Electronics/Inductors/Special Cases
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This section list formulas for inductances in specific situations. Beware that some of the equations are in Imperial units.
The permeability of free space, μ_{0}, is constant and is defined to be exactly equal to 4π×10^{7} H m^{1}.
Contents
 1 1. Basic inductance formula for a cylindrical coil
 2 2. The selfinductance of a straight, round wire in free space
 3 3. Inductance of a short air core cylindrical coil in terms of geometric parameters:
 4 4. Multilayer air core coil
 5 5. Flat spiral air core coil
 6 6. Winding around a toroidal core (circular crosssection)
1. Basic inductance formula for a cylindrical coil[edit]
 L = inductance / H
 μ_{r} = relative permeability of core material
 N = number of turns
 A = area of crosssection of the coil / m^{2}
 l = length of coil / m
2. The selfinductance of a straight, round wire in free space[edit]
 L_{self} = self inductance / H
 b = wire length /m
 a = wire radius /m
 = relative permeability of wire
If you make the assumption that b >> a and that the wire is nonmagnetic (), then this equation can be approximated to

 (for low frequencies)

 (for high frequencies due to the skin effect)
 L = inductance / H
 b = wire length / m
 a = wire radius / m
The inductance of a straight wire is usually so small that it is neglected in most practical problems. If the problem deals with very high frequencies (f > 20 GHz), the calculation may become necessary. For the rest of this book, we will assume that this selfinductance is negligible.
3. Inductance of a short air core cylindrical coil in terms of geometric parameters:[edit]

 L = inductance in μH
 r = outer radius of coil in inches
 l = length of coil in inches
 N = number of turns
4. Multilayer air core coil[edit]

 L = inductance in μH
 r = mean radius of coil in inches
 l = physical length of coil winding in inches
 N = number of turns
 d = depth of coil in inches (i.e., outer radius minus inner radius)
5. Flat spiral air core coil[edit]
 L = inductance / H
 r = mean radius of coil / m
 N = number of turns
 d = depth of coil / m (i.e. outer radius minus inner radius)
Hence a spiral coil with 8 turns at a mean radius of 25 mm and a depth of 10 mm would have an inductance of 5.13µH.
6. Winding around a toroidal core (circular crosssection)[edit]
 L = inductance / H
 μ_{r} = relative permeability of core material
 N = number of turns
 r = radius of coil winding / m
 D = overall diameter of toroid / m