A Pacific storm front is approaching UCLA (about 100m above sea level), and a th

Question

A Pacific storm front is approaching UCLA (about 100m above sea level), and a thunderstorm moves over campus. Charging within a cold region of the cloud from ice crystal collisions is estimated to occur around 5000m above sea level.

a. If a thunderstorm that moves over UCLA is able to generate an electric field of about 1x106 V/m between the cloud and the ground, what is the potential difference?
b. Modeling the UCLA campus and a cloud that just barely covers the campus as the plates on a giant capacitor, estimate the charge that has accumulated on the cloud immediately before lightning occurs. (Draw a diagram and label and quantify height, area, and potential difference or electric field.)
c. If the same thunderstorm were to move to the northeast over Mt. San Antonio (3000m above sea level), what would the strength of the electric field be over the mountain, assuming the same potential difference and charging height of cloud? Is lightning more or less likely to occur, and why?
d. Assume the electric field between the cloud and Mt. San Antonio reaches the breakdown field in air of 3e6 V/m, so lightning strikes! During a lightning strike, the potential difference between the cloud and the ground accelerates electrons in the cloud downward, which then collide with air molecules to release more electrons, in a chain where different electrons ultimately hit the ground. As a first (very rough) approximation, you can model this as a single electron accelerated between two charged plates. If the electron starts at rest, what will its kinetic energy be when it reaches the summit of Mt. San Antonio?
e. Assume the lightning strike transfers all charge stored from the cloud to the ground. How much energy is transferred?
f. It turns out average lightning strikes transfer 1-10 billion Joules of energy. Is your value from (e) higher or lower? Why do you think that is?

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