Inductance as a function of position

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Inductance in an electromagnet varies with the position of magnetic material, modeled by the equation L(y) = L1 + L0 / (1 + (y / a)). This equation suggests that as the material moves closer to the reference point, the inductance increases, while a greater distance reduces it. The constants L1, L0, and a are essential for understanding the relationship between position and inductance. The user expresses initial confusion about the equation's derivation but later clarifies their understanding of how the position affects inductance. The discussion highlights the importance of position in non-linear systems and the behavior of inductance in relation to distance.
Jimbo
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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
 
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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
 

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