Tuesday Feb. 10, 2009
The first set of homework problems has been graded and was returned in
class together with a set of solutions (not that you really needed
them).
Be sure you get the E field polarities right in the dE/dz
calculation.
When you are figuring out the E field at values of r < R, only
a portion of the space charge is inside the Gaussian surface. For
values r > R, all of the space charge is inside the volume.
Your two expressions for E(r) should be the same at r = R.
There will always be an attractive force between a charge and a
conducting plane. The charge will cause charges of the opposition
polarity to be induced on the surface of the conductor.
Be sure to multiply the surface charge density by an increment of
area when determining the total amount of charge induced on the
conduction plane.
These next
few pages show some actual measurements of current density, E field,
and conductivity (fair weather values).
There was pretty good agreement among measurements made with
different sensors.
The authors mentioned that the measured values of Jz were almost
exactly half of what one would obtain by multiplying the total
conductivity by the electric field. The explanation for this is
shown below:
One of the Jz sensors consisted of two conducting hemispheres
insulated from each other. Charge is induced on the two
hemispheres by the ambient electric field. The figure above shows
that the sensor is only capturing half of the charge carries in the
atmosphere and therefore only measuring half of the current density, Jz.
Some additional measurements from "the yellow book." Note
how uniform Jz is with altitude.
Next we
will look at ionizing radiation (from the ground, gases in the ground
that escape into the air, and cosmic rays). Ionized air molecules
become "small ions." The small ions are what gives the air its
conductivity.
Radioactive materials in the ground emit alpha and beta particles, and
gamma rays. Alpha particles (helium nucleus: two protons and two
neutrons) are a strong source of ionization but only in the first few
cm above the ground. Beta particles (electrons) ionize air in a
layer a few meters thick. The effects of gamma radiation extend
of 100s of meters. Radon gas is discussed in more detail
below. Cosmic rays are the dominant source of ionization over the
ocean and above 1 km over land.
A short handout with some information about radon was distributed in
class. You can download a copy of the handout here.
The following figure shows a portion of the decay series that
ultimately yield isotopes of radon.
The
following calculation is an example of how you might go about
calculating the ion pair (ip) production rate.
We first determine the number of alpha particles emitted in a cubic
centimeter of air per second.
Next we determine how many air molecules an alpha particle can ionize.
Multiplying the alpha particle emission rate by the number of
ionized air molecules per alpha particle gives the ion pair production
rate.
This next figure gives some typical ip production rates from the
various radiation sources as a function of altitude.
Finally a
little information about cosmic rays
And some historical information
Here is some information on cosmic ray
showers. Very few of the primary particles reach the
ground. Rather they interact with gas molecules in the atmosphere
and produce a wide variety of types of secondary particles.
