Re: Equivalent lumped inductance and toroidal coils

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Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 

Hi Paul,

Yes, R=0 is a problem if you assume all the current is all concentrated at
R=0.  The wire has a radius (Rs) and you can calculate the H field at the
surface of the wire (call this Hs).  At DC, the current density will be
uniform within the conductor and the H field will decrease linearly from Hs
to 0 as the radius is decreased from Rs to 0.  At TC frequencies, skin
effect will come into play and the current density will drop as the radius
is decreased from Rs to 0.  One could incorporate the skin effect into the
current density or neglect the contribution from inside the wire depending
on how accurate you wanted to get.

Gerry R.

 > Original poster: "Paul Nicholson" <paul-at-abelian.demon.co.uk>
 >
 > The difficulty comes with the self inductance - some of the sample
 > points approach the source wire so R tends to zero in the
 > denominator in the integral for H.   Antonio mentioned a trick
 > by Maxwell to get around this:
 >
 >  > Self-inductances can be calculated as the mutual inductance between
 >  > two toroidal coils placed at a certain distance, that depends on the
 >  > radius of the wire (Maxwell's gmd method)
 >
<snip>
 >
 > Of course, in the numerical solutions, you still have the problem
 > of R=0 when the source and sample elements are the same.  Your only
 > recourse is to replace this contribution to the integral with the
 > closed form value for the self inductance of the element, or to
 > apply Maxwells trick.
 >