The magnetic induction of round curl with current J depends on radial variable r as B := (R*J/(2*Pi))*mu0*ln((sqrt(r)+sqrt(R))/(-sqrt(r)+sqrt(R)))/((R+r)*sqrt(R*r)) where R is the ring radius. The wire has zero width. If we tend the R to infinity and replace r by R-z with z being the distance between the probe point to the wire then we should receive the magnetic field of direct infinite wire. But we receive 0. What is the matter?
Thanx
You mean the magnetic field from a thin radius-R circular, planar wire, as measured in the plane of the circle? From where did you get that formula? It does not look correct.
The field can be evaluated from the Biot-Savart law. The result involves the complete elliptic integrals K(x) and E(x), where x=4rR/(R2 + r2 + z2). In the plane of the circle, z=0. But this does not reduce the elliptic integrals to more elementary functions.
The correct result does reproduce your expected limiting behaviour.
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