# Air gap for a coil calculation [closed]

i would a help calculating the necessary air gap for a coil assuming an ideal magnetic material:
Cross sectional area of active material = 100 mm2
number of turns= 30
Inductance= 1mH

• What are your calculations or references so far? Do you know that inductance is defined as flux linkage per amp for instance? – Neil_UK Aug 12 '20 at 6:55
• Use the reactance equation, Rcore=(MLT/(ur x u0 x Ae) Rgap=(AirGap/u0 x Ae) L=Nturn/(Rcore +Rgap) you adjust the AirGap to meet 1mH. ur= core permeabilty and u0=air permeability (1.257* 10^-6) – Delphesk Aug 12 '20 at 7:36
• If you want help we need far more information than currently provided. – Andy aka Aug 12 '20 at 8:44

We could just plug numbers into the formula, but it's more instructive to do it from first principles. Then if you forget the exact form of the formula, you can re-derive it.

You've already suggested some numbers for turns and pole area, so let's do it for a specific airgap as well, say 1 mm. Inductance is inversely proportional to it (assuming perfect magnetic material), so it's easy to scale afterwards.

Inductance is flux linkage per amp.

1 amp in 30 turns is 30 Ampere.Turns. This produces an H field across a 1 mm airgap of 30 kA/m.

This produces a B field in the airgap of μ0H = 4π*10-7 * 30k = 37.7 mT

This produces a flux of B*pole_area = 37.7m * 100μ = 3.77 μW

This produces a total flux linkage of flux*turns = 113 μW

So the inductance with a 1 mm airgap would be 113 μH.

On the face of it, all we have to do is scale down the airgap from 1 mm to 113 μm to get 1 mH. However, with an airgap this small, I doubt that we could approximate the magnetic core as ideal, and so the actual gap would need to be reduced further to allow for the finite reluctance of the core.

• @csabahu Neil is right. – a concerned citizen Aug 12 '20 at 20:14
• That's the great advantage of presenting it step by numeric step, you get peer review. I'm always losing minus signs, and powers of 10! – Neil_UK Aug 12 '20 at 21:03