Formula: Inductance of Two Current-Carrying Wires Distance Length Radius
$$L ~=~ \frac{\mu_0 \, l}{\pi} \, \left[ \frac{1}{2} + \ln\left(\frac{d-R}{R}\right) \right]$$
$$L ~=~ \frac{\mu_0 \, l}{\pi} \, \left[ \frac{1}{2} + \ln\left(\frac{d-R}{R}\right) \right]$$
$$d ~=~ R\, \left[ \exp\left( \frac{\pi \, L}{\mu_0 \, l} \right) + 1 \right]$$
$$l ~=~ \frac{\pi \, L}{\mu_0} \, \left[ \frac{1}{2} + \ln\left(\frac{d-R}{R}\right) \right]^{-1}$$
$$R ~=~ \frac{d}{\exp\left( \frac{\pi \, L}{\mu_0 \, l} \right) + 1}$$
Inductance
$$ L $$ Unit $$ \mathrm{H} = \frac{ \mathrm{Vs} }{ \mathrm{A} } $$
Inductance of two current-carrying wires whose currents flow in opposite directions. The wires are inductively coupled.
Distance
$$ d $$ Unit $$ \mathrm{m} $$
Distance between the two wires.
Length
$$ l $$ Unit $$ \mathrm{m} $$
Length of one conductor. The two conductors have the same length.
Radius
$$ R $$ Unit $$ \mathrm{m} $$
Radius of a cylindrical wire.
Vacuum permeability
$$ \mu_0 $$ Unit $$ \frac{\mathrm{Vs}}{\mathrm{Am}} = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A}^2 \, \mathrm{s}^2 } $$
The vacuum permeability is a physical constant and has the following experimentally determined value:
$$ \mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}} $$