  We consider the Brans-Dicke Reissner-Nordstrom spacetime in isotropic
coordinates and the electrostatic field of an electric point charge placed
outside its surface of inversion. We treat the static electric point charge as
a linear perturbation on the Brans-Dicke Reissner-Nordstrom background. We
develop a method based upon the Copson method to convert the governing Maxwell
equation on the electrostatic potential generated by the static electric point
charge into a solvable linear second order ordinary differential equation. We
obtain a closed form fundamental solution of the curved space Laplace equation
arising from the background metric, which is shown to be regular everywhere
except at the point charge and its image point inside the surface of inversion.
We also develop a method that demonstrates that the solution does not contain
any other charge that may creep into the region that lies beyond the surface of
inversion and which is not covered by the isotropic coordinates. The
Brans-Dicke Reissner-Nordstrom spacetime therefore is linearly stable under
electrostatic perturbations. This stability result includes the three
degenerate cases of the fundamental solution that correspond to the Brans Type
1, the Reissner-Nordstrom and the Schwarzschild background spacetimes.
