Droplets of absolutely stable strange quark matter (strangelets) immersed in a lepton background may be the energetically preferred composition of strange star crusts and of the interior of a new class of stars known as strangelet dwarfs. In this work we calculate the surface tension $sigma$ and the curvature coefficient $gamma$ of charged strangelets as a function of the baryon number density, the temperature, the chemical potential of trapped neutrinos, the strangelet size, the electric potential and the electric charge at their boundary. Strange quark matter in chemical equilibrium and with global electric charge neutrality is described within the MIT bag model. We focus on three different astrophysical scenarios, namely cold strange stars, proto strange stars and post merger strange stars. Finite size effects are implemented within the multiple reflection expansion framework. We find that $sigma$ decreases significantly as the strangelets boundary becomes more positively charged. This occurs because $sigma$ is dominated by the contribution of $s$ quarks which are the most massive particles in the system. Negatively charged $s$-quarks are suppressed in strangelets with a large positive electric charge, diminishing their contribution to $sigma$ and resulting in smaller values of the total $sigma$. We verify that the more extreme astrophysical scenarios, with higher temperatures and higher neutrino chemical potentials, allow higher positive values of the strangelets electric charge at the boundary and consequently smaller values of $sigma$. In contrast, $gamma$ is strongly dominated by the density of light ($u$ and $d$) quarks and is quite independent of the charge-per-baryon ratio, the temperature and neutrino trapping. We discuss the relative importance of surface and curvature effects as well as some astrophysical consequences of these results.
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