The current, I, is a coarse, average quantity that tells what is happening in
an entire wire.
If we want to describe in more detail how the charges move through a
conductor, we use the concept of the current density 
:
where n is the number of free charged particles per unit volume,
q is their charge, and 
is their average drift velocity.
Since it is a vector quantity, it can indicate the direction of the
current flow.
Now for the bad news.
This formula says that if free electrons are drifting to the right,
then the resulting current flows to the left because the electrons
are negative.
It is difficult to keep this straight, so when we work
with circuits, we usually just think of current as moving positive
charges, even though we know that the electrons carry the current.
The current density is an area density, I.e., is the current per
unit area.
In fact, the current through an area A is simply the flux
of the current density through that area:
Or, if the current density is uniform and flows straight into the area,
