# Inductance

## Electro Magnetic Field - *EMF* - induced into a circuit

Inductance is a property of an electrical conductor by which a change in current flowing through it will induces an electromagnetic field - *EMF (e.m.f.) - *and an electromotive force in the conductor itself and in nearby conductors by mutual inductance.

The unit of inductance is *henry *- *H. *

A circuit has an inductance of* one henry *when an e.m.f. of *one volt* is induced by a current changing at the rate of *one ampere per second*.

The induced electromagnetic field - *EMF* - in a coil can be expressed as

E = -n dΦ / dt (1)

where

E = electromagnetic field - EMF (volts)

n = turns

dΦ = change in flux (webers, Wb)

dt = time (s)

Alternatively, the induced electromagnetic field - *EMF* - in a coil of inductance *L *can be expressed as

E = -L dI / dt (2)

where

L = inductance (henrys, H)

dI = change in current (amperes)

dt = time (s)

### Example - Inductance

The *EMF* induced in a coil with *500 turns* with a change of flux of *30 mWb* in *30 ms *can be calculated as

E = -500 (30 10^{-3}Wb) / (30 10^{-3}s)

= -500 Volts

### Coil Inductance

For an air filled cylindrical wire coil the inductance can be calculated with the empirical formula

*L = μ _{o} n^{2} A / (l + 0.45 d) (3)*

*where *

*μ _{o} = permeability for vacuum µ_{0} = 4π 10^{−7} H/m ≈ 1.2567 10^{−6} H/m*

*A = cylinder cross section area (m ^{2}) *

*n = number of wire turns*

*l = length of coil (m) *

*d = diameter coil (m)*

The equation is valid for *l > 0.5 d*.

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