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# Re: [femm] inductance/flux calculations in 2D/3D

- To: femm@yahoogroups.com
- Subject: Re: [femm] inductance/flux calculations in 2D/3D
- From: David Meeker <dmeeker@foster-miller.com>
- Date: Tue, 10 Jul 2001 10:14:56 -0400
- Organization: Foster-Miller, Inc.
- References: <25585.994768825@www46.gmx.net>

corneliuspaul@gmx.de wrote:

> OK Dave, many thanks for the advice.
> I tried out some configurations and it really seems to work
> in practice and I am ready to accept it as the "basic rationale"

> Although I still have difficulties understanding WHY it is like that.
> A very simple hypothetical experiment:

> - take a core with a quadratic cross section

> - wind a one turn coil around it. that is, this coil consists of
> 4 wires, each on every side of the core

> - now every wire produces a H-Field around it H = I/(2*pi*r)
> where r is the distance from the wire surface, I is current

> - if the core is of linear material then B = mu * H

> - flux = integrate B over cross section

> THIS IS WHY I "FEEL" EVERY ONE OF THE 4 WIRES PRODUCES ONE FOURTH
> OF THE INDUCTION OR FLUX IN THE CORE.

> WHERE DOES "the only parts of the wire that actually "drive" flux are those

> that get encircled by the flux path" COME FROM???

> what am I missing ?

Why, this is just a statement of Ampere's Loop Law:

| ó (ç) õ | (B/m) ·dl = | ó õ |  | ó õ | J ·dA

The left-hand side is the line integral of magnetomotive force drop on a path around the core. The right-hand side is then the current that is enclosed by the path. The end-turns aren't enclosed by this path (i.e., each turn in the coil contributes only once to the integral on the right-hand side, not once for each side of the coil). You can draw paths that loop around the end turns, but they typically traverse a lot of air and don't add much flux (they are high-reluctance flux paths and the left-hand side integral is dominated by the parts of the flux path in air because of it low m).

I think what is playing games with your intuition is that the "H = I/(2*pi*r)" formula only works for a wire in air, not for problems that have iron.

Dave

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- References:
  - inductance/flux calculations in 2D/3D
    - From: corneliuspaul@gmx.de

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