Chapter 1

# Current density vector and intensity

### Fondamental :

The system considered is a set of particles of charge .

Its particular density is and the average drift velocity is .

Let :

be the density of mobile charges.

How can the intensity going through a given surface be defined ?

Definition of intensity

The amount of electric charges going through the elementary surface during the time is :

Yet :

Thus :

We have defined the current density vector :

The intensity :

can be interpreted as the flux of the current density vector through the oriented surface .

The intensity passing through the finite surface becomes :

### Attention : Definition of intensity

The current intensity is interpreted as the surface integral of current density vector through the oriented surface :

### Complément : Differences between volume and surface models

For a current density :

For a surface current repartition :

Surface current

Instead of counting the charges passing through a given surface, we count the charges that cross a segment of length of normal vector .

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Local Ohm's law