Talk:Solenoidal vector field

message: 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.
--12:27, 16 Mar 2005 (UTC)
thread_title:  Much of it should go methinks 

message: 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)
thread_title:  My recent reversion 

message: 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)
replies: text: 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)
thread_title:  B is divless not H 

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

message: 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)
thread_title:  Simply connected domain 

message: The introductory section includes this sentence:
"A common way of expressing this property is to say that the field has no sources or sinks."
No, that is most definitely not a common way of expressing the property of a vector field's having zero divergence. It is not a way at all. It is not true, as the simplest examples show.50.205.142.35 (talk) 10:35, 31 December 2019 (UTC)
replies: text: What counter-examples had you in mind? catslash (talk) 13:08, 31 December 2019 (UTC)
thread_title:  Terrible introduction 

message: These fields are almost certainly called solenoidal because of their relationship to solenoidal magnetic fields (i.e. magnetic fields generated from pipe-like coils of current-carrying wires).  This seems to me to be a folk etymology (and a quite bizarre one at that), it definitely needs a source. INLegred (talk) 21:24, 20 February 2023 (UTC)
replies: text: Wiktionary says the word comes from Ancient Greek σωληνοειδής "pipe-shaped"; Liddell & Scott's dictionary confirms that such a word was used in Ancient Greek. How it came to be applied to the vector field I don't know, though your explanation does seem rather more plausible. - LaetusStudiis (talk) 00:18, 23 March 2023 (UTC)
replies: text: It's "solenoidal" because of the curl. You can imagine each vector in the field as being a tiny pipe, and the pipes must always be connected so that there's just as much coming in as there is going out: the pipes don't leak. So instead of the conventional "combing hair without flat spots or peaks", think "combing pipes so they're always connected". I'm guessing this is a 19th century idea. If you read James Clerk Maxwell's diaries, they're filled with these esoteric thoughts of mechanistic fluids sloshing around in cycles. The concept of a vector field, clearly popular in the 19th cent, its hard to imagine that its much older than that. 67.198.37.16 (talk) 16:23, 22 March 2024 (UTC)
thread_title:  There is no way solenoidal comes from Greek "constrained as if in a pipe"