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  • $\begingroup$ Not clear why you suggest that for a straight wire the field would be zero. It would if you are exactly in the center, but it seems more interesting to compute the field at the surface of the wire, which case exactly is the question about? (And anyway, for the loop you can probably get some complete Elliptical integral as a result if you do the calculation.) $\endgroup$
    – Jos Bergervoet
    Commented May 5 at 14:03
  • $\begingroup$ Yes, it will be an elliptical integral, but I don't know how to interpret that. $B = const * \int_0^1 \frac{dm}{m\sqrt{1-m^2}}$,, now according to mathematica, it would never converge, but that is not the case, we should get some value of finite field at the particular point in the wire. 'm' is some substitution of $\theta$ $\endgroup$
    – Gandalf73
    Commented May 5 at 14:48
  • $\begingroup$ Maybe a definition problem? I already asked about that here: math.stackexchange.com/questions/4901060/… $\endgroup$
    – Jos Bergervoet
    Commented May 5 at 14:55
  • $\begingroup$ Please try to solve what comes to you. My approach was to take two infinitesimal lengths on the circle, Q and P, as dl, and find the r vector between them, and integrate the whole thing from 0 to $2\pi$. Thanks in advance $\endgroup$
    – Gandalf73
    Commented May 5 at 15:09
  • $\begingroup$ Is $r$ the distance to the plane of the current loop and $a$ its radius? $\endgroup$
    – my2cts
    Commented May 5 at 17:37