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The equations governing a collisionless obliquely-flowing plasma around anion-absorbing object in a strong magnetic field are shown to have an exactanalytic solution even for arbitrary (two-dimensional) object-shape, whentemperature is uniform, and diffusive transport can be ignored. The solutionhas an extremely simple geometric embodiment. It shows that the ion collectionflux density to a convex body's surface depends only upon the orientation ofthe surface, and provides the theoretical justification and calibration ofoblique `Mach-probes'. The exponential form of this exact solution helpsexplain the approximate fit of this function to previous numerical solutions.

Ion collection by oblique surfaces of an object in a transversely-flowing strongly-magnetized plasma