Inductance of a simple coil


I am trying to confirm some basic quantities, before design more complicated topologies, in Maxwell 3D. So, I begun with the inductance of a simple coil, as shown below

Coil is copper, core and region vacuum and current is set to 0.1 A.

On parameters, I setup a matrix for current and in post processing I set the 20 turns

Now, from equation

L = μ0 * Ν^2*Α / L

with μ0 = 4π*10^-7, N = 20, A = 7.854e-3 and L = 0.086, inductance must be ~ 45.9 μH. But, simulation computes a value of 31.239 μΗ

Assigning a different material to core (eg ferrite), produces even worse results.

Why is this? Any suggestions? Simulation file is attached.

Thank you for your time :)

Best Answer

  • thecethece Member
    Accepted Answer

    OK, apparently I was wrong on how inductance is calculated for such a "short" coil.

    By using Wheeler's approximation formula

    L = 30.534 μH, pretty close to simulation results (with 2% error)

    I attach Wheelers' paper (which is nearly 100 years old)


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