BYOE: Building Robust VR Learning Environments: Best Methods to Visualize divergence-free Vector Fields

Alex Shaffer; Raluca Ilie

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Conference: 2025 ASEE Annual Conference & Exposition
Location: Montreal, Quebec, Canada
Publication Date: June 22, 2025
Start Date: June 22, 2025
End Date: August 15, 2025
Conference Session: ELOS Technical Session 5: BYOE (Bring Your Own Experiment): Innovative Tools and Techniques for Experiential Engineering Education
Tagged Division: Experimentation and Laboratory-Oriented Studies Division (DELOS)
Page Count: 8
DOI: 10.18260/1-2--56047
Permanent URL: https://peer.asee.org/56047
Download Count: 7

Paper Authors

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Alex Shaffer University of Illinois at Urbana - Champaign

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Raluca Ilie University of Illinois Urbana-Champaign orcid.org/0000-0002-7305-2579

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Prof. Ilie is an Assistant Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign. Her primary research is the development and application of high-performance, first principles computational models to describe and predict the conditions in near-Earth space leading to geomagnetic storms.
Prof. Ilie’s research focus is on developing new approaches to study the dynamics of plasmas and electromagnetic fields in the geospace environment, and to advance the predictive capabilities of the complex dynamics occurring in the solar wind-magnetosphere-ionosphere system. She combines both theoretical and observational work to develop predictive tools that form the basis of operational warning systems and hazard mitigation.

Prof. Ilie has been recognized as an emerging leader in education by her selection to the Strategic Instructional Innovations Program, to develop Virtual reality (VR) simulations and learning environments to support student learning for electrical engineering courses.

Prof. Ilie earned her Ph.D in Space and Planetary Physics from the University of Michigan and has been an NSF Postdoctoral Fellow at Los Alamos National Laboratory. As part of the Center for the Space Environment Modeling at University of Michigan, she was a core member of the software developing team for the Space Weather Modeling Framework. She is a recent awardee of the NSF CAREER, NASA Heliophysics Early Career Investigator and Air Force Young Investigator Program awards.

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Abstract

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.

Citation
Format

Shaffer, A., & Ilie, R. (2025, June), BYOE: Building Robust VR Learning Environments: Best Methods to Visualize divergence-free Vector Fields Paper presented at 2025 ASEE Annual Conference & Exposition , Montreal, Quebec, Canada . 10.18260/1-2--56047

TY - CPAPER
AB - The theory of electromagnetism (E&amp;amp;M), encapsulated in the four Maxwell&#39;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&#39;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&#39;s method, Heun&#39;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&#39;s law for electrodynamics, as they can be adopted to build VR experiences to visualize other physical phenomena for educational purposes.
AU - Alex Shaffer
AU - Raluca Ilie
CY - Montreal, Quebec, Canada
DA - 2025/06/22
PB - ASEE Conferences
TI - BYOE: Building Robust VR Learning Environments: Best Methods to Visualize divergence-free Vector Fields
UR - https://peer.asee.org/56047
DO - 10.18260/1-2--56047
ER -