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ATMO/ECE 489/589 Midterm Exam
March 7, 2017
Everyone should answer Question #1.
Then answer any 3 of the remaining 4 questions
(please start each problem on a new sheet of paper) Allow about 15 minutes per question
1.
(15 pts) Answer any three of the following short answer questions allowing about 5
minutes per question.
1a.
We generally assume that the current density, Jz, is constant with altitude. When or why
is that a reasonable assumption?
1b.
What is meant by the term electrical mobility? Do positively-charged small ions have a
larger, smaller, or the same electrical mobility than(as) negatively-charged small ions?
Why?
1c.
Would the small uncharged metal ball (hanging
from the insulating string) be attracted to,
repelled, or unaffected by the negatively charged
bell in the figure at right? What if the left bell
were positively charged?
1d.
In 10 balloon flights between 1911 and 1913 Victor Hess observed that the rate of the of
ionization of air initially decreased with increasing altitude. By 5000 ft. altitude,
however, the rate of ionization was higher than at sea level. What explanation was given
for these observations? Incidentally, Hess and Carl D. Anderson were awarded the Nobel
Prize in Physics in 1936.
1e.
What does q in the three expressions below stand for or represent? (underlined variables
in bold font are vectors)
J=2Nqv
dn/dt = q - αn2
E = q Q r /( 4πεo r3 )
What does λ in the two expressions below stand for or represent?
Er (r) = λ/(2πεo r)
J = λE
What does α in the two expression below stand for or represent?
radon α decay
1f.
dn/dt = q - αn2
Does the E field sounding shown at right indicate a cloud
layer that is positively or negatively charged? How can you tell?
2.
(15 pts) What is the capacitance of two 1 m x 1 m metal plates a distance d apart? You
can assume that there is no bending of the electric field lines at the edges of the plates
(i.e. for the purposes of determining the electric field it's as if the plates are of infinite
horizontal extent).
3.
(15 pts) A simplified small ion balance is given below
dn/dt = q - αn2 - βnZ
Derive an expression for n(t) for the case where ion-particle attachment is the dominant
loss process and ion-ion recombination can be neglected. Note you are being asked to
find n(t), not n at steady state. Assume that n(t) = 0 at t = 0.
4.
(15 pts) Given the thunderstorm cloud charge distribution
shown at right, determine the charge, q, that would be
needed in order for the E field to be zero at D = 0 on the
ground directly underneath the charge centers. Assume that
the ground is a flat conducting surface.
5.
(15 pts) On the first day of class we made a rough estimate of the time it would take the
fair weather current in the global electric circuit to discharge (neutralize) all of the charge
residing on the earth's surface:
As charge on the earth is neutralized the electric field and also J (J = λ E) will also
decrease. That is something we didn't include in the estimate above. Derive an
expression, Q(t), for how the charge Q on an area A of the earth's surface will change
with time taking into account the fact that E and J both depend on Q. Assume that
Q = Qo at time = 0.