  The longitudinal current density induced by the inhomogeneous electric field
in the hot magnetized quark-gluon plasma has been investigated and utilized in
obtaining the conductivity of the medium. The analysis has been done in the
regime where inhomogeneity of the field is small so that the collision effect
could be significant. The modeling of the QCD medium is based on a
quasiparticle description where the medium effects have been encoded in the
effective quarks, antiquarks and gluons. The temperature dependence of the
linear longitudinal current density (in terms of the electric field) and the
additional components of current density due to the inhomogeneity of electric
field (in terms of its derivatives) have been obtained by solving the
$(1+1)-$dimensional effective covariant kinetic theory with a proper collision
term. The conductivity has been obtained from the current density in the
presence of the inhomogeneous field. The collisional aspects of the medium have
been captured by including both thermal relaxation approximation and the
Bhatnagar-Gross-Krook collision kernels in the analysis. Further, the hot QCD
medium effects and higher Landau level contributions to the current density and
the conductivity have been investigated. It has been seen that the effects of
inhomogeneity of the field and the mean field corrections to the current
density and the conductivity are more visible in the temperature regions which
are not far from the transition temperature.
