# Inductance of toroidal shell

1. May 25, 2010

### borsuk

I've got the probem with determination the formula of inductance in the toroidal coil.
This coil has a shape of toroidal shell (like one torus inside the second).
1 torus: (x-R0)^2-y^2=r1^2
2 torus: (x-R0)^2-y^2=r2^2

The shell is a magnetic material with given permeability "ur".

The winding is put inside the shell and the current direction is parallel with the lenght of the shell (2*3.1415*R0).

I've tried to determine the elementary flux in the core and integrate it in the whole geometry, but my results are not proper.

The main problem is that in this case of magnetic circuit the way of the magnetic flux is perpendicular to the

winding and is a parallel to the cross section of the shell while the cross section of the coil is along the

current direction. The magnetic field is only outside of the winding (in the shell magnetic core).

How can I deduce the formula of the self inductance of this type of coil? Which type of coordinet system should be

used (cylindrical or spherical)?

in advance thanks for the suggestion.

borsuk