# 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

```Vcoil = -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:

```Vcoil = L di/dt
```

## References

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