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Trying to resolve a discrepancy with vector and scalar potentials with Maxwell's Equations, specifically Ampere's law.

In my E&M textbook (Balanis, 1989, Eqn 6-17), Ampere's law with a magnetic vector potential and electric scalar potential can be expressed as

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

where [tex] \phi [/tex] is the electric scalar potential, and A is the magnetic vector potential.

Now, in a paper I am referencing in my work, I see Ampere's expressed as the following:

[tex] E=-j \omega(A- \nabla \phi) [/tex]

When you distribute this equation, you get the [tex] -j \omega A + j \omega \nabla \phi[/tex]

where now the scalar potential is positive, and also has a [tex] j \omega [/tex] in front of it, where the first equation doesn't.

Is it because of the scalar potential being arbitrary since it's a function of position? Or is there something else?

I also checked Harrington, but no luck there either.

Thanks!

VV5

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# Discrepancies with Maxwell's Eqns - vector potentials

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