differential form.

Areas of Agreement / Disagreement

Participants express various viewpoints on the implications of magnetic monopoles and duality in electromagnetism, but no consensus is reached on the best approach or the validity of the proposed modifications.

Contextual Notes

Some limitations include the dependence on specific definitions of magnetic currents and the potential variations in interpretations of duality across different texts.

Who May Find This Useful

This discussion may be of interest to those studying electromagnetism, particularly in the context of theoretical modifications, engineering applications, and advanced physics education.

spaghetti3451
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Hi,

I am trying to re-derive, or should I say modify, the existing theory of classical electromagnetism by postulating the existence of magnetic monopoles. Where should I begin?
 
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This is a subject that is covered in many engineering books. In the end, it makes Maxwell's Equations symmetrical. The divergence of the magnetic flux density is the magnetic charge density, just like how the divergence of the electric flux density is the electric charge density. There will also be magnetic currents as well. You can change between the electric and magnetic fields for a given equation in such a system by making use of duality. I do not have my references on hand but basically it allows you to replace the electric field in an equation with the magnetic field and something similar with the permittivity, permeability, charges and currents.

Allowing for magnetic currents is often done in computations because the behavior of magnetic currents is like the "dual" of the electric currents. For example, I can excite the same electromagnetic wave from a given electric current by a magnetic current. The magnetic and electric currents will be related to each other along the lines of the curl operator. So a linear dipole electric current is equivalent to a loop of magnetic current and vice-versa. This can allow us to more easily express the excitations of a field using magnetic currents.

Weng Cho Chew's "Waves and Fields in Inhomogeneous Media" discusses duality but many electrical engineering texts will probably have it (more so if they deal with computational methods or antennas since magnetic currents often arise in those subjects).
 
It was also discussed in the edition of Halliday and Resnick's first-year physics textbook that I used nearly forty years ago. I don't know if the current editions still do this.
 
Thanks! I'll use the books and if I have any further questions, I hope you won't mind answering them. :-)
 
It might be useful to know, if you are using the Maxwell-Herz equations in differential form, to sign the magnetic current using the convention

[tex]-\nabla \times E - \frac{\partial B}{\partial t} = J_{magnetic}[/tex]
 

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