The energy gained by electrons as they are accelerated by an electric field is

The energy gained by an electron as it is accelerated by an electric field is equal to the work done by the electric field itself, and this is equal to the product between the charge of the electron and the potential difference across which the electron traveled:
(1)
where e is the electron charge, and  is the potential difference between the initial and the final point of the electron, and this is equal to
(2)
where E is the intensity of the electric field and d is the distance covered by the electron. If we substitute (2) into (1), we find a final expression for the energy gained by the electron

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