#### 2.1.2 Two-dimensional systems

The field depends on the inverse of the square of the
distance,
as we have shown before. However, when studying many interesting
academic
problems, such as an infinitely long charged line, we are actually
considering
problems in two dimensions. The symmetry with respect to an axis, say
the
z-axis, makes the field an any other related quantity depend only on
the
transverse coordinates, x and y in a cartesian system. It is therefore
a 2-D problem. In fact, by choosing any plane z=const. we get a
visualization
of the 2-D system, which remains invariant under a z-translation. In
this
way, a couple of parallel charged lines would correspond in two
dimensions
to a couple of point charges.

Coulomb's Law must be suitably modified to work in
two
dimensions, and the 1/r*2 law changes to 1/r.*

The following example is designed to visualize the
field
of a charged line:

The charge line is simulated by means of 40 charges
aligned,
of 1000 u each. Four unit charges are assumed to be located at 100, 200
and 400 units of distance from the line. It can be observed that the
force
on the unit charges decreases as the inverse of the distance from the
line.
To check this, select the test charges with the right button of the
mouse
and read position and force values on the inspector panel.

The field results to be radial to the line, as shown
in
the following
exmple:

Wait for a few seconds until all the field lines
have
been plotted. Rotate the figure. You will see that
the field lines differ noticeably from those expected for an infinite
line,
due to the finite length of the simulated line compared to the
dimensions
of the observation region.