The exact electron factorization formalism can be adopted on ground and excited states likewise and naturally distinguishes components of the effective potential that depend on slowly-varying features of the quantum state, which are typically easier to model, from those that are instead responsible for peaks and steps, which are important to generate a correlated density. Therefore, it seems a priviledged standpoint to devise approximations that can model such stark features for ground as well as for excited states. Nonetheless, for the latter, it is important to consider not only the scalar potentials generating peaks and steps but also the role of the mentioned vector potential. This work offers a first study in this direction by showcasing a simple example of the electronic vector potential associated with a complex current-carrying state.