Fall ‘12
PHY 122 Homework Solutions #2
Chapter 21 Problem 40
Two parallel circular rings of radius R have their centers on the x
axis separated by a distance l , as shown in Fig. 21–60. If each ring
carries a uniformly distributed charge Q, find the electric field, at
E(x) points along the x axis.
Chapter 21 Problem 41
(a) Two equal charges Q are positioned at points (x=l, y=0) and (x=-l,
y=0). Determine the electric field as a function of y for points along
the y axis. (b) Show that the field is a maximum at
.
Chapter 21 Problem 61
A positive charge q is placed at the center of a circular ring of radius
R. The ring carries a uniformly distributed negative charge of total
magnitude 2Q. (a) If the charge q is displaced from the center a small
distance x as shown in Fig. 21–69, show that it will undergo simple
harmonic motion when released. (b) If its mass is m, what is its
period?
Chapter 22 Question 4
What can you say about the flux through a closed surface that
encloses an electric dipole?
Solution
The net flux will be zero. An electric dipole consists of two charges
that are equal in magnitude but opposite in sign, so the net charge of
an electric dipole is zero. If the closed surface encloses a zero net
charge, than the net flux through it will be zero.
Chapter 22 Question 11
A point charge Q is surrounded by a spherical surface of radius r0,
whose center is at C. Later, the charge is moved to the right a
distance ½ r0, but the sphere remains where it was, Fig. 22–23. How
is the electric flux FE through the sphere changed? Is the electric field
at the surface of the sphere changed? For each “yes” answer, describe
the change.
Solution
The electric flux through the sphere remains the same, since the same
charge is enclosed. The electric field at the surface of the sphere is
changed, because different parts of the sphere are now at different
distances from the charge. The electric field will not have the same
magnitude for all parts of the sphere, and the direction of the electric
field will not be parallel to the outward normal for all points on the
surface of the sphere. The electric field will be stronger on the side
closer to the charge and weaker on the side further from the charge.
Chapter 22 Problem 2
The Earth possesses an electric field of (average) magnitude 150 N/C
near its surface. The field points radially inward. Calculate the net
electric flux outward through a spherical surface surrounding, and
just beyond, the Earth’s surface.
Chapter 22 Problem 3
A cube of side l is placed in a uniform field E0 with edges parallel to
the field lines. (a) What is the net flux through the cube? (b) What is
the flux through each of its six faces?
Chapter 22 Problem 6
Figure 22–26 shows five closed surfaces that surround various
charges in a plane, as indicated. Determine the electric flux through
each surface S1,S2,S3,S4 and S5. The surfaces are flat “pillbox” surfaces
that extend only slightly above and below the plane in which the
charges lie.
Chapter 22 Problem 9
In a certain region of space, the electric field is constant in direction
(say horizontal, in the x direction), but its magnitude decreases from
E = 560 N/C at x = 0m to E = 410N/C at x = 25m. Determine the
charge within a cubical box of side l = 25m, where the box is
oriented so that four of its sides are parallel to the field lines (Fig. 22–
28).
Chapter 22 Problem 21
A spherical cavity of radius 4.50 cm is at the center of a metal sphere
of radius 18.0 cm. A point charge Q = 5.50μC rests at the very center
of the cavity, whereas the metal conductor carries no net charge.
Determine the electric field at a point (a) 3.00 cm from the center of
the cavity, (b) 6.00 cm from the center of the cavity, (c) 30.0 cm from
the center.
Chapter 22 Problem 34
A very long solid nonconducting cylinder of radius R0 and length l
(R0 << l) possesses a uniform volume charge density ρE C/m3. Fig.
22–34. Determine the electric field at points (a) outside the cylinder
(R > R0) and (b) inside the cylinder (R < R0). Do only for points far
from the ends and for which R << l.