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A free-fall technique has been used to measure the net vertical component of force on electrons in a vacuum enclosed by a copper tube. This force was shown to be less than $0.09mg$, where m is the inertial mass of the electron and g is 980 cm/sec². This supports the contention that gravity induces an electric field outside a metal surface, of magnitude and direction such that the gravitational force on electrons is cancelled.
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Witteborn et al. (1967) studied this question.
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