Solenoids and Toroids

An infinitely long coil (a.k.a solenoid) with n turns/unit length contains a constant, uniform magnetic filed with magnitude

The direction is along the axis of the coil.

A toroid is coil that is wrapped in a circle. The magnetic field is azimuthal along the axis of the toroid with magnitude

where N is the total number of turns and r is the distance from the center.