Tuesday Feb. 1, 2011
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We leave the electrostatic stuff behind and today look at currents in the atmosphere.

In the atmosphere we normally speak of a current density (Amps/square meter) rather than current.  Positive and negatively charged small ions transport charge in air (just the free electrons carry charge in a wire).  Small ions are charged nitrogen and oxygen molecules that are surrounded by water molecules.  We'll look at the creation of small ions in more detail in a week or so.

In a conduction current, the charge carriers drift at a velocity equal to the product of electrical mobility and electric field.  The random thermal velocities are much larger.  Convection currents can also potentially be larger than conduction currents. 


Here we consider N charge carriers (each with charge q) moving in the same direction and derive an expression for J the current density.  In general you would need to sum contributions from different charge carriers such as carriers with +q moving in one direction and oppositely charged carriers (-q) moving in the opposite direction.

We've assumed that the number density of positive and negative charge carriers is the same.

Next we derive a continuity equation that relates changes in the space charge density in a volume to net flow of charge into or out of the volume.

Note that under steady state conditions and where J has just a z component, the current density Jz is constant with altitude.

Next we use our just derived expression for current density together with the definition of electrical mobility to derive an expression for conductivity.


Siemens/meter has replaced mhos/m, you may find mhos/m in some older literature.

Again if two types of charge carriers are present, the expression for conductivity would have two terms:

Negatively charged small ions generally have higher electrical mobility than postively charged small ions.
Resistivity is the reciprocal of conductivity.  Resistivity is not the same as resitance, but it is relatively easy to relate the two.


Resistivities of some common materials are listed below.  This was on a handout distributed in class.

Note how the conductivity of air is a function of air temperature.  A lightning return stroke will heat air to a peak temperature of about 30,000 K for a short time.

Later in the semester we will look at some fast time resolved measurements of lightning electric fields that were being used to try to determine characteristics of the fast time varying currents in lightning strokes.  The measurements were made in a location where propagation between the lightning source and E field antenna was over salt water to preserve as much of the high frequency content of the signals as possible.

Here is a better estimate of how quickly a fair weather current would neutralize the negative charge on the earth's surface than was done of the first day of class. 


An important example problem showing what happens along an air-cloud boundary where there is an abrupt change in conductivity.  The following two pages of notes were copied over to a handout that was distributed in class.

Conductivity inside a cloud is lower than in the air outside a cloud.

Surface charge builds up along the air-cloud boundary.

Charge along the could edges intensifies the electric field inside the cloud.  The product of higher field times lower conductivity is able to keep the current density constant with altitude.

Screening layers that form along the edges of a thunderstorm effectively mask the main charge centers inside the cloud.