Space-time computation and visualization of the electromagnetic fields and potentials generated by moving point charges

We present a computational method to directly calculate and visualize the directional components of the Coulomb, radiation, and total electromagnetic fields, as well as the scalar and vector potentials, generated from moving point charges in arbitrary motion with varying speeds. We explicitly calculate the retarded time of the point charge along a discretized grid which is then used to determine the fields and potentials. Our computational approach, implemented in Python, provides an intuitive understanding of the electromagnetic waves generated from moving point charges and can be used in conjunction with grid-based numerical modeling methods to solve real-world computational electromagnetics problems. The method can also be used to help students visualize problems related to moving potentials, which are often only treated analytically for very simple problems, and can be used to compute electromagnetic sources for non-trivial electron beams with other approaches in computational electromagnetics.