So I'm reading through Jackson's Electrodynamics book (page 39, 3rd edition), and they're covering the part about Green's theorem, where you have both [itex]\Phi[/itex] and [itex]\frac{\delta \Phi}{\delta n}[/itex] in the surface integral, so we often use either Dirichlet or Neumann BC's to eliminate one of them.(adsbygoogle = window.adsbygoogle || []).push({});

So for Dirichlet, we simply say G(x,x') = 0 and the integral simplifies a little.

But for Neumann, he says the obvious choice is to use [itex]\frac{\delta G}{\delta n} = 0[/itex] because that eliminates that part of the integral. But then he says, wait, we can't, because applying Gauss' theorem to [itex]\nabla ^2 G(x, x') = -4\pi \delta(x - x')[/itex] shows that [itex]\oint \frac{\delta G}{\delta n'} da' = -4\pi [/itex] (over the surface S), so we have to choose [itex]G(x,x') = \frac{-4\pi}{S}[/itex], where S is the total surface area of the surface S.

Why? I don't really get what he means by 'applying Gauss' theorem'... I know what the theorem is but don't see how to use it or why we can't just choose that dG/dn = 0 here.

Thanks!

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# Neumann Boundary Conditions question

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