  In this paper, we investigate the time evolution an accreting magneto-fluid
with finite conductivity. For the case of a thin disk, the fluid equations
along with Maxwell equations are derived in a simplified, one-dimensional model
that neglects the latitudinal dependence of the flow. The finite electrical
conductivity is taken into account for the plasma through Ohm law; however, the
shear viscous stress is neglected, as well as the self-gravity of the disk. In
order to solve the integrated equations that govern the dynamical behaviour of
the magneto-fluid, we have used a self-similar solution. We introduce two
dimensionless variables, $S_0$ and $\epsilon_\rho$, which show the magnitude of
electrical conductivity and the density behaviour with time, respectively. The
effect of each of these on the structure of the disk is studied. While the
pressure is obtained simply by solving an ordinary differential equation, the
density, the magnetic field, the radial velocity and the rotational velocity
are presented analytically. The solutions show that the $S_0$ and
$\epsilon_\rho$ parameters affect the radial thickness of the disk. Also, the
radial velocity and gas pressure are more sensitive to electrical conductivity
in the inner regions of disk. Moreover, the $\epsilon_\rho$ parameter has a
more significant effect on physical quantities in small radii.
