Drift Speed of Electrons in Conductor with Applied Field

[person_random_normal]

for an electron, randomly moving inside a conductor , having applied an external electric field we have those electrons moving with a net speed called drift speed , against the direction of field.
so initially as electrons are moving randomly we consider their initial velocity o
and after time t =at
where a = acc. of electrons = e(field)/mass of electron
t = mean time between consecutive collisions of electrons
courtesy PHYSICS by halliday resnick krane vol 2
but i don't understand why don't we average the initial and final speed of electrons ie
drift speed = (0 + at)/2
??

 

[EM_Guy]

The acceleration of an electron in a real conductor is not constant. I think when subjected to an electric field, the speed of the electrons increases monotonically up to its "steady-state" drift velocity. If the applied field is not changing (DC), then after an initial transient time, the electrons are flowing at the drift velocity. If the applied field is a sinusoidal function (AC), then the current (and thus drift velocity) will also vary sinusoidally. An accelerating charge (i.e. a varying current) establishes an electromagnetic wave.

 

[Drakkith]

I think drift speed is already an average since every electron will be moving at different speeds and constantly interacting with the material and the applied field.

 

[tommyxu3]

For the acceleration happened just a moment (average), the drift velocity is the average speed electrons have in the conductor after the generation of the electric field.

 

[vanhees71]

The electron in a (normal) conductor is under the influence of the electromagnetic force and to a friction force. The notion of a friction force is already a coarse grained description of the full complicated dynamics of the many-body (quantum!) system. On the level of linear-response theory you come astonishingly far with very simple classical pictures introducing some phenomenological transport coefficients (like electric conductivity) and response functions. On a microscopic level, you have to calculate appropriate correlation functions in statistical many-body QFT. See Landau-Lifshitz vol. X for a very good introduction into both classical and quantum transport phenomena.