One places oneself in a having material of the free carriers of load q, to which one applies an electrostatic field \ vec {E} permanent (to also note the absence of field \ vec {B} ). Then let us apply the basic principle of dynamics in the Référentiel of the conducting supposed galiléen (see electromagnetic Force):

m \ frac {D \ vec {v}} {dt} =q \ vec {E}

from where \ vec {v} = \ frac {Q \ vec {E}} {m} T + \ vec {v} _0

Consequently speed diverges and thus the Vecteur density of current also because \ vec {J} =qn< \ vec {v} >

consequently the intensity diverges, which is impossible.

It is necessary thus that the speed tightens towards a finished value .

Moreover \ vec {v} is colinéaire with \ vec {E} (in the abscence of \ vec {B} ), one thus poses:

\ vec {v} = \ driven \ vec {E}

\ mu is known as the mobility , it depends on material, the charge carrier, the temperature, ||\ vec {E}||,…

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