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We analyse the effect of electrical charge on collisions of hydrodynamically interacting, micron-sized water droplets settling through quiescent air. We show that the relative dynamics of oppositely charged, settling droplets exhibits a basin of attraction determined by hydrodynamic and electrostatic forces. We analyse the resulting collision dynamics using dynamical-systems methods. There is a saddle point with an associated separatrix. Trajectories on one side of the separatrix collide, while those on the other side do not.