  In this work, we study the 1+1 longitudinal acceleration expansion of hot and
dense quark matter as a conducting relativistic fluid with the electric
conductivity $\sigma$. The plasma has embedded in the presence of electric and
magnetic fields which are perpendicular together in the transverse plane. In
order to be more realistic, we generalize the Bjorken solution, which includes
the acceleration effects on the fluid expansion. We apply a perturbation
fashion in initial condition to solve the relativistic magneto-hydrodynamics
equations. This procedure leads us to achieve the exact algebraic expressions
for both electric and magnetic fields. We also find the effects of the
electromagnetic fields on the acceleration of the fluid, and the correction of
energy density obtained from the magneto-hydrodynamics solutions.
