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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeSep 27th 2012

    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.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeSep 27th 2012
    • (edited Sep 27th 2012)

    Needs some explanations, like why and how DD and HH come in terms of EE, BB and metric. The integral form is written in terms of EE and BB only. DD and HH are usually motivated either by controlling the Hodge star operation, either by physics of materials.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 27th 2012

    Thanks, that’s good to have. I’ll try to join in later.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2019

    added pointer to

    (for no particular reason, but it’s an interesting read with some history and some reflections)

    diff, v7, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2023

    touched the formatting:

    e.g. turned all the humongous integral signs into \textstyle

    diff, v9, current

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 14th 2023

    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?

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2023

    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.

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 14th 2023

    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.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2023

    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.

    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 14th 2023
    • (edited Jun 14th 2023)

    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.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2023

    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.

    • CommentRowNumber12.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 14th 2023
    • (edited Jun 14th 2023)

    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.

    • CommentRowNumber13.
    • CommentAuthorMike Shulman
    • CommentTimeJun 14th 2023

    The displaystyle integral sign looks the correct size to me in Firefox, and too small in Chrome.

    • CommentRowNumber14.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 15th 2023

    A bigger problem than apparently too-large integral signs was mentioned in #2: the sudden and unexplained switch to the vector fields DD and HH.

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJun 15th 2023

    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.

    diff, v11, current

    • CommentRowNumber16.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 15th 2023

    I took the liberty of correcting a typo just before “Related concepts”.

    diff, v12, current

    • CommentRowNumber17.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 16th 2023

    @Urs thanks for that!

  1. added a section on Maxwell’s equation in the geometric algebra formalism of electromagnetism, and two references in the References section.

    Susan

    diff, v14, current

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2023

    added pointer to:

    diff, v19, current