On magnetic field of ring current

The explicit expression for magnetic induction vector of a ring current at arbitrary point in toroidal coordinates is presented in terms of the full elliptic integral of the first kind and its derivative over integral modulus. There is a conjugated point for any observation point: it is an image of the latter in a sphere with the ring current as its equator. The conjugated point lies on the same vector and has the same integral modulus as the initial point.