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I'm trying to evalueate the magnetic field generated by circular current carrying loop. My manual says that for the symmetry of the sytem only the magnetic field along the $z$ axis (which is the symmetry axis of the conductor) is not zero. I don't understand the reason. It seems that if I consider a point $P$ on the $xy$ plane, $\mathbf{H}$ should not vanish following my calculations. The elementary magnetic field generated by a infinitesimal segment is:

$$d\mathbf{H} = I\frac{ x \hat{r}}{4\pi r^2}d\mathbf{s}$$

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  • $\begingroup$ as you said "the magnetic field along the z axis( which is the symmetry axis of the conductor) is not zero.", i.e, the field is not zero in the middle per your calculation. Note that in your formula "$d\vec s \hat r$" refers to a vector product and when you are at the center the vectors are orthogonal. $\endgroup$
    – hyportnex
    Commented Oct 4, 2020 at 11:24
  • $\begingroup$ I think the manual is calculating the magnetic field only on the $z$ axis ignoring points outside it. For points along $z$ I think it is saying, there are no components of the magnetic field along $x$ and $y$. $B_y = B_x = 0$. $\endgroup$ Commented Oct 4, 2020 at 11:29
  • $\begingroup$ indeed, and it follows from the cylindrical symmetry about the z axis. $\endgroup$
    – hyportnex
    Commented Oct 4, 2020 at 11:32
  • $\begingroup$ why Does it limit the treatment to a particular axis and does not consider as well points on $xy$ plane for example? $\endgroup$ Commented Oct 4, 2020 at 11:34
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    $\begingroup$ everywhere else off axis the result of integration is a nasty elliptic integral not expressible in elementary functions $\endgroup$
    – hyportnex
    Commented Oct 4, 2020 at 11:37

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