The following handout gives a rough, back-of-the-envelope kind of estimate of the factor of enhancement.

This might require a little explanation.

First you write down the potential at the surface of two conducting spheres of radius a and b, carrying charges Q and q (really just the potential a distance a or b from a point charge Q or q)

Then you connect the two spheres with a wire which forces the two potentials to be equal (this would of course cause the charge to rearrange themselves and turn this into a much more complex problem, but we will ignore that).

Finally we write down expressions for the relative strengths of the electric fields at the surfaces of the two spheres (we assume Q and q would be uniformly spread out over the two spheres which wouldn't be true).  We see that the field at the surface of the smaller sphere is a/b times larger than the field at the surface of the bigger sphere.

Here is a real example of field enhancement that lead to triggering of a lightning strike and subsequent loss of a launch vehicle (you'll find the entire article here)

In this case the rocket body together with the exhaust plume created a long pointed conducting object.  Enhanced fields at the top and bottom triggered lightning.

Lightning also strikes aircraft.  Here's an example.  Often the discharge is initiated by the airplane.


We'll talk about triggered lightning later in the course.  I'm referring to lightning that is purposely trigger so that it can strike instrumentation on the ground and studied at close range.
The basic idea is to launch a small rocket (about 3 feet tall) in a high electric field under a thunderstorm.  A spool of wire is mounted on the tail fins of the rocket.  One end of the wire is connected to ground and the other end runs up to the nose of the rocket.  Wire un-spools (probably the hardest part is to keep the wire from breaking) once the rocket is launched forming a narrow tall conducting object.  Field enhancement at the top of the rocket is enough often times to initiate an upward leader discharge that then triggers lightning.

An example from the ICLRT (International Center for Lightning Research and Testing) operated by the University of  Florida.

Enhancement of the E field at the top of a mountain (or tall building or structure) is sometimes high enough to trigger lightning also.

Here's an example of a very cleverly designed instrument that has been used to measure electric fields above the ground and inside thunderstorms (you can download the complete Winn et al. 1978 publication here). 

As the spheres spin, a current will move back and forth between them.  The amplitude of the current will depend on the charge induced on the spheres by the electric field.  The induced charge will, in turn, depend on the intensity of the E field.
Determining how the two conducting spheres will enhance the electric field is a more complex problem than we considered in the last lecture but it has been worked out analytically (don't worry we won't be looking at the details).  You could also work it out numerically or determine the enhancement experimentally.  Note that the two spheres also act an antenna for transmitting data back to the ground.

The next figure shows an example of data obtained with an instrument like this (it is from a different publication which you can download here, but a similar instrument was used).