# Electronics/Inductors/Special Cases

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 4

*π*×10

^{-7}H m

^{-1}.

## 1. Basic inductance formula for a cylindrical coil[edit | edit source]

*L*= inductance / H*μ*= relative permeability of core material_{r}*N*= number of turns*A*= area of cross-section of the coil / m^{2}*l*= length of coil / m

## 2. The self-inductance of a straight, round wire in free space[edit | edit source]

*L*= self inductance / H_{self}*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 self-inductance is negligible.

## 3. Inductance of a short air core cylindrical coil in terms of geometric parameters:[edit | edit source]

*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 | edit source]

*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 | edit source]

*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 cross-section)[edit | edit source]

*L*= inductance / H*μ*= relative permeability of core material_{r}*N*= number of turns*r*= radius of coil winding / m*D*= overall diameter of toroid / m