# RE: Quarter Wavelength Frequency

```Original poster: Jim Lux <jimlux-at-earthlink-dot-net>

At 01:18 PM 7/12/2004 -0600, you wrote:

<snip>

>So I'm back to my original question, is there an equation that quantifies
>the resonant frequency in terms of the actions of the electrons and photons?
>And I'll state again, if the quarterwave is not the sole determinant of the
>resonant frequency because photons are carrying magnetic flux to the other
>end of the coil before the primary coil induced electrons get there, then
>photons must be influencing the resonant frequency of the coil via RF.
>There must be a way to quantify this and get a perfectly accurate resonant
>frequency formula for a Tesla coil.
>
>Dave

While, in fact, the duality of particle vs wave descriptions for EM
radiation would allow one to model or analyze a TC in terms of its particle
behavior, such a model might not be useful.

One should choose an analytical technique that provides the most insight
into the operation and function of that which you are analyzing.  We use
Ohm's Law as a model for many things because it is more convenient and
intuitive than modeling the motion of the electrons within the substances.
It's also computationally less intensive.

I suggest that for Tesla Coils, the optimum models are those based on wave
theory (i.e. Maxwell's equations).  One can either approach the problem
analytically or as a finite element type problem. Since most "real" tesla
coils are constructed in a way that does not lend themselves to simple
closed form analytical expressions (i.e. a long coil of wire in a
nonuniform (both spatial and temporal) field), numerical techniques are
probably most useful, and allow you to generate a description (i.e.
resonant frequency) that is arbitrarily precise.

Relatively few people analyze antennas in terms of photons, until you get
into the optical frequency range where the quantum energy of a photon is
significant compared to the system power, and you start to see quantization
effects.

Of course, if you wish to use particle models as an academic intellectual
exercise, then more power to you.

```