Magnetic field of a loop with a stationary current in a xy plane with center in the origin is usually computed on the z axis. Out of the z axis the calculation results into elliptic integrals. I would like to know whether some geometric analysis of the fields' behavior out of this axis is known. More specifically, whether a torus (having its 'equator' in xy plane) may be an integral surface of the field. Thinking about symmetry of the problem, it should be sufficient whether a circle in xz or yz having its origin on the loop plane is a possible integral curve. Thus, the question title ''Force Lines...''
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... having its origin on the loop (source of the magnetic field) is a possible integral curve. [The word plane is misleading, loop plane. Should be loop simply.] – Svata Mar 19 '17 at 17:36