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omega_minus

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I am reading Griffith's "Introduction to Electrodynamics" 4ed. I'm in the chapter on relativistic electrodynamics where he develops the electromagnetic field tensor (contravariant matrix form) and then shows how to extract Maxwell's equations by permuting the index μ. I am able to follow the argument for the μ=0 case as it appears straightforward: He takes the spatial derivative of the corresponding matrix element and out pops Gauss' Law, etc. But when the time derivative term is not zero (μ≠0) there always appears an additional factor of 1/c on that term. I can see in the end this term is required to get the corresponding equation, but I don't understand where it comes from. For example when he takes the time derivative of the F

^{10}term (the -E

_{x}/c term) he ends up with a factor of -1/c

^{2}.

I'm a grad student in electromagnetics engineering and we didn't learn this formalism but I enjoy studying special relativity so I'm making an effort to understand it. I'm not enrolled this summer (no professors to bother...) so I was hoping someone here might point me in the right direction. Google has not been much help and the book didn't seem to address it before. The answer is probably staring me in the face...

Thanks in advance for any help.