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The magnetic field is composed of closed loops (assuming there is no magnetic monopole). How does one prove any two magnetic loops do not knot to form a link?

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    $\begingroup$ What makes you think they can't form knots? $\endgroup$ Dec 25 '20 at 2:55
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    $\begingroup$ @Hans It's obviously not true if there is magnetic material (long bendy magnet) or conductive material (long bendy solenoid) present that can be tied in a knot. This presumably includes plasma. But I'm guessing it has to be true in any empty volume where the field has to obey the Laplace equation. $\endgroup$
    – Roger Wood
    Dec 25 '20 at 6:51
  • $\begingroup$ You are both right. I am embarrassed by my stupid question. $\endgroup$
    – Hans
    Dec 25 '20 at 7:50
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    $\begingroup$ @RogerWood There seem to be some papers about knotted and linked vacuum solutions to Maxwell's equations, like arXiv:1502.01382. $\endgroup$
    – benrg
    Dec 25 '20 at 8:16
  • $\begingroup$ @benrg: You seem to have answered my new question physics.stackexchange.com/q/602923/17354.Care to provide a detailed answer there? $\endgroup$
    – Hans
    Dec 25 '20 at 8:39
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You don't.

Take a set of short permanent magnets. Chain them together. Make a knot out of the chain, and connect the ends.

Or form two chains. Make them into linked closed loops.

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