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We investigate the effect of electrical charge on collisions of hydrodynamically interacting, micron-sized water droplets settling through quiescent air. The relative dynamics of charged droplets is determined by hydrodynamic interactions, particle and fluid inertia, and electrostatic forces. We analyse the resulting relative dynamics of oppositely charged droplets by determining its fixed points and their stable and unstable manifolds. The stable manifold of a saddle point forms a separatrix that separates colliding trajectories from those that do not collide. The qualitative conclusions from this theory are in excellent agreement with experiments.