The CUBE Virtual Reality Immersion

TL;DR

The CUBE paper presents a Unity-based VR tool that visualizes electromagnetic fields around a moving charge to build intuition for near-field geometry, radiation, and relativistic effects. It supports displaying ${\mathbf E}$, ${\mathbf B}$, and ${\mathbf S} = {\mathbf E} \times {\mathbf B}/\mu_0$ with options for magnitudes or flux through wall surfaces, and provides a separate radiation-field visualization via ${\mathbf E}_{\text{rad}}$, ${\mathbf B}_{\text{rad}}$. A speed-of-light slider enables comparisons between non-relativistic and relativistic radiation patterns, with a practical approximation $t_r \approx t$ for room-scale visualization. The work emphasizes three contributions: a 3D cubical visualization platform, explicit separation of near-field versus radiation-field dynamics, and practical implementation notes to facilitate extension and education. It also shares a public repository and outlines future directions, including spherical geometries, true retarded-time calculations, and field-line visualization, and provides a public repository for researchers and educators.

Abstract

The purpose of this note is to introduce the CUBE, a virtual reality immersion that was developed to help visualize electromagnetic fields, particularly the less familiar radiation fields students typically encounter in upper level physics courses. We discuss the pedagogical motivation for different features found in the software, and provide a brief overview of its use.

Figures (7)

• Figure 1: The menu where users select which type of field, ${\bf E}$, ${\bf B}$, or ${\bf S}$ (the Poynting vector) to display, whether to show the magnitude ($E \equiv |\bf E|$) or the flux (${\bf E} \cdot d{\bf a}$) at the wall's surfaces, and other display options.
• Figure 2: A screenshot, from outside the CUBE in the Unity editor, showing the magnitude of the electric field on the walls for a charge located at the center of the CUBE.
• Figure 3: On the left, a screenshot of the flux of ${\bf B}$ at the walls of the cube, for a charge moving down. On the right, the same screenshot for a charge moving up.
• Figure 4: On the left is a screenshot of four walls of the CUBE as a user starts moving a charge vertically in an oscillatory manner -- you can see large radiated power deposited on the walls (where $\sin\theta \approx 1$ from (\ref{['LarmorS']})), with little on the ceiling and floors. In the middle image, the same setup shown as the charge moves through an "equilibrium" position at the center of the cube, now the Poynting vector is small everywhere because ${\bf a} \sim 0$. Finally, on the right, we see the Poynting vector flux as the charge nears the top of its trajectory, where acceleration is again large (slowing to a stop).
• Figure 5: Slow uniform circular motion, on the left, has power that is perpendicular to the acceleration, and equal in magnitude in both the forward and backward direction. For a particle moving close to the speed of light (right), the power is focused in the forward direction.