When working with toroids, there are times when the current in the winding only helps the B field inside the toroid. This means that there is no contribution to the magnetic B field that is outside the winding. The simple answer to why this happens is found in Ampere's circuital laws. It is important to have a full understanding of your industrial application, so that you can have a full understanding of your B field.
If there is no circumferential current or axially symmetric layout, you can create the proper conditions for confining the internal B field. The B flux creates circles that remain at a constant intensity. This circle is centered on the axis of symmetry. According to Ampere's law, there must be zero intensity outside the winding. In order to maintain zero intensity, the current must be encircled within the toroidal winding.
There are common and uncommon ways to wind toroids, so it is important that your toroids meet your business' specifications. Common winding is both inside and outside the core, which disrupts the possibility to contain the B field. The inside/out winding is not symmetrical by the near region. Although at times the common toroid might look symmetric, there will always be a problem with the circumferential current. Even with incredibly thin wires, common winding cannot contain the B field. This is because all common toroids will always have at least one coil loop.
There are mathematical equations that can be performed that calculate the exact B field strength. The same equations can be used to find the E field. The only thing that needs to be known for the equation is the scalar electric potential field. Considering the intricacy of these equations, it is best to trust a professional who has experience calculating B fields. The equation has multiple steps, and so if a mistake is made at any point your final result will be wrong.
Toroid coils are used in a wide array of different industries. Different toroids produce different results, and it is important for each person to get a proper toroid. Improper toroids will either slow down business or stop it completely. The facts that you can customize size, material, core, winding all suggests that a good deal of thought must be made before purchasing. The best option is to reach out to professionals in the industry, who can help you determine exactly what you need.