October 29, 2014
Hans P. Paar
4C QUIZZ # 2
This Quizz is closed book.
The electron’s mass m = 9.11 × 10−31 Kg and its charge |e| = 1.6 × 10−19
C, 1/(4π0 ) = 9 × 109 Nm2 /C2 .
PROBLEM 1.
A potential difference between the point (x, y, z) and infinity is given by
V (x, y, z) = a/(x2 + y 2 ).
a. Calculate the electric field as function of x, y, z.
b. There are at least two peculiarities about this electric field. What are
they?
PROBLEM 2.
A conducting cylindrical sheet of radius R and infinite length is initally
neutral. It is being charged by an observer who brings infinitely small charges,
one at a time, from r = a (a > R) to the shell until the shell has a net charge
Q.
a. Calculate the electric field in the region r > R when the total charge on
the shell is q.
b. Calculate the amount of work done by the observer when the shell reaches
a net final charge of Q.
c. How much work was done by the electric field? Explain carefully!
d. What is the potential energy of the shell after the observer is done charging
it? Explain carefully!
PROBLEM 3.
A nonconduction solid sphere of radius R0 is uniformly charged with a volume charge density ρ. It is surrounded by a concentric conducting spherical shell
of inner radius R1 and outer radius R2 which carries a charge +Q. Calculate
the electric field in the following regions:
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a. 0 < r < R0 .
b. R0 < r < R1 .
c. R1 < r < R2 .
d. r > R2 .
PROBLEM 4.
A slab of nonconducting material carries a uniform charge density ρ. The
slab has a thickness d which is small relative to the height and breath of the
slab. Define the coordinate x perpendicular to the surfaces of the slab with
x = 0 at the center of the slab. Calculate the electric field as function of x in
the following regions:
a. Inside the slab.
b. Outside the slab at a distance of order d.
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