  The effects of the Ohmic and magnetic density currents are investigated in
the linearized Euler-Heisenberg electrodynamics. The linearization is
introduced through an external magnetic field, in which the vector potential of
the Euler-Heisenberg electrodynamics is expanded around of a magnetic
background field, that we consider uniform and constant in this paper. From the
Euler-Heisenberg linearized equations, we obtain the solutions for the
refractive index associated with the electromagnetic wave superposition, when
the current density is ruled by the Ohm law, and in the second case, when the
current density is set by a isotropic magnetic conductivity. These solutions
are functions of the magnetic background $({\bf B})$, of the wave propagation
direction $({\bf k})$, it also depends on the conductivity, and on the wave
frequency. As consequence, the dispersion and the absorption of plane waves
change when ${\bf B}$ is parallel to ${\bf k}$ in relation to the case of ${\bf
B}$ perpendicular to ${\bf k}$ in the medium. The characteristics of the
refraction index related to directions of ${\bf B}$ and of the wave
polarization open a discussion for the birefringence in this medium.
