As is shown in "The Secret
of Coulomb's Constant" page Coulomb's constant is equal to:
(1.1)
From this, inductance can be defined as:
(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 in reference to Coulomb's constant. Wheeler's formula (for
the inductance of an air core solenoid coil) outputs inductance in terms of
thousand inches.
(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 the Coulomb's
constant formula requires. So if the units of Wheeler's formula are
converted to meter and the two formulas are combined then:
(1.4)
and this can be simplified to:
(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:
(1.6)
where the values are Coulomb's
constant, light speed, permeability, and permittivity.
A practical simplification of the this formula is:
(1.7)
where the value N is a number, and R and H are in inches, and
the result is in henry.
If you use MathCAD or another program that automatically
converts inches to meters then use equation (1.8):
(1.8)
If you're looking for an inductance formula where the input is
in meters instead of inches, you can use this formula:
(1.9)
Formula (1.9) can be used for either solenoid or flat spiral
coils. For flat spiral coils use the average radius for R and the width of
the coil windings for H. Both R and H are in meters. N is the number
of turns.
