A device that can induce a voltage when current is changed is said to have inductance. A typical inductor is a coil of wire in the form of a solenoid. Inductance is measured in henrys which is denoted by H.

A current flowing through a conductor induces a magnetic field. In the case of a wire, coiling the wire into the form of a solenoid increases the strength of the field and we can calculate the magnetic field strength B (measured in teslas) as follows:

B = μ_{0}IN/l

where I is current, N is the number of turns of the wire, l is the length of the wire, and μ_{0} is the
permeability of free space (4×π×10^{-7} Hm^{-1} = 1.2566×10^{-6} Hm^{-1}).

A change in current leads to a change in magnetic field and an EMF is induced in the coil which opposes the change in current. We can calculate the voltage with the following:

V = -dΦ/dt = -μ_{0}AN/l di/dt

where Φ is magnetic flux and this is calculated by Φ=B×A where B is magnetic field strength, and A is the cross-sectional area of the coil.

This is the voltage induced in each turn of the wire. To calculate the total voltage induced in the coil we just multiply by N to give

V_{coil}= -μ_{0}AN^{2}/l di/dt

Inductance (L) in henrys is given by

L = -μ_{0}AN^{2}/l

So the voltage across an inductor can be more simply written as:

V_{coil}= L di/dt

Fischer-Cripps. A.C., *The Electronics Companion.* Institute of Physics, 2005.

Copyright © 2014 Barry Watson. All rights reserved.