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Grains in desert sandstorms spontaneously generate strong electrical charges; likewise volcanic dust plumes produce spectacular lightning displays. Charged particle clouds also cause devastating explosions in food, drug and coal processing industries. Despite the wide-ranging importance of granular charging in both nature and industry, even the simplest aspects of its causes remain elusive, because it is difficult to understand how inert grains in contact with little more than other inert grains can generate the large charges observed. Here, we present a simple yet predictive explanation for the charging of granular materials in collisional flows. We argue from very basic considerations that charge transfer can be expected in collisions of identical dielectric grains in the presence of an electric field, and we confirm the model’s predictions using discrete-element simulations and a tabletop granular experiment.