sci wrote:

Looking for a direct mathmatical comparison between the magnetic field
produced by an electronic current (i) and that of a fixed magnet of a
given strength.

See: http://scienceworld.wolfram.com/physics/Magnetism.html
Note the differences in
o diamagnetism
o ferromagnetism <===
o Paramagnetism

Ferromagnetism
http://scienceworld.wolfram.com/physics/Ferromagnetism.html

"The development of extremely strong magnetic properties in certain
materials which occurs when magnetic domains (regions at most 1 mm in
dimension) become aligned in the absence of an applied field, below a
temperature known as the Curie temperature. The net magnetization
depends on the magnetic history (the hysteresis effect). Above the
Curie temperature, these materials become paramagnetic. Iron, nickel,
cobalt, and gadolinium are ferromagnetic at room temperature.
Ferromagnetism is believed to be caused by magnetic fields generated
by the electrons' spins in combination with a mechanism known as
exchange coupling, which aligns all the spins in each magnetic
domain".