Charge distributions in nature always have a finite
volume. The concepts of point charge or line charge
are useful approximations for the case when the distance
between the source charge and the observation point
is far greater than the size of the source itself.
However, it is sometimes useful to know what the
field behavior is not only far outside the source
but also inside it.
Figure 1 shows the cross-section
of a charged cylinder of radius mm and the surrounding space (vacuum).
The cylinder has a uniform charge density . Outside the cylinder, the field is equivalent
to that of an infinite line charge (which would
be located at the axis of the cylinder) of line
charge density C/m.
It behaves as , being the radial distance from
the cylinder’s center, .
This is well observed in Figure
2.
Notice, however, that inside the cylinder the E-field
magnitude grows linearly. Why that is so can be
easily shown using Gauss Law discussed in Chapter
3. Here, we only point out that our plot is not
just an approximation: theory shows that the field
strength is indeed a linear function of the radial
distance inside the source.
It is interesting to note that this is true for
spherical charges as well. In a uniformly charged
sphere, the radial electric field has a strength
which grows as , while outside the sphere it behaves exactly
like the field of a point charge: (see Figure 3). |