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Re: [TCML] Re: Re: Spark models, revisited



On 10/25/12 5:13 AM, Udo Lenz wrote:
Kurt Schraner wrote:

This thread is really interesting. Would be nice, to have a formula for
spark capacitance, relevant for TC's. Antonio's appoach seems very
convincing, because it only relies on basic physics law's and the
model of
a transmission line. May be, the transmission-line model can be
questioned for this case. On the other hand, the formulas given in
Wikipedia
http://en.wikipedia.org/wiki/Capacitance seem well established. I see kind
of a dilemma.

I think Antonio's transmission line approach is correct. Along a straight
wire, capacitance and inductance conspire in such a way to make the
velocity equal to c.
I do have a problem with his assumption of the inductance of 1uH/m
being mostly independent of the radii we consider here.


It's really like that.. inductance is weakly dependent on diameter of the conductor. The original work in the area was done by E.B. Rosa at NBS. The book/report is online (I can't recall where.. but hunting for it will find it)

Here's a sort of qualitative explanation why.

Consider a small long wire.. It has an inductance of X.

Now, consider another parallel wire just like it, at some large distance away. It too has an inductance of X.

Put them in parallel. The inductance is X/2. Now start bringing them closer together.

The magnetic field from wire 1 starts to interact with wire 2, so the mutual inductance gets larger. In the limit, when they are co-located, the mutual inductance is large enough that the parallel combination has inductance X, again.

A large diameter wire is like a number of smaller wires all in parallel and close to each other.

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