Exploring the magnetic field of Helmholtz and Maxwell coils: a computer-based approach exploiting the superposition principle

Abstract

Teaching magnetism is one of the most challenging topics at undergraduate level in programmes with scientific background. A basic course includes the description of the magnetic interaction along with empirical results such as the Biot-Savart law's. However, evaluating the magnetic field due to certain current carrying system at any point in space is not an easy task, especially for points in space where symmetry arguments cannot be applied. In this paper we study the magnetic field produced by both Helmholtz and Maxwell coils at all points in space by using a hybrid methodology that combines the superposition principle and an analytical result. We implement a computational approach, that is based on iterating n times the magnetic field produced by a finite current-carrying wire, to evaluate the magnetic field at any point in space for coils arrangements without using advanced calculus. This methodology helps teachers and students to explore the field due to systems with different levels of complexity, combining analytical and computational skills to visualize and analyse the magnetic field. After our analysis, we show that this is an useful approach to emphasize fundamental concepts and mitigate some of the issues that arise when evaluating the magnetic field for systems proposed in introductory physics textbooks.

The Magnetic field for an n-cusped Epi-and Hypo-Cycloids loop current

“…The present work is intended to serve as an example for future attempts to evaluate the magnetic field in non-standard cases using the BS law. A different approach to calculate the magnetic field of a loop at any point of space using a regular n-sided polygon and the superposition principle is discussed in [19].…”

PT Symmetry-Based AUV Dual Transmission Coil Wireless Power Transfer System Design

“…It places the receiving coil in a double transmitting coil. The receiving coil is placed in a strongly coupled region with uniform and concentrated magnetic induction lines, effectively improving the robustness of the PT symmetric WPT [25]. The magnetic fields generated by the Helmholtz and Maxwell coils at various points in space are investigated using a hybrid approach combining superposition principles and analytical results.…”

Design and Development of a Helmholtz Pair System for Production of a Low-Magnetic Field of up to 7.5 mT

“…Magnetic fields generated by each coil system (2-coil, 3coil, 4-coil) were calculated using MATLAB with a fixed mesh size of 2 mm and solving the general magnetic vector potential equations [28]. The magnetic field vector for a single winding was calculated by the superposition principle as well as the net magnetic field [29].…”