This paper employs Mathematica for visualizing electromagnetic fields in circular waveguides, effectively addressing pedagogical challenges related to theoretical abstraction and computational complexity. We first derive the exact solutions for guided modes, then summarize the steps for visualizing electromagnetic fields using Mathematica, propose educational strategies, and showcase simulation results. The Mathematica code is provided, allowing for dynamic parameter adjustment and real-time field change observation. This approach significantly enhances undergraduate students' understanding of...
