- #36
Phrak
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kcdodd said:Phrak: When someone says the EM wave equation, this is what I think of. Not of E and B, but of A.
[tex]\nabla^2\phi - \partial^2_t\phi = -\rho[/tex]
[tex]\nabla^2\vec{A} - \partial^2_t\vec{A} = -\vec{J}[/tex]
I could be horribly mistaken, but though these are certainly wave equations, they are not the wave equations of light.
For instance, the homogeneous solution of the wave equation of E is,
[tex]\Box \textbf{E} = 0 \ .[/tex]
[tex] \textbf{E} = - \nabla \phi - \partial _t \textbf{A}[/tex]
[tex]\Box (\nabla \phi + \partial _t \textbf{A}) = 0[/tex]
The last equation is certainly third order in all terms.
It's interesting to note the authors of electromagnetic wave equation on Wikipedia agree with you.
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