A charged particle of mass m and charge e is released from rest in an electric field of constant magnitude E. The kinetic energy of the particle after time t is `E_k` and the linear momentum is p. We have

Options

A. `p=Eet`
B. `p=2eEt`
C. `E_k=(e^2E^2t^2)/(2m)`
D. `E_k=(e^2E^2t^2)/(m)`

Answer

A, C

Explanation

Acceleration of the electron in the electric field is, `a=eE//m`. The speed acquired by the electron in time t is, `v=at=(eEt)/(m)`. The momentum acquired by the electron,
`p=mv=m(eE)/(m)t=eEt`
The kinetic energy acquired, `E_k=1/2mv^2`
`=1/2mxx((eEt)/(m))^2=(e^2E^2t^2)/(2m)`