ADDITIONS TO WOLFSON PROBLEMS AND PROBLEMS FROM OTHER TEXTS
JULY 6  JULY 12
WOLFSON  CHAPTER 23
4. Assume the ball is made mostly of carbon, for which
the number of protons is equal to the number of neutrons.
32. (b) Sketch the net electric field lines qualitatively.
E1. This is the exercise accompanying Example 236 on page 582.
(P prefixes) HRW Problem Supplement #1  CHAPTER 23
25. A semiinfinite nonconducting rod (i.e. infinite in one
direction only) has uniform positive linear charge density
lambda. Show that the electric field at point P makes an
angle of 45 degrees with the rod and that this result is
independent of the distance R. (HINT: Separately find
the parallel and perpendicular (to the rod) components
of the electric field at P, and then compare those
components.)
rod
starts
here
_ +++++++++++++++++++++++++ =====> very long
 

R 

 
 P <== this point is a distance R from the end
of the rod
55. A charge (uniform linear density = 9.0 nC/m) lies on a
string that is stretched along an x axis from x = 0 to
x = 3.0 m. Determine the magnitude of the electric
field at x = 4.0 m on the x axis.
59. An electric dipole swings from an initial orientation i
to a final orientation f in a uniform external electric
field E. E points in the +y direction, in orientation i
the dipole points 20 degrees below the x direction, and
in orientation f the dipole points 20 degrees above the
x direction. The electric dipole moment is 1.60 x
10^{27} Cm; the field magnitude is 3.00 x 10^6 N/C.
What is the change in the dipole's potential energy?
(P prefixes) HRW Problem Supplement #1  CHAPTER 24
24. A charge of uniform linear density 2.0 nC/m is distributed
along a long, thin, nonconducting rod. The rod is coaxial
with a long, hollow, conducting cylinder (inner radius =
5.0 cm, outer radius = 10 cm). The net charge on the
conductor is zero. (a) What is the magnitude of the
electric field 15 cm from the axis of the cylinder? What
is the surface charge density on (b) the inner surface and
(c) the outer surface of the conductor?
55. The figure for this problem is Wolfson Fig. 249(a). An
electric field given by E = 4i  3(y^2 + 2)j pierces the
Gaussian cube shown in the figure. (E is in N/C and y is
in m.) The i direction is to the right, the j direction is
toward the top of the page, and the z direction is out of
the page (i.e. perpendicular to face A). The distance s is
2.0 m, with y = 0 at the bottom of the cube. What is the
electric flux through (a) the top face (face B), (b) the
bottom face, (c) the left face, and (d) the back face.
(e) What is the net electric flux through the cube?
(f) What net charge is enclosed by the Gaussian cube?
66. A thin, metallic, spherical shell of radius a has a charge
Qa. Concentric with it is another thin, metallic,
spherical shell of radius b (where b > a) and charge Qb.
Find the electric field at points a distance r from the
common center, where (a) r < a, (b) a < r < b, and
(c) r > b. (d) Determine how the charges are distributed
on the inner and outer surfaces of the shells (give the
surface charge densities).
FISHBANE PROBLEMS  CHAPTER 24
38. Two large, thin, metallic plates are placed parallel to
each other, separated by 15 cm. The top plate carries a
uniform charge density of 24 microC/m^2, while the bottom
plate carries a uniform charge density of 38 microC/m^2.
What is the electric field (magnitude and direction) (a)
halfway between the plates? (b) above the two plates?
(c) below the two plates? (d) What are the surface charge
densities on the top and bottom surfaces of both plates?
45. A metal sphere of radius a is surrounded by a metal shell
of inner radius b and outer radius R. The flux through a
spherical Gaussian surface located between a and b is
Q/epsilon0, and the flux through a spherical Gaussian
surface just outside radius R is 2Q/epsilon0. (a) What
are the total charges on the inner sphere and on the shell?
(b) Where are the charges located, and (c) what are the
charge densities?
Halliday and Resnick  2nd Edition  CHAPTER 25
1. Water in an irrigation ditch of width w = 3.22 m and
depth d = 1.04 m flows with a speed of 0.207 m/s. The
mass flux of the flowing water through an imaginary
surface is the product of the water's density (1000 kg/m^3)
and its volume flux through that surface. Find the mass
flux through the following imaginary surfaces: (a) a
surface of area wd, entirely in the water, perpendicular
to the flow; (b) a surface with area 3wd/2, of which wd
is in the water, perpendicular to the flow; (c) a surface
of area wd/2, entirely in the water, perpendicular to the
flow; (d) a surface of area wd, half in the water and
half out, perpendicular to the flow; (e) a surface of
area wd, entirely in the water, with its normal 34 degrees
from the direction of flow.
(P prefixes) HRW Problem Supplement #1  CHAPTER 25
88. Three particles with the same charge q and same mass m are
initially fixed in place to form an equilateral triangle
with edge lengths d. (a) If the particles are released
simultaneously, what are their speeds when they have
traveled a large distance (effectively an infinite distance)
from each other? (Measure the speeds in the original rest
frame of the particles.)
Suppose, instead, the particles are released one at a time:
The first one is released, and then, when the first one is
at a large distance, a second one is released, and then, when
that second one is at a large distance, the last one is
released. What then are the final speeds of (b) the first
particle, (c) the second particle, and (d) the last particle?
WOLFSON  CHAPTER 26
E2. This is the exercise accompanying Example 261 on page 660.