Analysis of the magnetic field in space of an infinitely long current-carrying solenoid of arbitrary cross-section

A solenoid is composed of a long straight wire wound into a densely arranged helical coil. The magnetic field inside the infinite-length densely wound current-carrying downstream solenoid can be found out by the limiting method, but the magnetic field outside the tube is not discussed in detail in many textbooks. This paper analyzes and demonstrates the distribution of the external magnetic field of the infinite-length densely wound current-carrying solenoid according to the Biot-Saval's law and the Ampere's Loop Theorem.