Analytical Study of Magnetic Flux Density for Circular Spiral and Square Spiral Coils

This paper analyses different types of coil systems to produce volumes of uniform magnetic field. The square spiral coils are easier to implement than the circular ones. In this paper, a new analytical calculation for magnetic flux density of the spiral coils is presented, which is simpler than the greenhouse method. This paper presents a comparative study of the magnetic field distribution for circular and square coils. The magnetic flux density is obtained using the Biot- Savart's law, furthermore a detailed analysis is performed in order to obtain simple mathematical expressions that relate the area, with uniform magnetic field, to the length of the different coils and number turns of the coils. Two adaptations of the Biot- Savart's law are developed in this paper which offer a means of calculating the flux density given the position of interest, the coil geometry, and the amount current passing through the coil. The calculation of the magnetic flux density using analytical formulas and finite element simulations are compared. Finally, a cube volume of uniform magnetic field in each coil is calculated. In this paper magnetic flux densities are determined for different currents at various locations for circular coil as well as square coil. Computational models are constructed and simulated using ANSYSS Maxwell software in order to validate the calculated results of the magnetic field distribution of each geometry considering similar parameters.