  We calculate the lowest-order corrections to the static potential for both
the generalized Born-Infeld Electrodynamics and an Euler-Heisenberg-like model,
in the presence of a constant external magnetic field. Our analysis is carried
out within the framework of the gauge-invariant but path-dependent variables
formalism. The calculation reveals a long-range correction ($
{\raise0.7ex\hbox{$1$} \mathord{\left/ {\vphantom {1
{r^5}}}\right.\kern-\nulldelimiterspace} \lower0.7ex\hbox{${r^5}$}}$-type) to
the Coulomb potential for the generalized Born-Infeld Electrodynamics.
Interestingly enough, in the Euler-Heisenberg-like model, the static potential
remains Coulombian. Therefore, contrary to popular belief, the quantized
truncated action and the truncated quantized action do not commute at all.
