# Average drift velocity of electron in conduct

Gold Member
I have a question on the derivation of the average drift velocity in a conductor: drift velocity is the average velocity which a free charge moving in a conductor has due to the influence of an electric field applied to the conductor. In a metal, the free charge will be an electron. As they move through the conductor, electrons will frequently bump into ions. If τ is the mean free time of the electron, i.e. the average time between successive collisions, then between two collisions, the action of an external electric field will make the electron accelerate by (E*e/m)*τ, where E is the strength of the field (and this strength is constant), e the charge of an electron, an m the mass of the electron.

In common textbooks this quantity (E*e/m)*τ is equal to the magnitude of the drift velocity in the conductor. This confuses, since the quantity expresses the average maximum speed gained by the electron, i.e. the speed it has just before it collides with the next ion. But drift velocity is supposed to be the average velocity of the electron due to the field, so I think its magnitude should be just one-half of this quantity.

Delta2
Homework Helper
Gold Member
Your claim that "the quantity expresses the average maximum speed gained by the electron, i.e. the speed it has just before it collides with the next ion" is not valid.

Its like you saying that the electron loses all its energy after each collision which isnt necessarily true.

Wikipedia has an entry about Drude model and what happens in the DC case http://en.wikipedia.org/wiki/Drude_model#DC_field.

I ve to say that my statistics background fails me abit atm but in Wikipedia analysis it claims that (E*e/m)*τ is both the deviation and the average of the drift velocity (<p> symbolizes the mean value of p if i remember well ).