Abstract
This paper presents a simple, didactical and compact solution for the components of the magnetic vector potential and magnetic field generated by a circular arc filament carrying a direct current using the well-known incomplete elliptic integrals, their properties and formulas. Using a well-defined method, the expressions are obtained in Cartesian coordinates and then easily transformed to a compact expression in cylindrical coordinates. The paper provides numerical data for different study cases where arbitrary arc filaments are considered. Through Gauss' magnetic law, special cases, and comparisons with numerical methods, a degree of validation is provided for the derived expressions.These solutions represent a computational advantage for magnetic field calculations for applications like wireless power transfer. Finally, new integral formulas are derived using elliptic integrals.
Highlights
The interest for wireless power transfer (WPT) using magnetic coupling in different common applications has been booming since the Massachusetts Institute of Technology (MIT) developed a highly efficient WPT resonant system in 2007 [1]
For wireless power transmission resonant systems, the ability to measure or predict the magnetic coupling between the coils of the system is fundamental, and having expressions to compute the magnetic field generated by the coils is very useful
We derive expressions for the magnetic vector potential and magnetic field vector using incomplete elliptic integrals, and we present several integral formulas useful for magnetic field problems concerning cylindrical geometries
Summary
These kinds of expressions are specially useful because we can usually break down complex geometries into simple shapes None of these efforts have: 1.) derived analytical expressions for the magnetic vector potential and magnetic field vector of circular arc filaments carrying a direct current using only elliptic integrals, 2.) defined a didactical method to solving these magnetic field integrals and 3.) offered numerical study cases for filaments with different geometrical properties. We derive expressions for the magnetic vector potential and magnetic field vector using incomplete elliptic integrals, and we present several integral formulas useful for magnetic field problems concerning cylindrical geometries.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
