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Prove that when a particle of constant mass and charge is accelerated from rest in an lectric field, its final velocity is proportional to the square root of the potential difference through which it is accelerated.

Prove that when a particle of constant mass and charge is accelerated from rest in an lectric field, its final velocity is proportional to the square root of the potential difference through which it is accelerated.

Grade:12th pass

1 Answers

Narendran
34 Points
5 years ago
Friend,
The electron gains energy from the electric field which it converts to kinetic energy,
therefor simply:
(1/2)*mv2=qE.(where the symbols depicts their usual meanings).
rearranging the terms we get:
v=\sqrt{2qV/m}
hence you can find your required answer from the above equation. 
 

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