Finite Element Methods (FEM) are increasingly being used to facilitate the study, design and solving of complex engineering problems. However, in more classical fields such as physics, the analytical aspect of problem solving is sometimes the only angle taken by authors and teachers in the context of academic courses. Electric and magnetic fields are often seen as abstract constructs that are difficult to grasp for some students. The goal of this paper is to show how the use of FEM software can help improve the learning experience in the area of electromagnetics. Case studies are reported to show three main benefits offered by such tools: providing a means of visualizing abstract notions such as vector fields, allowing the treatment of cases that have no analytical solution, and facilitating the exploration of modifications to design parameters.