2025 ASEE Annual Conference & Exposition

The theory of electromagnetism (E&M), encapsulated in the four Maxwell's equations, is at the core of Electrical Engineering. Understanding the abstractions built into these laws of physics requires the ability to visualize these vector fields and their interactions in a 3D environment.

Therefore, field line visualizations are fundamentally important for the purposes of building intuition regarding Ampere's law and any vector fields in general. However, the divergence-free property of the magnetic field introduces additional complexity when numerically tracing the magnetic field lines.

The methods by which field line visualizations are made in real-time can be complex, and different approaches must be used to handle different electromagnetic systems. This paper discusses the implementation of various visualization techniques that are performing well on VR platforms as well as how they impact student understanding. These visualizations are embedded into immersive virtual environments. Students participate in a narrative featuring the visualizations and take part in an assessment within the environment to measure their understanding.

This study focuses on the two main systems, those consisting of infinitely long current-carrying wires and those containing circular current-carrying wire loops. To visualize the magnetic field sourced by a distribution of infinitely long wires, it is possible to use numerical integration techniques such as Euler's method, Heun's method, and higher-order Runge-Kutta methods. However, this is further complicated by the fact that the differential equations being solved are stiff, affecting the stability of different integration techniques. For the case of wire loops, closed-form equations for the magnetic field at arbitrary points in space are computationally expensive and unfit for use on VR platforms. Therefore, it is necessary to employ approximate computational methods that yield qualitatively appropriate solutions for magnetic field line tracing.

This study also explores the domain of applicability for these visualization techniques that not only can be applied to visualize magnetic fields but any other vector fields that are divergence-free (i.e. incompressible flows in fluids of plasmas). Therefore, the application of these methods goes beyond Ampere's law for electrodynamics, as they can be adopted to build VR experiences to visualize other physical phenomena for educational purposes.