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We present extensive Molecular Dynamics simulation results for the structure,static and dynamical response of a droplet of 1000 soft spheres carryingextended dipoles and confined to spherical cavities of radii $R=2.5$, 3, and 4nm embedded in a dielectric continuum of permittivity $\epsilon' \geq 1$. Thepolarisation of the external medium by the charge distribution inside thecavity is accounted for by appropriate image charges. We focus on the influenceof the external permittivity $\epsilon'$ on the static and dynamic propertiesof the confined fluid. The density profile and local orientational orderparameter of the dipoles turn out to be remarkably insensitive to $\epsilon'$.Permittivity profiles $\epsilon(r)$ inside the spherical cavity are calculatedfrom a generalised Kirkwood formula. These profiles oscillate in phase with thedensity profiles and go to a ``bulk'' value $\epsilon_b$ away from theconfining surface; $\epsilon_b$ is only weakly dependent on $\epsilon'$, exceptfor $\epsilon' = 1$ (vacuum), and is strongly reduced compared to thepermittivity of a uniform (bulk) fluid under comparable thermodynamicconditions.  The dynamic relaxation of the total dipole moment of the sample is found tobe 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.Comment: 12 pages including 17 figure

Dielectric response of a polar fluid trapped in a spherical nanocavity