  Motivated by recent experiments, we append long ranged Coulomb interactions
to dominant strong local correlations and study the resulting $t$-$J$-$V_C$
model for the 2-dimensional cuprate materials. This model includes the effect
of short ranged Hubbard-Gutzwiller-Kanamori type correlations and long ranged
Coulomb interactions on tight binding electrons. We calculate the $
\{\vec{q},\omega\}$ dependent charge density fluctuations in this model using
the extremely correlated fermi liquid theory, characterized by quasiparticles
with very small weight $Z$. We develop a novel set of formulae to represent the
dynamical charge susceptibility and the dielectric function, using a version of
the charge-current continuity equation for a band system valid for arbitrary
$\vec{q}$. Combining these ingredients, we present results for the dynamical
charge susceptibility $\widetilde{\chi}_{\rho\rho}(\vec{q},\omega)$,
(longitudinal) dielectric function $\varepsilon(\vec{q},\omega)$, current
susceptibility $\widetilde{\chi}_{J J}(\vec{q},\omega)$, conductivity
$\sigma(\vec{q},\omega)$, and the plasma frequency for any $\vec{q}$. We also
present calculations for the first moment of the structure function and discuss
a characteristic energy scale $\Omega_p(\vec{q})$, which locates a peak in $\Im
m \, \widetilde{\chi}_{\rho\rho}(\vec{q},\omega)$.
