Maxwell equations + scalar and vector potentials

  • Thread starter JamesGoh
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  • #1
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Main Question or Discussion Point

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 Im not sure exactly what he is referring to ?? Can anyone shed some light ?
 

Answers and Replies

  • #2
CompuChip
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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]?)
 
  • #3
Meir Achuz
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The author probably assumes you have read an intermediate level EM textbook.
 
  • #4
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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]?)

j = sqrt(-1). The textbook assumes a general vector potential (where at this stage only the curl of the vector potential has been defined)
 
  • #5
CompuChip
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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,
 
  • #6
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Sorry, didn't notice your wikipedia link. Will look into it and get back to you !
 
  • #7
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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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