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Steady-State Magnetohydrodynamic Flow Around an Unmagnetized Conducting Sphere

The non-collisional interaction between conducting obstacles and magnetized plasma winds can be found in different scenarios, from the interaction occurring between regions inside galaxy clusters to the interaction between the solar wind and Mars, Venus, active comets or even the interaction between Titan and the Saturnian's magnetospheric flow. These objects generate, through several current systems, perturbations in the streaming magnetic field leading to its draping around the obstacle's effective conducting surface. Recent observational results suggest that several properties associated with the magnetic field draping, such as the location of the polarity reversal layer of the induced magnetotail, are affected by variations in the conditions of the streaming magnetic field. To improve our understanding of these phenomena, we perform a characterization of several magnetic field draping signatures by analytically solving an ideal problem in which a perfectly conducting magnetized plasma (with frozen-in magnetic field conditions) flows around a spherical body for various orientations of the streaming magnetic field. In particular, we compute the shift of the inverse polarity reversal layer as the orientation of the background magnetic field is changed.