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On the inside of a solenoid, is the electromagnetic field reverse that on the outside?

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  • $\begingroup$ It can even be zero. $\endgroup$ – my2cts May 6 at 12:41
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Figure 1 shows the solenoid field with a single-layer winding and a component of the field $B_z$ in the middle section, depending on the distance from the axis $z$. It is seen in this case, the field component $B_z$ changes sign at the intersection of the winding. Figure 1

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  • $\begingroup$ This answer is good because it's very obvious from it that whilst the direction outside is reversed, the magnitude is much smaller. Btw is that your own simulation? $\endgroup$ – jacob1729 May 6 at 12:39
  • $\begingroup$ @jacob1729 Yes, I use Mathematica 12 for simulation. $\endgroup$ – Alex Trounev May 6 at 12:44
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What do you mean by reverse here? The magnetic field lines in current carrying solenoid resemble that of a bar magnet. they form closed loops going in and out of the solenoid. In that sense, yes, the field lines, are in opposite direction inside the solenoid.

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  • $\begingroup$ trivial to see what I mean with reverse. the poles on the outside of the solenoid, are they reverse on the inside, so that the north pole of a bar magnet is attracted to the inside of the outer north pole of the solenoid, which is south pole. like this i.imgur.com/W6MTtMo.jpg $\endgroup$ – user612 May 6 at 12:16
  • $\begingroup$ Yes, it is true. If on a magnetic field line, you assume a magnet, the north pole will be along the field line, in the direction of field line, while the opposite direction at that point will be the south for the magnet. For a solenoid, you define poles at the two ends of solenoid, in emerging direction, a north pole and the face into which lines go as the south pole. Definitely, there are corresponding opposite poles inside the solenoid at a face. As I wrote in my answer, the pole can be determined by direction of field line at that point. Hope you got it! $\endgroup$ – Tojrah May 6 at 12:31
  • $\begingroup$ what would the magnetic field look like if the solenoid was a spherical coil, and it was surrounded by a spherical iron shell? $\endgroup$ – user612 May 6 at 13:11
  • $\begingroup$ What do you mean by spherical coil? The term is ,as far as I know is not well defined. $\endgroup$ – Tojrah May 6 at 13:21
  • $\begingroup$ wind a coil in a sphere $\endgroup$ – user612 May 6 at 13:30
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I think in your question you are alluding to the surprising opposite direction of the H field relative to the direction of the B field in a permanent magnet, and maybe you are wondering whether that is the case also for a solenoid.

In vacuum the two fields H and B are parallel and proportional, and the factor between them (MKS: $4\pi 10^{-7}$) is just a definition of their physical dimension. In magnetizable (and magnetized) matter they are different and the reason for the change is that the appearance and accumulation of excess magnetic excess surface charges whose induced dipole field is in the opposite direction.

If the solenoid has no core (ie., has no magnetizable matter inside) then the H and B fields are related as they are in vacuum. If, on the other hand the solenoid has a core then outside the core the relationship between H and B are the same as in vacuum but inside the core depending on the core material (low $\mu$ paramagnet, high $\mu$ paramagnet or ferromagnet) H and B may be parallel or antipapralllel or be in something even more complicated relative direction, furthermore the functional relationship is strongly nonlinear.

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