Numerical modeling of the magnetic vector potential and the associated electromagnetic momenta

The idea that the magnetic vector potential A is associated with stored electromagnetic momenta dates back to Maxwell himself. Here, we present numerical modeling results that illustrate the connection between A and associated linear and angular electromagnetic momenta, expanding on previous work which mostly considered examples that could be analytically solved. We first focus on a stationary point charge q interacting with the magnetic fields of a solenoid, separately calculating A(r) and the electromagnetic momentum added to the system in bringing q to r from a distant location where A≈0. We then model the trajectory of q as it travels near the solenoid, tracking kinetic and electromagnetic angular momenta. We also evaluate the electromagnetic momentum associated with an extended charge distribution. The numerical modeling approach is straightforward and accessible to undergraduate students and can help them visualize the connection between theory and real-world scenarios.