Approximate Inductance of a Toroid 环形线圈的近似电感 Finding the magnetic field inside a toroid is a good example of the power of Ampere's law. The current enclosed by the dashed line is just the number of loops times the current in each loop. Amperes law then gives the magnetic field at the centerline of the toroid as 寻找通过环形线圈内部的磁场是一个很好的例子，展示了安培定律的威力。虚线所包围的电流仅仅是每圈电流乘以圈数。安培定律则给出了环形线圈中心线处的磁场为 The inductance can be calculated in a manner similar to that for any coil of wire. 电感可以像任何线圈一样进行计算。

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.