  Imposing the Petrov-like boundary condition on the hypersurface at finite
cutoff, we derive the hydrodynamic equation on the hypersurface from the bulk
Einstein equation with electromagnetic field in the near horizon limit. We
first get the general framework for spacetime with matter field, and then
derive the incompressible Navier-Stokes equations for black holes with electric
charge and magnetic charge respectively. Especially, in the magnetic case, the
standard magnetohydrodynamic equations will arise due to the existence of the
background electromagnetic field on the hypersurface.
