- #1

Hybird

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## Homework Statement

Electron placed in static electric field [tex]\vec{E}[/tex] = -[tex]\Psi[/tex][tex]\hat{x}[/tex] , its initial velocity is 0. Calculate V(t).

## Homework Equations

[tex]F_{e}[/tex]=[tex]\frac{d}{dt}[/tex]p(t)

p(t) = [tex]\gamma[/tex](t)mv(t)

Gamma is 1/sqrt(1-v^2/c^2) of course

## The Attempt at a Solution

This is how I go about it and want to know if I'm on the right track.

i) First you multiply the electric field by the charge of an electron to get:

[tex]F_{e}[/tex] = [tex]\frac{d}{dt}[/tex]p(t) = e[tex]\Psi[/tex]

ii) Then you integrate wrt time to get:

p(t) = e[tex]\Psi[/tex]t

iii) Then you relate momentum to velocity by:

p(t) = [tex]\gamma[/tex]mv(t)

iv) Finally you solve for V(t) from the above equation, expressing gamma explicitly I get the following formula:

v(t) = [tex]\frac{e{\Psi}t}{m}[/tex]*[tex]\frac{1}{ {\sqrt{1+ {\frac{ e^{2}{\Psi}^{2}t^{2} }{ m^{2}c^{2} }} }} }[/tex]

Does this seem to be the right method? I have to integrate this eventually to get x(t)..