  We present extensive Molecular Dynamics simulation results for the structure,
static and dynamical response of a droplet of 1000 soft spheres carrying
extended dipoles and confined to spherical cavities of radii $R=2.5$, 3, and 4
nm embedded in a dielectric continuum of permittivity $\epsilon' \geq 1$. The
polarisation of the external medium by the charge distribution inside the
cavity is accounted for by appropriate image charges. We focus on the influence
of the external permittivity $\epsilon'$ on the static and dynamic properties
of the confined fluid. The density profile and local orientational order
parameter of the dipoles turn out to be remarkably insensitive to $\epsilon'$.
Permittivity profiles $\epsilon(r)$ inside the spherical cavity are calculated
from a generalised Kirkwood formula. These profiles oscillate in phase with the
density profiles and go to a ``bulk'' value $\epsilon_b$ away from the
confining surface; $\epsilon_b$ is only weakly dependent on $\epsilon'$, except
for $\epsilon' = 1$ (vacuum), and is strongly reduced compared to the
permittivity of a uniform (bulk) fluid under comparable thermodynamic
conditions.
  The dynamic relaxation of the total dipole moment of the sample is found to
be strongly dependent on $\epsilon'$, and to exhibit oscillatory behaviour when
$\epsilon'=1$; the relaxation is an order of magnitude faster than in the bulk.
The complex frequency-dependent permittivity $\epsilon(\omega)$ is sensitive to
$\epsilon'$ at low frequencies, and the zero frequency limit
$\epsilon(\omega=0)$ is systematically lower than the ``bulk'' value
$\epsilon_b$ of the static primitivity.
