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)


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)


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 = μo n2 A / (l + 0.45 d)                       (3)


μo = permeability for vacuum µ0 = 4π 10−7 H/m ≈ 1.2567 10−6 H/m

A = cylinder cross section area (m2

n = number of wire turns

l = length of coil (m)

d = diameter coil (m)

The equation is valid for l > 0.5 d.

Related Topics

  • Electrical - Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors

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