  We analyse the impact of the inverse square law fall-off of the energy
density in a charged isotropic spherically symmetric fluid. Initially we impose
a linear barotropic equation of state $p=\alpha \rho$ but this leads to an
intractable differential equation. Next we consider the neutral isothermal
metric of Saslaw, Maharaj and Dadhich (1996) in an electric field and the usual
inverse square law of energy density and pressure results thus preserving the
equation of state. Additionally, we discard a linear equation of state and
endeavour to find new classes of solutions with the inverse square law fall off
of density. Certain prescribed forms of the spatial and temporal gravitational
forms result in new exact solutions. An interesting result that emerges is that
while isothermal fluid spheres are unbounded in the neutral case, this is not
so when charge is involved. Indeed it was found that barotropic equations of
state exist and hypersurfaces of vanishing pressure exist establishing a
boundary in practically all models. One model was studied in depth and found to
satisfy other elementary requirements for physical admissability such as a
subluminal sound speed as well as gravitational surface redshifts smaller than
2. The Buchdahl (1959), Bohmer and Harko (2007) and Andreasson (2009)
mass-radius bounds were also found to be satisfied. Graphical plots utilising
constants selected from the boundary conditions established that the model
displayed characteristics consistent with physically viable models.
