Capacitors are useful circuit elements because they store potential energy $U_{\text{C}}$ in the electric field. Similarly, a coil of wire can be a useful circuit element because it stores energy in the magnetic field. In circuits, a coil is called an inductor because, as you’ll see, the potential difference across an inductor is an induced emf. An ideal inductor is one for which the wire forming the coil has no electric resistance. The circuit symbol for an inductor is .

We define the inductance $L$ of a coil to be its flux-to-current ratio:

Strictly speaking, this is called self-inductance because the flux we’re considering is the magnetic flux the solenoid creates in itself when there is a current. The SI unit of inductance is the henry, named in honor of Joseph Henry, defined as

Practical inductances are typically millihenries $(\text{mH})$ or microhenries $(\mu \text{H})$.

It’s not hard to find the inductance of a solenoid. In Chapter 29 we found that the magnetic field inside an ideal solenoid having N turns and length l is

The magnetic flux through one turn of the coil is ${\text{Φ}}_{\text{per }\text{turn}}=AB$, where A is the cross-section area of the solenoid. The total magnetic flux through all N turns is

Thus the inductance of a solenoid, using the definition of Equation 30.31, is

The inductance of a solenoid depends only on its geometry, not at all on the current. You may recall that the capacitance of two parallel plates depends only on their geometry, not at all on their potential difference.