Calculation Magnetic Field of Toroidal Inductor Wound by Rectangular Cross-Section Wire

In this article, we present two methods for calculation of the magnetic flux density of a toroidal inductor wound by rectangular cross-section wire, taking into account that the current density is inversely proportional to the circular coil radius. The first method simplifies the helical toroidal coil into a thick-walled toroidal and provides a formula for calculating the magnetic flux density of the entire space of the toroidal inductor based on Ampere's law. The first method although simple, has large errors. The second method simplifies the helical toroidal coil into a collection of self-closing circular coils and provides a formula for calculating the magnetic flux density of the plane where the center circle of the helical toroidal coil is located based on Biot-Savart Law. The second method is complex but has high accuracy. Finally, we compared and analyzed the results calculated by the two methods proposed in this article and the results calculated by the finite-element method.