Maxwell equations + scalar and vector potentials

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Discussion Overview

The discussion centers on the scalar and vector potentials in electromagnetics, specifically examining the equation relating the electric field to these potentials. Participants explore the implications of this equation and its familiarity in the context of Maxwell's equations.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant presents the equation \(\vec{E} = -j\omega\vec{A} - \nabla\phi\) and seeks clarification on its familiarity as mentioned by the author.
  • Another participant questions the meaning of \(j\) and whether a specific form of the vector potential is assumed, suggesting \(A \propto e^{-j \omega t}\).
  • A different participant notes that the author likely expects readers to have prior knowledge from intermediate level electromagnetism textbooks.
  • One participant confirms that \(j\) represents \(\sqrt{-1}\) and mentions that the textbook assumes a general vector potential where only the curl has been defined at this stage.
  • Another participant connects the equation to Maxwell's equations, suggesting that if \(\vec{A}\) is of the form \(\vec{A} = \vec{A_0} e^{-j\omega t}\), it aligns with the presented equation.
  • One participant expresses uncertainty about the meanings of \(j\) and \(\omega\) but notes that the formula appears to satisfy Helmholtz's theorem.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the equation and its components, with no consensus on the familiarity of the result or the assumptions made about the vector potential.

Contextual Notes

Some participants indicate a lack of clarity regarding the definitions and roles of \(j\) and \(\omega\), as well as the specific form of the vector potential, which may affect the interpretation of the equation.

Who May Find This Useful

This discussion may be useful for students and practitioners of electromagnetics, particularly those interested in the theoretical foundations of scalar and vector potentials and their applications in Maxwell's equations.

JamesGoh
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Im doing some study on scalar and vector potentials in the area of electromagnetics, and the author of the book derived this equation

[tex]\vec{E} = -j\omega\vec{A} - \nabla\phi[/tex]

where [tex]\vec{A}[/tex] = vector potential and

[tex]\phi[/tex] = scalar potential and

[tex]\vec{E}[/tex] = time harmonic form of electric field

The author goes on to make a statement saying this may be a familiar result, however I am not sure exactly what he is referring to ?? Can anyone shed some light ?
 
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Looks like one of these.
What is j, is it [itex]\sqrt{-1}[/itex]? Is a specific vector potential given (say, [tex]A \propto e^{-j \omega t}[/tex]?)
 
The author probably assumes you have read an intermediate level EM textbook.
 
CompuChip said:
Looks like one of these.
What is j, is it [itex]\sqrt{-1}[/itex]? Is a specific vector potential given (say, [tex]A \propto e^{-j \omega t}[/tex]?)


j = sqrt(-1). The textbook assumes a general vector potential (where at this stage only the curl of the vector potential has been defined)
 
Well, as I said, the Maxwell equations contain
[tex]\vec E = \frac{\partial \vec A}{\partial t} - \vec\nabla\phi[/tex]
so if A is something like [tex]\vec A = \vec A_0 e^{-j\omega t}[/tex] then you would get what you posted. That's all I can guess based on your information,
 
Sorry, didn't notice your wikipedia link. Will look into it and get back to you !
 
i'm not quite sure about what j and omega presents,but the formula seems to be written in the form that satisfy helmhotlz's theorem,hope it help...
 

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