EXAM 1 October 7, 1987 PS 208
If you need a constant not given here or do not understand a
problem, please ask me about it. No notes, books, etc. may be
used during this exam.
2 -19
g = 9.8 m/sec e = 1.6 x 10 C
9 2 2
1/(4 pi epsilon ) = 9.0 x 10 N m / C
0
-31
The mass of the electron is 9.11 x 10 kg.
1. Two point charges Q and Q are a distance d apart,
1 2
and their combined charge is Q . If they repel each other
tot
with a force F, find the two charges in terms of Q , d , and
tot
F.
2. A force F = + kx acts on a particle of mass m.
(a) Show that the differential equation governing the motion of
2
d x
the particle is m --- - kx = 0 .
2
dt
alpha t
(b) Show that e is a solution of this equation and find the
appropriate value or values of alpha .
(c) Interpret the solution physically (i. e. by describing it
qualitatively or by sketching it). What is wrong with this
motion, and where does the problem arise?
3. (From homework). A thin cylindrical shell of radius R is
1
surrounded by a second concentric cylindrical shell of radius
R . The inner shell has a total charge of - Q and the outer
2 1
shell + Q , with Q > Q > 0 . Assuming the length L of the shells
2 2 1
is much greater than either radius, determine the electric field
as a function of r (the perpendicular distance from the common
axis of the cylinders) for all values of r .
4. A long thin rod is bent into the form of a semicircle of radius
b , with its ends on the x axis at x=+b and x=-b. The rod carries
a charge density
lambda = A cos (theta),
where A is a constant and the angle theta is measured from the right
end. Find the y-component of the electric field at the origin (the center
of the circle).