Consider two conducting earthed (hollow) spherical surfaces in space, centered at points given by the vectors $r_1$ and $r_2$, with radii of $R_1$ and $R_2$, respectively.

1 Find those points in space where one can place a point charge such that exactly half of the electric field lines from the point charge arrive on each sphere in the emerging static electric field.

There is no restriction on the values of the parameters. We even allow either (or both) spheres to have «infinite radii», i.e., to degenerate into planes.