# Subject: Re: Current Distribution in inductors (fwd)

```---------- Forwarded message ----------
Date: Sat, 6 Oct 2007 22:48:43 -0400
From: Jared Dwarshuis <jdwarshuis@xxxxxxxxx>
To: Pupman <tesla@xxxxxxxxxx>
Subject: Subject: Re: Current Distribution in inductors

Subject: Re: Current Distribution in inductors

Hi Jared,

I disagree that Paul made fundamental mistakes. Les to be mythical is
funny to me. You mentioned that inductance only occurs in regions of
voltage. Well, yes of course. It is current which causes the magnetic
interaction for inductance and there is no current without a potential
difference. Of course if there are two regions of potential, there will
be two regions of inductance and there will be interaction between these
two regions both inductively and capacitively dictated by their
arrangement and proximity. The two regions will have total inductive
affect across the entire coil. This is no different than Les. Les is an
"equivalent" series inductance which lumps all of these "regions"
together to derive the inductive relationship of the entire coil at it's
resonant frequency.

All Les says is that at higher frequency, the distribution of current in
"regions" of the winding are not the same throughout the length of the
winding. This is nothing new to physics. Paul did not invent this (the
physics of the universe did). Because of the current distribution along
the length of the winding, regions along the length of the winding will
have various inductances when comparing one region to another. Lump them
up into a single value, and you have Les. That's all it is. It's not
magic or a myth, it is simply a lumped value to describe the situation.
It's simply a representation of the equivalent inductance of the coil at
a specific frequency. It's no different than looking at two regions of
current distribution in a half wave coil and lumping those inductances
into their collective value.

There's really nothing here to disagree with. You can use Ldc and Cdc
for the same frequency. Intellectually, we know that Ldc and Cdc are no
longer "true" at the resonant frequency. Les and Ces are values to
describe what is real at Fr. There are probably more pieces to that
puzzle to include, but it's a very good start!

When Paul disagreed with you (early on), it is "my" opinion that it was
not out of "foolish arrogance", but simply his understanding of physics
versus your understanding of physics. In all my discussions with Paul,
I've never known him to be arrogant. He would be the first to admit a
mistake and would do it openly for all to witness. Foolish arrogance is
just not in his nature. If you had any discussions with Paul other than
the disagreements (which we all set back and read), you would understand
Paul is not as you've described.

Take care,
Bart

>Nicholson made some fundamental mistakes with his analysis, there is no
Fres
>or Fes
>these are entirely mythical.
>

>Inductance only occurs in regions of voltage. So for example if we have
>conditions where a half wave exists. we have two regions of inductance
where
>the LC response is dictated by each region.
>

- Show quoted text -

>We have pointed this out years ago and they paid no attention. ( foolish
>arrogance)
>
>Jared Dwarshuis
>
>
>
>
>
>
>

Hello Bart:

Thank you for the thoughtful response, clarifications are always a good
thing..

Inductance is the ratio of magnetic energy storage to current by definition.
Ldc as some call it would be the inductance at zero frequency.

We can take an inductor and cause; n periodic regions to form by selecting
an  appropriate frequency. Notice that periodicity means that each region is
the same in terms of region height, wire length, surface area, volume
enclosed and energy storage.

Let us define L(region) as the inductance of an individual periodic region.
Now we can write. Ldc  x Isqrd = n ( Lregion Isqrd). This is a statement of
the total energy stored in the inductor. Solving this equation shows that
Ldc = n (Lregion)

Now within the Lregion we find a maximum and a minimum voltage, we can
conclude that our self capacitance is also found in the same periodic
region.

The next issue to address is the relationship between frequency and
partitioning of Ldc. For this we will examine the results of a wire length
derivation for inductance.

It is already known that for a solenoid: E = u R N/ 2H   di/dt

We also know that V = Ed       so we can write:

V = uRN/ 2H    di/dt     distance

We also know that V = - L di/dt

Using L = n Nsqrd A / H   we find that the distance in question is (2 pi R
N) which is simply the wire length.

We also recognize that the E field is also along the entire length of wire
and write a more complete description for E as: E = u/ 4piH  x  (Wire
length)  di/dt

We can now see that the expression L = u Nsqrd A / H is equivalent to:

L = u/ 4pi H  x  (Wire length)sqrd

We can also write this as L = (wire/ C)sqrd  x 1/(4pi e H)

Waves of energy or information travel at a maximum of  C down a wire, this
becomes important when we talk about the formation of standing waves.

Since we have true periodic regions, a standing wave pattern does exist in
the inductor. We can use the mathematics of standing waves to describe the
partitioning.

Standing waves are a function of both position and time, they are composed
of two opposite traveling waves of equal amplitude and frequency. The
distance between nodes

( wavelength /2) is determined by frequency and wave propagation velocity
along the medium.

Since:  Velocity = Frequency x Wavelength

Now the regions of interest are always wavelength/4 in an inductor because
the amplitude varies from zero to a maximum in wavelength/4 regions.

I will continue part II of this discussion sometime between now and next
Saturday.