FIELD OF A SOLENOID

As with Gauss’ law, Ampere’s law is most useful when we already know the field structure and wish to calculate the strength of the field. The classic example to which ampere’s law is applied is the calculation of the magnetic field of a long straight solenoid.
A long solenoid is a coil of wire in which the length L of the coil is considerably larger than the diameter d of the individual turns. The shape of the field produced when a current i flows through the coil was illustrated in Figure (1). Iron filings gave us the shape of the field and Ampere’s law will tell us the strength.
The important and useful feature of a solenoid is that we have a nearly uniform magnetic field inside the coil and nearly zero field outside. The longer the solenoid, relative to the diameter d, the more uniform the field B inside and the more nearly it is zero outside.

Figure 1: Calculating the magnetic field of a long solenoid.