Editing Ohm's law (section)

==Microscopic origins==
[[File:Electrona in crystallo fluentia.svg|thumb|200 px|right|Drude Model electrons (shown here in blue) constantly bounce among heavier, stationary crystal ions (shown in red).]]

{{Main|Drude model}}

The dependence of the current density on the applied electric field is essentially [[quantum mechanics|quantum mechanical]] in nature; (see Classical and quantum conductivity.) A qualitative description leading to Ohm's law can be based upon [[classical mechanics]] using the [[Drude model]] developed by [[Paul Drude]] in 1900.<ref>{{cite journal
|last= Drude
|first= Paul
|title= Zur Elektronentheorie der Metalle
|journal= Annalen der Physik
|volume= 306
|pages=566–613
|issue=3
|url= http://www3.interscience.wiley.com/cgi-bin/fulltext/112485959/PDFSTART
|year= 1900
|doi= 10.1002/andp.19003060312 |bibcode = 1900AnP...306..566D |doi-access= free
}}{{dead link|date=February 2019|bot=medic}}{{cbignore|bot=medic}}
</ref><ref>{{cite journal
|last= Drude
|first= Paul
|title= Zur Elektronentheorie der Metalle; II. Teil. Galvanomagnetische und thermomagnetische Effecte
|journal= Annalen der Physik
|volume= 308
|issue=11
|pages=369–402
|url= http://www3.interscience.wiley.com/cgi-bin/fulltext/112485893/PDFSTART
|year= 1900
|doi= 10.1002/andp.19003081102 |bibcode = 1900AnP...308..369D }}{{dead link|date=February 2019|bot=medic}}{{cbignore|bot=medic}}
</ref>

The Drude model treats [[electron]]s (or other charge carriers) like pinballs bouncing among the [[ion]]s that make up the structure of the material. Electrons will be accelerated in the opposite direction to the electric field by the average electric field at their location. With each collision, though, the electron is deflected in a random direction with a velocity that is much larger than the velocity gained by the electric field. The net result is that electrons take a zigzag path due to the collisions, but generally drift in a direction opposing the electric field.

The [[drift velocity]] then determines the electric [[current density]] and its relationship to '''''E''''' and is independent of the collisions. Drude calculated the average drift velocity from '''''p'''''&nbsp;=&nbsp;−''e'''E'''τ'' where '''''p''''' is the average [[momentum]], −''e'' is the charge of the electron and τ is the average time between the collisions. Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field; this leads to Ohm's law.