Solenoid - Magnetic Field and Vector Potential For Finite Continuous Solenoid

Magnetic Field and Vector Potential For Finite Continuous Solenoid

A finite solenoid is a solenoid with finite length. Continuous means that the solenoid is not formed by discrete coils but by a sheet of conductive material. We assume the current is uniformly distributed on the surface of it, and it has surface current density K. In cylindrical coordinates:

The magnetic field can be found by vector potential. The vector potential for a finite solenoid with radius a, length L in cylindrical coordinates is is:

where

The, and are complete elliptic integral of first, second, and third kind.

By using

the magnetic flux density is:

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