On the Magnetic Field of a Finite Solenoid

The magnetostatic field of a finite solenoid with infinitely thin walls carrying a dc current oriented in the azimuthal direction is calculated everywhere in space in terms of complete elliptic integrals by direct integration of the Biot–Savart law. The solution is particularized near the solenoid axis and in the midplane perpendicular to the axis obtaining expressions that agree with some typical approximations that are made in introductory courses of electromagnetism or in the technical literature. The range of validity of these approximations has been studied comparing them with the obtained general expression.