The B-field is classified by multiple equivalent ways, which are based on different effects on local environments. Most commonly, the magnetic field is based on the forces exerted on a charged, moving particle, but it usually loosely associated with the velocity of the particle. Lorentz Force Law allows for individuals to separate forces on particles, which helps to determine B-field.
Determining B-field allows for specialized inductors to be made. Toroid coils are great for dealing with B-fields, especially inside the inductor. Considering that the toroid has a closed circuit and symmetry from winding, a toroid is better suited than a straight inductor like a solenoid. Working with toroid winding companies allows for individuals to get toroid coils that are specialized for specific functions and devices. B-fields are not the same from device to device and so each toroid, if meant to work properly, must be completely customized based on function/purpose. The benefits of using toroids do of course have their downsides.
As a result of Ampere's circuital law and symmetry, winding a toroid only contributes to the B field inside of the winding. It doesn't make a difference in the magnetic B field that is outside of the winding.