How to Calculate Self Inductance in a Toroidal Shell Coil?

[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 length 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

 

[eljose79]

Hello borsuk,

Thank you for sharing your problem with the community. I understand that you are trying to determine the formula for inductance in a toroidal coil. This can be a complex problem, but let's break it down step by step.

Firstly, it is important to understand the basic principles of inductance. Inductance is a property of an electrical circuit that opposes changes in current. It is measured in units of Henry (H) and is dependent on the geometry and material of the circuit.

In the case of a toroidal coil, the inductance is affected by the shape of the torus, the permeability of the magnetic material, and the current direction. The formula for inductance in a toroidal coil can be calculated using the following equation:

L = (u * N^2 * A)/l

where L is the inductance, u is the permeability of the magnetic material, N is the number of turns in the coil, A is the cross-sectional area of the coil, and l is the length of the coil.

To apply this formula to your specific problem, you will need to determine the cross-sectional area of your toroidal coil. This can be done by calculating the area of the cross-section of the torus. You can use either cylindrical or spherical coordinates to do this, but keep in mind that the magnetic field is perpendicular to the winding, so the cross-sectional area should be perpendicular to the winding as well.

Once you have determined the cross-sectional area, you can use the equation above to calculate the inductance of your toroidal coil. It is important to note that this formula assumes that the magnetic field is uniform and that the winding is tightly wound around the torus.

I hope this helps guide you in determining the formula for inductance in your toroidal coil. If you have any further questions, please don't hesitate to ask. Good luck with your research!