  We compute the expectation value of the energy-momentum tensor in the
in-vacuum state of the quantized Dirac field coupled to a uniform electric
field background on the Poincar$\rm\acute{e}$ path of the two dimensional
de~Sitter spacetime ($\mathrm{dS}_{2}$). The adiabatic regularization scheme is
applied to remove the ultraviolet divergencies from the expressions. We find,
the off-diagonal components of the induced energy-momentum tensor vanishes and
the absolute values of the diagonal components are increasing functions of the
electric field which decrease as the Dirac field mass increases. We derive the
trace anomaly of the induced energy-momentum tensor, which agrees precisely
with the trace anomaly derived earlier in the literature. We have discusses the
backreaction of the induced energy-momentum tensor on the gravitational field.
