I Inverse Square Law and various space dimensions

AI Thread Summary
The discussion centers on the derivation of the inverse square law in various dimensions using Green's functions, emphasizing the importance of integrating over a sphere. The original poster seeks resources or notes that clarify this concept. There is a reference to a specific theorem, possibly Green's theorem, that connects two integrals mentioned in the discussion. The divergence theorem, also known as Gauss's law, is identified as a relevant theorem in this context. Understanding these mathematical principles is crucial for grasping the derivation of the inverse square law.
Lapidus
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I am interested in the derivation of the inverse square law in various dimensions via Green's functions. I think the trick is to imagine a sphere and then to integrate over it. Does anyone know a book or notes where this is explained?

I found this below from here, but could not really understand what's going on:

Green.PNG


Is this some theorem that connects the two integrals (Green's theorem possibly?) in (1.7)?

thanks
 
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Lapidus said:
Is this some theorem that connects the two integrals (Green's theorem possibly?) in (1.7)?
The divergence theorem. (Gauss's law)
 
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