  In Wigner function approach with relaxation time approximation, we calculate
electric and magnetic conductivities of a fermion system in the strong magnetic
field. The linear response has been calculated to the perturbation of
electromagnetic fields on the background constant magnetic field. The Wigner
function is separated into an equilibrium part in the background magnetic field
and an off-equilibrium part induced by perturbative fields. The analytical
expression for the equilibrium part and the corresponding equilibrium
conditions are given. For the off-equilibrium part, we obtain the kinetic
equation at the leading order in $\hbar$ from the master equation of the Wigner
function. When perturbative fields only depend on the proper time, the
off-equilibrium part can be analytically solved from which the vector and axial
vector currents are obtained. We obtain the longitudinal and transverse Ohm
conductivities as well as Hall conductivity as the linear response of the
vector current to the perturbative electric field. The behaviors of these
conductivities as functions of the evolving time, relaxation time, particle
mass, and strength of the background magnetic field are investigated both
analytically and numerically.
