Every object consists of a certain amount of positive charge and
a certain amount of negative charge. For neutral objects, the
amount of each type of charge is equal in every tiny, or
infinitesimal, portion of the object. If the object has the shape
of a line, the amount of positive charge in each tiny segment of
length along the line is equal to the amount of negative charge in
each tiny segment of length. For a neutral three-dimensional
object, such as a cube, the amount of negative charge in each small
volume element of the total volume of the cube is equal to the
amount of positive charge in each small volume element. All neutral
objects have a charge density of zero throughout their volumes
despite the fact that they have charge. The charge density
describes the amount of excess charge per given region of space.
For objects that are not neutral, then, the charge density is
either positive or negative. A positive charge density expresses
the fact that an object has a given amount of positive charge more
than it has negative charge in a specific region of space.
Likewise, a negative charge density means the object has a given
amount of negative charge more than positive charge for a given
region of space. For a line of charge, the charge density is
expressed as Coulombs per meter when using SI units. For a
two-dimensional object, such as a disk, the charge density using SI
units is Coulombs per (meter^2). For objects that have uniform
excess charge throughout their volume, the charge density is
expressed as the total amount of excess charge on the body divided
by the total length/ area/ volume of the body. For objects that
have nonuniform charge excesses, the charge density must be
expressed as a function of position (and possibly, time) within the
object.
