Inductance

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 = μ₀IN/l

where I is current, N is the number of turns of the wire, l is the length of the wire, and μ₀ 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
  = -μ₀AN/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 = -μ₀AN²/l di/dt

Inductance (L) in henrys is given by

L = -μ₀AN²/l

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

V_coil = L di/dt

References

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