Helmholtz Theorem on Decomposition of Vectors

Gonçalo
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Does anyone know anything about this?

I got a look at wolfram.com and I didnt get much.

I would like to prove that in fact, any divergenceless vector field can be decompose in a toroidal part and a poloidal part. And I think the proof of this is somehow related with this theorem...
 
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query about toroidal and poloidal vector fields

Kindly bear with me. I am new to this forum and unfamiliar with it.

A websearch led me here. I wish to learn the meaning of the phrases "toroidal and poloidal vector fields" At the moment they are just words to me. Please tell me their meaning or tell me how to find out more about same.

I gather that a solenoidal field can be decomposed into a "toroidal part and a poloidal part" but again, I am not familiar with this decomposition. Please tell me how to learn about it.

With hope for your guidance,
Alan M. Wolsky
 

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