David Thomson's Coil Formula

As is explained in the Aether Physics Model, Coulomb's constant is equal to:

\(k_{C} = \frac{c \cdot Cd \cdot \mu_{0}}{\epsilon_{0}}\)

From this, inductance can be defined as:

induct2(1.2)

In equation (1.2) 1 meter equals 1 Henry.  .003 meter equals 3 mH, and so on.  The relationship of length to inductance is clearly shown by Coulomb's constant.  Wheeler's formula (for the inductance of an air core solenoid coil) outputs inductance in thousand inches. 

induct4(1.3)

where N is the number of turns, R is the radius in inches, and H is the length of windings in inches.

Equation (1.3) outputs in length, just what Coulomb's constant formula requires.  So if the units of Wheeler's formula are converted to meters and the two formulas are combined, then:

induct5(1.4)

And this can be simplified to:

induct6(1.5)

The values and units generated in equation (1.5) are accurate to the same degree as Wheeler's formula for inductance since it incorporates Wheeler's formula unchanged.  The exact value of Cd is equal to:

induct7(1.6)

the values are Coulomb's constant, light speed, permeability, and permittivity.

A practical simplification of the formula (1.5) is:

induct8(1.7)

where the value N is a number, R and H are in inches, and the result is in Henry.

If you use MathCAD or another program, which automatically converts inches to meters, then use equation (1.8):

induct9(1.8)

If you're looking for an inductance formula where the input is in meters instead of inches, you can use this formula:

induct10(1.9)

Formula (1.9) can be used for solenoid or flat spiral coils.  For flat spiral coils, use the average R radius and the coil windings width for H.  Both R and H are in meters.  N is the number of turns.