Re: Speaking of resonance...

To: tesla-at-pupman-dot-com
Subject: Re: Speaking of resonance...
From: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> (by way of Terry Fritz <twf-at-verinet-dot-com>)
Date: Sat, 12 Dec 1998 12:42:06 -0700
Approved: twf-at-verinet-dot-com

Tesla List wrote:

> For one, I know the general physics surrounding inductors, but tell me
> this:  they make -- If I buy a spool of laquered copper wire and whip
> myself up a coil, would there be any other physical properties that would
> significantly deviate this coil from the ideal L = (Mu0*N^2*Area)/Length?

Yes. This formula is derived for an inductor with lenght >> radius.
A better approximation is (Wheeler): L=u0*N^2*area/(lenght+0.9*radius)
u0=4*pi*1e-7, area=pi*radius^2, length and radius in meters.

> ...Besides the thing burning up from resistance? Will an extremely long,
> thin coil wound with thick wire have the same properties of an equally
> inductive very short coil of large area and high N^2/l ratio?

At low frequency, not, but coils are actually a kind of transmission
line,
and the high-frequency effects that come from this depend on the aspect
ratio, and on how is the coil mounted relative to the ground. For a
vertically mounted coil with the lower end grounded, the first effect 
that appears is equivalent to a grounded capacitance in parallel with
the 
coil, given by (units in meters) (Medhurst):
C= 11.6*length+16*radius+76.4*(radius^3/length)^0.5 picofarads

There are other effects of smaller importance, as additional resonance 
modes and irradiation, that vary with the aspect ratio and position too.

Antonio Carlos M. de Queiroz