Horizontally, the axis that is used is the cylindrical coordinate radius ρ from the axis of the unit radius current loop. The axis for ρ is from 0 to 1.9 in steps of 0.1.

Vertically, the axis that is used is the positive coordinate z along the axis of the unit radius current loop. The cylindrical coordinate z is ranging from 0 to 1.1 in steps of 0.1.

For negative z coordinates, the symmetry of the problem dictates the same field strength that the point at |z| and same ρ value. For those points, the radial component of the magnetic field B

The workbook contains worksheets for every elementary algebraic calculation. The symbol ρ is spelled

To accommodate the dimensions of the standard excel cell, increasing ρ values go in consecutive rows, while increasing z values go into increasing columns.

and

where

and

Note that

I've taken the radius to be unity but obviously all the results scale if you take a different radius.

Successive iterations of the AGM are calculated in the pairs of sheet {A,B},{C,D},{E,F},{G,H},...

Successive iterations of the MAGM are calculated in {L,M,N},{O,P,Q},{R,S,T},{U,V,W},...

after four AGM/MAGM iterations, results have converged to more (often, much more) than 7 decimal places.