The electrostatic potential problem for boundary conditions of a box as a tool for learning electromagnetism in an undergraduate physics course

Ever since James Clerck Maxwell published his brilliant work unifying electricity and magnetism, numerous practical applications of it have arisen. This paper discusses the two- and three-dimensional electric potentials obtained from the solution of Laplace’s equation, as well as the solution to the electric and magnetic fields for the Helmholtz equation with specific initial conditions. We explain the use of the superposition theorem in a clear electrostatics example. In particular, the problem of the electric potential in a rectangular box with Dirichlet boundary conditions was studied, making an application to waveguides and resonant cavities. Mathematica software was used to obtain the plots of the potential and electric field.

Keywords
Laplace equation; electrostatic potential; rectangular boundary conditions