The Biot-Savart-Laplas law.

Or in the vector form   
Calculation of a field for two-dimensional case (plane XZ) is made under formulas:

The module of a radius-vector from an element of a current in a point of supervision

It is visible, that at a conclusion of the equation of a vector field, there is an elliptic integral of the second sort [ ds = f (j) ]. It cannot be expressed in elementary functions for simple numerical calculations.

For simplification of calculations we shall accept:
- System factor k = 1;
- Radius of approximated sphere R = 1 (further Rs = 1).
Δl we shall designate, as Δs (Δ s = R•Δj = Δj ).

The initial data:

Radius of approximated CHC	Rs = 1
Quantity of strings of a current	NL = 400	n = 0.. NL - 1
An angular step between strings	Δq = 2 × p / NL
Quantity of elements of a current	NΔl = 200	m = 0.. NΔl - 1
An angular step centre to centre elements	Δj = p / NΔl
Number of points of supervision	Na = 100	a = 0.. Na - 1
Coordinate of "X" points of supervision	s(a) = a×( R / Na )
A superficial current	Is = 1
A current in a string	i = Is / NL

Because of axial symmetry of system pays off only tangential, q-component of MF.
In a considered case it is an Y-component, that is designated in Mathcad, as an index ( ₁) at vector product.

Accuracy of approximation of CHC can be increased by more quantity of strings of a current.

NL = 1000;  NΔl = 1000

NL = 2000;  NΔl = 2000

NL = 5000;  NΔl = 5000

In this case, accuracy of the account is sufficient to believe result authentic.
Check by  BASIC  confirms calculation. File sphere.bas

In practice as more as possible exact approximation of electromagnetic properties of CHC on distance (0 ÷ 0.85) R from the center is interesting.
On the schedule it is visible, that the initial data satisfy to this condition.

Calculation of a magnetic field from bringing conductors 1 and 1a  along axis . Is = I LC .

     Number of elements of splitting of a bringing conductor      z:= 0..NDL - 1