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I expanded Maxwell’s equations by adding the integral form in SI system and then a shorter version of discussion from electromagnetism for the differential form of the equations, both in 3d and 4d formulations. Note also that Ampère’s law is about producing magnetic field from current; while it is Maxwell’s equation, or Ampère-Maxwell which adds the term with the change of electric field, the main discovery of Maxwell. Some people nowdays say generalized Ampère’s law what I wrote, but I am not happy about it as the general form does not generalize it in the straightforward manner, but adds new physics what needs a separate attribution.
Needs some explanations, like why and how and come in terms of , and metric. The integral form is written in terms of and only. and are usually motivated either by controlling the Hodge star operation, either by physics of materials.
Thanks, that’s good to have. I’ll try to join in later.
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(for no particular reason, but it’s an interesting read with some history and some reflections)
Re #5: In my browser (Firefox) the new integral signs look considerably worse than the old ones, to the extent that they no longer look like integral signs, their size being smaller than that of an ordinary letter… Could this be a problem specific to your browser?
In my browser (Firefox) the new integral signs […] no longer look like integral signs, their size being smaller than that of an ordinary letter.
Interesting problem with your browser. So all inline integral symbols you get are unrecognizable, then? Could you share a screenshot to give an impression of what you are seeing?
I’ll try to collect more data on this problem. Last time we discussed such issues (here) others reported getting overly large displaystyle.
Here is a screenshot: https://dmitripavlov.org/screenshot.png.
With respect to this matter, a better solution is to adjust the CSS style, changing the font size for the integral sign.
This has the following advantages:
(1) It can be adjusted according to the browser and/or the available font;
(2) When the nLab switches to a different math typesetter (e.g., MathJax or KaTeX), the formulas will continue to make sense.
Thanks. That’s what I am seeing, too. Looks like the usual inline size of integrals to me (a little larger than the largest letters), as expected for the \textstyle-command.
Have added the issue with the overly large displaystyle to what is now a little issue list in the Sandbox – I’ll bring up this issue to the technical team.
I have never seen such small integral signs used in books or articles, and in its current size it simply does not feel or read like an integral sign. For comparison, the integral signs in the Wikipedia article integral look perfectly normal.
On that page all integral signs are in displayed equations (displaystyle). The inline integral signs are usuall typeset smaller (textstyle), not to disrupt the line spacing too much.
Re #11: The screenshot in #9 is that of a displayed formula (the Ampere-Maxwell law), not an inline formula.
TeX, MathJax, KaTeX typeset inline formulas in \textstyle and displayed formulas in \displaystyle automatically, there is no need to manually adjust the style.
The displaystyle integral sign looks the correct size to me in Firefox, and too small in Chrome.
A bigger problem than apparently too-large integral signs was mentioned in #2: the sudden and unexplained switch to the vector fields and .
I don’t want to delve at the moment into the task of making this page a globally coherent and comprehensive account of Maxwell’s equations,
but I have added a few words to the section Differential equations (here, whose previous author had left it in somewhat telegraphic style) to briefly explain why there are now four fields instead of two, and how they are related.
@Urs thanks for that!
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