The application of Faraday's law to calculate the voltage induced in the toroid is of the form
This can be used with the magnetic field expression above to obtain an expression for the inductance.
This is a single purpose calculation which gives you the inductance value when you make any change in the parameters.
Small inductors for electronics use may be made with air cores. For larger values of inductance and for transformers, iron is used as a core material. The relative permeability of magnetic iron is around 200.
This calculation is approximate because the magnetic field changes with the radius from the centerline of the toroid. Using the centerline value for magnetic field as an average introduces an error which is small if the toroid radius is much larger than the coil radius.
Magnetic field concepts