  In this paper, we consider a quantum scalar field propagating on the
Reissner-Nordstr\"om black hole spacetime. We compute the renormalized
stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh
states. When the field is in the Hartle-Hawking state, we renormalize using the
recently developed ``extended coordinate'' prescription. This method, which
relies on Euclidean techniques, is very fast and accurate. Once, we have
renormalized in the Hartle-Hawking state, we compute the stress-energy tensor
in the Boulware and Unruh states by leveraging the fact that the difference
between stress-energy tensors in different quantum states is already finite. We
consider a range of coupling constants and masses for the field and a range of
electric charge values for the black hole, including near-extreme values.
Lastly, we compare these results with the analytic approximations available in
the literature.
