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A charged particle of mass m and charge ...

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

A

`p=Eet`

B

`p=2eEt`

C

`E_k=(e^2E^2t^2)/(2m)`

D

`E_k=(e^2E^2t^2)/(m)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
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)`
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