A novel exact analytical expression for the magnetic field of a solenoid

Abstract

In this paper we present the analytical calculations to derive the magnetic field of a solenoid by solving exactly a fractional integral with the use of a novel method. Starting from the Biot-Savart law, we consider a coil of negligible thickness with a stationary electric current. We derive the expressions of the on- and off-axes magnetic field components. The results have been compared to some simplified and known analytical formulae as well as to a commercial numerical code showing a good agreement.

Keywords:

• Particle acceleration
• linear accelerators
• accelerator applications
• accelerator subsystems and technologies
• mathematical physics

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Instituto Nazionale di Fisica Nucleare.