Maxwell equations + scalar and vector potentials

[JamesGoh]

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

$$\vec{E} = -j\omega\vec{A} - \nabla\phi$$

where $$\vec{A}$$ = vector potential and

$$\phi$$ = scalar potential and

$$\vec{E}$$ = 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 ?

 

[CompuChip]

Looks like one of these.
What is j, is it $\sqrt{-1}$? Is a specific vector potential given (say, $$A \propto e^{-j \omega t}$$?)

 

[Meir Achuz]

The author probably assumes you have read an intermediate level EM textbook.

 

[JamesGoh]

Looks like one of these.
What is j, is it $\sqrt{-1}$? Is a specific vector potential given (say, $$A \propto e^{-j \omega t}$$?)

j = sqrt(-1). The textbook assumes a general vector potential (where at this stage only the curl of the vector potential has been defined)

 

[CompuChip]

Well, as I said, the Maxwell equations contain
$$\vec E = \frac{\partial \vec A}{\partial t} - \vec\nabla\phi$$
so if A is something like $$\vec A = \vec A_0 e^{-j\omega t}$$ then you would get what you posted. That's all I can guess based on your information,

 

[JamesGoh]

Sorry, didn't notice your wikipedia link. Will look into it and get back to you !

 

[kof9595995]

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...