Vector Field Platform for Visualizing Electric and Magnetic Fields in Matter using Mathematica

Vector fields can be used to represent physical quantities in various area of physics, including gravitational field and electromagnetic field with vector differential operators. As this involves abstract, three-dimensional fields that are sometimes very difficult to visualize, electromagnetism in matter can be rather conceptual. A visual representation of abstract vector fields in matter is invaluable to students or researchers working in this field and helps teachers to teach electromagnetism to physics or engineering students. We visualized the most fundamental concepts of electromagnetic vector fields: E = −∇ϕ, D = E, B = ∇× A, H = −∇φ ∗ , and B = μH , all of which were calculated using the vector differential operators in Mathematica. This visualization based on vector calculations can be used as a starting platform for exploring electromagnetic vector fields.