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The two books I know about electromagnetism do not provide the derivation of the general expression of the magnetic field near a cirular loop. Perhaps because they are introductory books. The names of the books are Purcell, Electricity and Magnetism and Griffiths, Introduction to Electrodynamics.

I have tried internet too, but without finding anything.

I am looking for this general expression, because it is a prerequisite expression in the proof, proving that the magnetic field outside an ideal solenoid is zero.

Do you have some advanced book reference, where I could find the derivation of the circular wire magnetic field?

PS: I should specify that I have an intermediate level (not advanced at all).

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    $\begingroup$ see "the Jackson", section 5.5 $\endgroup$
    – hyportnex
    Commented Oct 9 at 14:17
  • $\begingroup$ Related: physics.stackexchange.com/q/142419/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Oct 9 at 18:06
  • $\begingroup$ Note that the fields outside an infinite solenoid is zero regardless of the solenoid's cross section; see my answer here. So knowing the field for a circular coil isn't necessary to prove that the field outside an infinite solenoid vanishes. $\endgroup$
    – Michael Seifert
    Commented Oct 12 at 13:15

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