Why is the magnetic field inside (primarily at the geometric centre) a thin tube $0$ whereas for a loop it is $\frac{\mu_0 I}{2R}$


For thin tube, the argument often made is that the amperian path inside the tube encloses no current, however the same argument can also be made for a loop of a current which is just an infinitesmial cross section of the tube.

Secondly if the argument is made that in a thin tube, the upper contribution of infinite loop counteracts the lower contribution, then the argument mainly depends on how much cross sections we have. If we have even cross sections, then upper cross sections will equal lower and hence no magnetic field will be there but the same case is not for odd cross sections.

  • $\begingroup$ Can you explain the geometry more clearly? The magnetic field inside an infinitely long solenoid - which is a hollow cylinder - is contant, not $0$. $\endgroup$ Apr 1, 2018 at 18:43
  • $\begingroup$ Thin tube, would be the accurate phrasing I guess. $\endgroup$ Apr 1, 2018 at 18:51
  • $\begingroup$ But how does the current circulate around that tube? $\endgroup$ Apr 1, 2018 at 18:52
  • $\begingroup$ The circulation vector of the current is along the long axis of the tube, in my opinion. $\endgroup$ Apr 1, 2018 at 18:54
  • $\begingroup$ Then why compare it to a loop? Your problem is like having a sequence of 2 parallel wires with current in the same direction. The magnetic field on a line in the middle of these two wires would be trivially $0$. $\endgroup$ Apr 1, 2018 at 18:56


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