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Question

The standard argument about the vanishing of the magnetic field outside an infinite solenoid pertains to the longitudinal component, parallel to the solenoid axis. But there must be a non-zero toroidal field. However tightly the solenoid is wound, there is a net current in the longitudinal direction. Thus, by Ampere's law, there is a toroidal $B$ field whose magnitude dies off as $1/r$. Why is this field never mentioned? Or am I wrong?

https://physics.stackexchange.com/a/292696/78842 – Aritro Pathak Mar 20 '21 at 09:56 — Aritro Pathak, Mar 20 '21 at 09:56

score 0 · Answer 1 · answered Oct 08 '20 at 17:30

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I'm fairly sure you're correct, and in fact, it's mentioned on Wikipedia:

Of course, if the solenoid is constructed as a wire spiral (as often done in practice), then it emanates an outside field the same way as a single wire, due to the current flowing overall down the length of the solenoid.

answered Oct 08 '20 at 17:30

DanDan0101

2,565

In his pioneering experiments in the 1820s, Ampère knew about this field due to the longitudinal current in a coil, and corrected for it. – Philip Wood Oct 08 '20 at 19:27
See Example 5.9 in the fourth edition of "Introduction to Electrodynamics" by David J. Griffiths. – Physics_Et_Al Oct 08 '20 at 22:00
These were interesting and instructive answers. – Steve Stahler Oct 11 '20 at 00:29

More on magnetic field outside an infinite solenoid

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