Electrostatics and Magnetostatics
Current density vector and intensity
The system considered is a set of particles of charge .
Its particular density is and the average drift velocity is .
be the density of mobile charges.
How can the intensity going through a given surface be defined ?
The amount of electric charges going through the elementary surface during the time is :
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 :
Instead of counting the charges passing through a given surface, we count the charges that cross a segment of length of normal vector .