  In natural and laboratory magnetized plasmas, an equilibrium electric field
may exist perpendicular to the background magnetic field. In such a situation
all the plasma species experience a common drift and the unperturbed
distribution functions have a common shift in velocity space. In this work the
susceptibility tensor is first derived in the laboratory frame for such a
situation using the commonly used method of integration along unperturbed
trajectory. Then the Lorentz transformation method is adopted to verify the
results. As an application we give an analysis of the waves propagating
parallel to the background magnetic field for a simple electron plus single
charged ion plasma. A qualitative new phenomenon is the appearance of a
resonance at the plasma Langmuir frequency if a transverse equilibrium electric
field is present.
