imported>Least Action: /* Must the field decay at infinity? */ Reply

2025-04-09T15:13:49Z

Must the field decay at infinity?: Reply

New page

{{WikiProject banner shell|class=Start|vital=yes|1=
{{WikiProject Mathematics|priority=Low}}
{{WikiProject Physics|importance=high}}
}}

==needs to include a relativistic treatment==
This article needs to include a relativistic treatment using differential forms as well. [[User:Phys|Phys]] 19:21, 24 Jul 2004 (UTC)

== Article needs a complete rewrite ==

This article, dealing with a more than 100-year old topic, is mostly original research. The interpretation is certainly novel, and rests on at least one false assertion: The article states that a vector field which has the same direction at every point must have zero divergence. Also, the calculation of curl curl A in the example is wrong. The whole thing should be rewritten from scratch. [[User:Brian Tvedt|Brian Tvedt]] 01:25, 17 August 2005 (UTC)

:Oh dear, indeed, its a disaster, isn't it. Unfortunately, many of the articles in WP are in a similar sorry shape; it becomes rather plainly visible when the topic is elementary. [[User:Linas|linas]] 05:59, 17 August 2005 (UTC)

The article has been rewritten by Oleg Alexandrov and is much better now.[[User:Brian Tvedt|Brian Tvedt]] 11:15, 18 August 2005 (UTC)
: I was too lazy though to theck the exact conditions when that theorem holds though. Meaning, how smooth the vector field should be and how fast it must decay in order to admit a vector potential. Hope somebody will get to it one day. [[User:Oleg Alexandrov|Oleg Alexandrov]] 17:01, 18 August 2005 (UTC)

==SI units==

It would be nice if at least the SI unit of the vector potential was given somewhere.

==Use==

I'd love it if somebody could add a bit on what the heck use it is. My experience so far involves a physicist who always worked with A. I was running physical experiments on the device he had derived a theory for. He insisted the device would have "no magnetic field". I whipped out the gaussmeter and measured the magnetic field. He would not accept the readings, as he considered the B field an illusion. Yet he was unable to direct me to an instrument that could measure vector potential, and could not convert A to B due to the pesky gauge factor problem. [[User:Tomligon|Tomligon]] ([[User talk:Tomligon|talk]]) 22:57, 1 February 2009 (UTC)

:There is no instrument that can measure vector potential, since only gauge-invariant quantities are measurable. If he cannot convert A to B, you should tell him that B=curl A. --[[User:Sbyrnes321|Steve]] ([[User talk:Sbyrnes321|talk]]) 04:58, 2 February 2009 (UTC)

==Must the field decay at infinity?==

(''copied from above'')

Hold on. It is a fact that _any_ smooth vector field defined on all of R^3 which has divergence 0, is the curl of another vector field, is it not? This is the Poincare Lemma. It does not require any assumptions on decaying at infinity! It is only the given formula that would fail to work if we didn't have some nice decay property.

Anyway, the first and primary thing the article should say is, having divergence = 0 and domain all of R^3 is sufficient. I'll start changing it soon, if nobody has any objections. [[User:Kier07|Kier07]] ([[User talk:Kier07|talk]]) 15:07, 8 August 2012 (UTC)

:I have only seen this stated with the proviso about decaying at infinity. What you say might be true but I suggest you find it stated explicitly. --[[User:Sbyrnes321|Steve]] ([[User talk:Sbyrnes321|talk]]) 02:12, 9 August 2012 (UTC)
:I think you're right. -- [[User:Least Action|Least Action]] ([[User talk:Least Action|talk]]) 15:13, 9 April 2025 (UTC)

==Wiki Education assignment: 4A Wikipedia assignment==
{{dashboard.wikiedu.org assignment | course = Wikipedia:Wiki_Ed/Riverside_City_College/4A_Wikipedia_assignment_(spring_2023) | reviewers = [[User:JiachengGeng|JiachengGeng]], [[User:Peytonpjccooney|Peytonpjccooney]] | start_date = 2023-02-13 | end_date = 2023-06-12 }}

<span class="wikied-assignment" style="font-size:85%;">— Assignment last updated by [[User:Lzepeda12|Lzepeda12]] ([[User talk:Lzepeda12|talk]]) 21:07, 26 April 2023 (UTC)</span>

Talk:Vector potential - Revision history

imported>Least Action: /* Must the field decay at infinity? */ Reply