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In the Feynman Lectures on Physics, Volume II section 5-10 “The field in a cavity of a conductor” Richard Feynman states the following in the penultimate paragraph:

“… no static distribution of charge inside a closed conductor can produce any fields outside.”

But this must be incorrect. Any charge contained within a cavity in a conductor is expressed on the external surface of that conductor as a uniform charge distribution. In the case of a conducting spherical shell with a charge anywhere in the cavity that charge will appear as a point charge with radial field lines external to the shell.

See: Purcell Electricity and Magnetism 3rd Ed section 3.2 “Conductors in the electrostatic field”.

Surely Feynman cannot be wrong?

In the case of the adjective “grounded” being accidentally missed by the printer of the Commemorative Issue, the paragraph has little value and is quite “un-Feynman like”. ANY grounded conductor cannot have a static surface charge distribution!

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    $\begingroup$ It depends on the conditions of the conductor. If it’s grounded, the field of the charge in its cavity will be perfectly shielded and the outside field will not depend on the charge inside. $\endgroup$
    – LPZ
    Feb 5, 2023 at 15:27
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    $\begingroup$ Your quote is inaccurate and left out an essential word: "grounded". The actual sentence is "…no static distribution of charges inside a closed grounded conductor can produce any fields outside." $\endgroup$ Feb 5, 2023 at 15:30
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    $\begingroup$ The quote, from my volume, is accurate. I am using the three volume Commemorative Issue published in 1989. But there are numerous downloadable excerpts for you to note his words. $\endgroup$
    – adlibber
    Feb 5, 2023 at 15:49
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    $\begingroup$ But the passage you yourself linked to has the word “grounded”, so it is clear that some editions omitted a critical word. $\endgroup$
    – Ghoster
    Feb 5, 2023 at 18:12
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    $\begingroup$ This error is in fact described in the preface to the new millenium edition: feynmanlectures.caltech.edu/I_90.html. $\endgroup$
    – jacob1729
    Feb 6, 2023 at 11:17

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Yes, Feynman is wrong here and by his own admission. In the Preface to the New Millienium Edition of the Feynman Lectures it is stated that:

It is remarkable that among the 1165 errata corrected under my auspices, only several do I* regard as true errors in physics. An example is Volume II, page 5-9, which now says “…no static distribution of charges inside a closed grounded conductor can produce any [electric] fields outside” (the word grounded was omitted in previous editions).

Feynman in fact was alerted to this by several people, including one who lost marks on an exam due to quoting the incorrect statement to which he replied:

Your instructor was right not to give you any points, for your answer was wrong, as he demonstrated using Gauss’s law. You should, in science, believe logic and arguments, carefully drawn, and not authorities. You also read the book correctly and understood it. I made a mistake, so the book is wrong. I probably was thinking of a grounded conducting sphere, or else of the fact that moving the charges around in different places inside does not affect things on the outside. I am not sure how I did it, but I goofed. And you goofed, too, for believing me.

So you have an old edition. There are published lists of errata online here and the online text of the lectures is I think up to date.

*The 'I' quoted here is Kip Thorne, not Feynman.

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  • $\begingroup$ Thank you very much for the link jacob1729! Feynman is my hero just as he is for so many others. Anyone can make a mistake. Unfortunately whoever edited the "correction" could IMO have done a better job! But of course by that time the professor was dead. $\endgroup$
    – adlibber
    Feb 6, 2023 at 11:32
  • $\begingroup$ Kip Thorne’s comment is quite famous. However the intelligent naïve student reading the Physics Bible will be quite disturbed by errors in Physics. She would question her own understanding and perhaps lose confidence in both herself and the book. This was a “simple” error of ommision on Feynman’s part. That it took nearly twenty years after Feynman’s death for the error to be corrected is concerning. $\endgroup$
    – adlibber
    Feb 9, 2023 at 15:59
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Let's quote Feynman at greater length:

You should notice carefully one important qualification we have made. We have always said “inside an empty” cavity. If some charges are placed at some fixed locations in the cavity—as on an insulator or on a small conductor insulated from the main one—then there can be fields in the cavity. But then that is not an “empty” cavity.

We have shown that if a cavity is completely enclosed by a conductor, no static distribution of charges outside can ever produce any fields inside. This explains the principle of “shielding” electrical equipment by placing it in a metal can. The same arguments can be used to show that no static distribution of charges inside a closed grounded conductor can produce any fields outside. Shielding works both ways! In electrostatics—but not in varying fields—the fields on the two sides of a closed grounded conducting shell are completely independent.

These are two special cases of Gauss's law. If there are no internal charges, there are no internal fields; and if the charges a conductor enclose total $0$, making it grounded, they cannot cause external fields. But Feynman notes an interesting symmetry: exchanging inner and outer, we can see the latter fact as implying the former.

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  • $\begingroup$ The word “grounded” is missing from the text in my book. Of course there can be no surface charge on any grounded conductor! Please give me a link to your text that mentions grounded. Upon verification I will alter my text and notify the publishers. $\endgroup$
    – adlibber
    Feb 5, 2023 at 15:51
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    $\begingroup$ @adlibber I don't know of an online link, but I'm apparently quoting the Millennium Edition. However, your link contains the phrase "closed grounded conductor" in exactly the same place. $\endgroup$
    – J.G.
    Feb 5, 2023 at 17:14
  • $\begingroup$ Have you tried imagining what’s going on in a grounded spherical shell containing an internal charge? What’s the microscopic physics? A grounded conductor surely can’t have ANY surface charge can it so … $\endgroup$
    – adlibber
    Feb 5, 2023 at 17:20
  • $\begingroup$ On vs in, $\int_{\partial\Omega}$ vs $\int_\Omega$... $\endgroup$
    – J.G.
    Feb 5, 2023 at 18:20
  • $\begingroup$ @adlibber A grounded conductor surely can’t have ANY surface charge Yes, it can. $\endgroup$
    – Ghoster
    Feb 5, 2023 at 23:18
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Feynman is correct; your book contains a misprint. What he says according to the web version of the Lectures is

The same arguments can be used to show that no static distribution of charges inside a closed grounded conductor can produce any fields outside.

If the conductor is grounded, there will be no potential difference between the surface of the conductor and the ground, and hence no electric field outside. This is in contrast to an isolated conductor containing a cavity with charge inside, in which case conservation of charge together with Gauss's law requires a net surface charge on the outer surface of the conductor, which is the case you are probably imagining. Grounding the conductor causes charge within the conductor to no longer be conserved.

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  • $\begingroup$ My volume from the 1989 Commemorative Issue does not contain the word “grounded”. Of course any grounded conductor cannot have any static charge on its surface! $\endgroup$
    – adlibber
    Feb 5, 2023 at 15:54
  • $\begingroup$ @adlibber I see. That's an unfortunate omission! I wonder if the original text of the lectures contained the word grounded, or if it was left out mistakenly and added to a later edition. $\endgroup$
    – d_b
    Feb 5, 2023 at 16:05
  • $\begingroup$ @adlibber - The (written) Feynman lectures are a cleaned-up reconstruction from transcripts and lecture notes of his actual lectures, which are a bit more free-flowing and conversational in nature, so the text is not word-for-word (a fair bit, actually). It is possible there are omissions in there. Here are the audio recordings of the actual lectures. $\endgroup$ Feb 5, 2023 at 17:50
  • $\begingroup$ Thanks Filip. But if he does use the word grounded that makes for quite an interesting problem doesn’t it? A grounded conductor surely can have no static surface charge so what’s the microscopic physics? I have raised this issue with David Morin and await his comments. $\endgroup$
    – adlibber
    Feb 5, 2023 at 18:03
  • $\begingroup$ @adlibber A grounded conductor surely can have no static surface charge. Yes, it can. $\endgroup$
    – Ghoster
    Feb 5, 2023 at 23:17
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In the online version of the Feynman Lectures, I read

We have shown that if a cavity is completely enclosed by a conductor, no static distribution of charges outside can ever produce any fields inside.

It must have been a typo in your edition.

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  • $\begingroup$ That’s what mine effectively says. No mention of grounded! $\endgroup$
    – adlibber
    Feb 5, 2023 at 15:52
  • $\begingroup$ @adlibber The order of the words outside and inside is flipped with respect to your post. $\endgroup$ Feb 5, 2023 at 16:51
  • $\begingroup$ Ahh! No problem with that comment! $\endgroup$
    – adlibber
    Feb 5, 2023 at 17:16
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On the 29th March 2000 I purchased The Feynman Lectures on Physics, Commemorative Issue from Amazon in the U.K. the three volume set was printed by Addison Wesley, copyright 1964, 1989 by Caltech.In the penultimate paragraph of section 5-10, “The field in a cavity of a conductor” in Volume II the text reads “… closed conductor …” and “… closed conducting shell …”.

From the Caltech website today, copyright 1963, 2006 and 2013, the same paragraph has the following text “… closed grounded conductor …” and “… closed grounded conducting shell …”.

The key point omitted in 5-10 is that the closed conducting surface MUST be held at a constant potential for any internal charge distribution to have NO effect on the outside field. Feynman obviously realised this and it was so obvious that a simple omission occurred. All this leads up to the concept of Image Charges dealt with in section 6-7 “The method of images” in which the text states “ … We found there that the fields in the two regions are quite independent of each other …”. Yes, as long as the conductor surface is held at the correct constant potential (not necessarily grounded).

When this omission was discovered, subsequent to the printing of my book, rather than make the point that the conductor must be held at the correct potential the editor introduced the special and simple case of the zero equipotential by inserting the word GROUNDED twice!

Section 6-7 assumes that the GENERAL point regarding the constant potential has been made previously. But it hadn't been dealt with and the naïve student is left confused. Had Feynman appreciated this he would most certainly have done something about it.

So this was no typographical mistake.

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