Lab Exercise 02:
PRELIMINARY MATERIAL TO BE READ BEFORE LAB PERIOD
When we consider a charge distribution consisting of
point charges, it is
convenient to introduce the idea of a
, which will allow us to treat the distribution as being
A “purist” might object to this, pointing out that ultimately, at the atomic scale, all distributions are
composed of individual point charges (protons and electrons).
However, if we view the distribution at a
scale, even a region that
would consider to be pointlike—e.g., a box of length 0.1 mm on a
side—is of vast size in comparison to atomic scales, and would consist of tens of millions of individual point
In that context, treating a general charge distribution as being continuous is not all that unrealistic.
charge density function
, then, is a means of describing how a certain amount of charge is
over some particular region.
Depending upon the
of region that is being spread over, we have three
different “categories” of density functions:
If an amount of charge is spread throughout a three-dimension volume, we have a
, conventionally denoted by the symbol “
(This is, perhaps, suggestive of the familiar
that describes distributions of matter.)
A volume charge density describes the
charge found charge per unit volume examined
Thus, if you were to state that the volume density at
some point were 15
, you would essentially be asserting that a
box around that point
(again, lets say, of dimension 0.1 mm on a side) would contain a total charge of:
(15 x 10
= 15 nC.
If an amount of charge is spread over some two-dimensional
, we have a
, and will use the symbol
to represent such a distribution.
It is important to recognize that we
are treating such a distribution as having “zero thickness”—even though, technically, there is
non-zero thickness to a typical “
Provided, however, that the thickness “
is very small compared
to the area of the surface, we can neglect
and treat the distribution as if it were truly “2D”.
charge density is then calculated in a manner comparable to volume charge density.
In this case,
however, we measure the amount of charge found
per unit area of the surface examined.
Keep in mind, as well, that there is no
reason why the surface in question has to be
completely possible to deal with a situation where charge is spread over the curved surface of a sphere
If charge is spread along a