Talk:Solenoidal vector field

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Is there any reason at all not to edit this down so that it just says (1) solenoidal means zero divergence and (2) this is equivalent to having a vector potential? I don't think there's any other content on this page that isn't either incorrect or irrelevant. Perhaps it's worth adding that incompressible fluid flow => a velocity field with zero divergence.

Contents 1 Much of it should go methinks 2 My recent reversion 3 B is divless not H 4 Name 5 Simply connected domain

[edit] Much of it should go methinks

True, most of the article seems to go on and on and the essence of the subject gets lost. What I find odd is that the article starts by saying that a solenoidal vector field is when div v = 0 and ends by saying that [...] is why div v = 0. Maybe mathematics is a tautology but that's too much for me. A rewrite (leaving out the talk of cars highways and gears) would be good thing. --Eruionnyron 12:27, 16 Mar 2005 (UTC)

OK: done, rather brutally. Gareth McCaughan 14:11, 2005 Mar 20 (UTC)

While here - there is certainly a connection with the Poincaré lemma. Now, what is this page trying to achieve? Is it going to state the lemma, in effect, in vector calculus terms, so as not to frighten the horses? Is it going to state some valid special case? Is it going to try to prove (better, sketch a proof of) something? Anyway these points seem bound up with trying to get our necessary and our sufficient conditions clearer.

Charles Matthews 17:03, 20 Mar 2005 (UTC)

[edit] My recent reversion

I just reverted an anon contribution, and hit "Return" before finishing my comment. I meant to say that the proof in the article is rigurious. Even if the curl is not the same as the cross-product, they obey the same laws. Oleg Alexandrov (talk) 22:55, 13 November 2005 (UTC)

[edit] B is divless not H

I notice that Special:Contributions/83.131.29.96 has changed magnetic flux density to magnetic field in a number of articles. It's clearly incorrect in this case (I reckon), so I've reverted it. Please discuss the matter here if you disagree. Also, it'd be helpful if you registered a user name. Thanks, --catslash 17:04, 7 July 2007 (UTC)

What does "divless" mean? Just as electric flux is integral of E over an area, so is magnetic flux integral of B over an area, and just as E is an electric field, so is B an magnetic field. H is just an magnetic analogue of electric displacement field D, and it is not itself an magnetic field, just as D is not itself an electric field. Flux density of an field is the field itself ("Conversely, one can consider the flux the more fundamental quantity and call the vector field the flux density."), and magnetic flux density redirects to magnetic field for more than a year anyway. --83.131.8.91 10:46, 8 July 2007 (UTC)

[edit] Name

Why is it called solenoidal? --Abdull 13:46, 12 September 2007 (UTC)

[edit] Simply connected domain

div f = 0 => F such that f = curl F is only supposed be true on specific domains (I'm not sure whether it's star-like or simply connected one implying the other anyway). Don't you think it should be added ? —Preceding unsigned comment added by 81.245.62.57 (talk) 08:48, 21 May 2008 (UTC)