Inductance as a function of position

[Jimbo]

Hello
I am doing some research on non-linear systems, and have come across a equation regarding inductance and I am unsure how it was derived:[p]
The inductance of the electromagnet depends on the position of the magnetic material, and can be modeled as,
L(y) = L1 + L0 / (1 + (y / a))
where y is the position of the material from a reference point, and L1, L0, and a are positive constants
Is this equation an adaptation of a more fundamental equation?
I get the gist that, as the material gets further away the inductance decreases and vice versa, but am just unsure about how the equation was formed?
Thanks for any guidance
Jimbo

 

[Jimbo]

Sorry, looking at it again I think I understand:

As the position decreases the denominator will approach 1, making L0 (I assume the inductance when very close) to make the biggest impact on the L(y) value. If y was very large, the denominator would be large, limiting L0s affect on the equation.

Sorry if my post was a bit of a waste of space :(

Jimbo

 

[tacman]

Hello Jimbo,

The equation for inductance as a function of position is derived from the fundamental equation for inductance, which is L = N^2μA/l, where N is the number of turns in the coil, μ is the permeability of the material, A is the cross-sectional area of the coil, and l is the length of the coil. This equation represents the inductance of a simple, ideal solenoid.

However, in real-world systems, the inductance can vary with the position of the magnetic material. This is because the magnetic material can affect the magnetic field generated by the coil, thus altering the inductance. The equation you have mentioned is an adaptation of the fundamental equation, taking into account the position of the material.

The term L1 represents the inductance when the material is at the reference point, and the term L0/(1 + (y/a)) represents the change in inductance as the material moves away from the reference point. The constant a is a measure of how quickly the inductance changes with the position of the material.

I hope this helps to clarify the equation for you. Let me know if you have any further questions.