# Why is charge = nALe

Sorry if this question is a bit broad but I can't find any info on this by just searching.

The equation q = neAL where L is the length of a conductor, A is the area of cross section, n is the number of charges and e is the fundamental charge. This equation clearly does not make sense from a dimensional point of view at first glance. So why is it true and why is it assumed true in most derivations for charge density in terms of drift velocity?

• I think $n$ is meant to be the number of electrons per unit volume. – By Symmetry Apr 30 '15 at 19:42

## 1 Answer

$n$ is the particle density: Number of particles per cubic meter in SI units. $e$ would be the charge on a particle (Coulombs), here equal to the elementary charge (they could be protons). With that I think that you will see the the dimensions are correct.

• Thank you very much. Similar symbols for similar equations can be quite cumbersome to work with. @BySymmetry commented first so I upvoted his comment. I will mark this as the answer when the time limit is up. – Jaja Apr 30 '15 at 19:45
• A common convention is to use uppercase characters ($N$), for extrinsic properties (i.e., the total number), and lowercase characters ($n$) for intrinsic properties (number per unit volume). This way, $q = Ne$ is also valid, but less informative. – KidElephant Apr 30 '15 at 20:03