ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS
JULY 14 - JULY 20
Young and Freedman - 12th Ed - CHAPTER 24
9. In showing your work for this problem, you should first
work out, from the definition of capacitance, the
capacitance per unit length for infinitely long coaxial
cylinders. Then apply that result to these coaxial
cylinders of finite length.
64. Add part (c) What is the energy stored in each
combination before the switch S is thrown?
YOUNG - 11e - CHAPTER 24
62. A 4.00 microF capacitor and a 6.00 microF capacitor are
connected in series across a 660-V supply line.
(a) Find the charge on each capacitor and the voltage
across each. (b) The charged capacitors are disconnected
from the line and from each other and then reconnected
to each other, with terminals of like sign together.
Find the final charge on each and the voltage across each.
Young and Freedman - 12th Ed - CHAPTER 25
48. In part (b), Y&F want the NET power output of the
battery, i.e. the power output of the EMF minus the
power dissipated in the internal resistance of the
battery. In part (c), you are to assume that the 8 volt
battery is rechargeable; i.e., running current "backward"
through the battery will result in the conversion of
electric potential energy into chemical energy of the
battery. Also in part (d), Y&F are again asking for the
net rate of energy conversion, i.e. the rate of
production of thermal energy in the internal resistance
of the battery plus the rate of energy storage in the
battery's chemicals. (Running current "backward" through
a non-rechargeable battery would result in a dramatic
increase in the internal resistance of the battery; i.e.,
all of the energy would then be converted into thermal
energy.)
60. In my copy of Y&F 12e, there is a misprint in this problem.
The total length of the composite wire is 2.0 m (not 2.0 mm).
64. It is very important to do this problem by the general
method for finding resistance: (1) imagine a selected
current I flowing between the two relevant locations on
the conducting material; (2) find J in the material in
terms of I and in terms of location within the material,
then E in the material (in terms of location and I), and
then the voltage V between the two relevant locations;
and (3) use the DEF of resistance for an Ohmic material,
namely R=V/I -- your selected I will drop out, leaving
only geometry and resistivity.
YOUNG - 11e - CHAPTER 25
58. The available kinetic energy per unit volume, due to the
drift speed of the conduction electrons in a current-
carrying conductor, can be defined as
K/volume=n((1/2)m(v_d)^2). Evaluate K/volume for the
copper wire and current of Example 25.1 (page 850).
(b) Calculate the total change in electric potential
energy for the conduction electrons in 1.0 cm^3 of
copper if they fall through a potential drop of 1.0 V.
How does your answer compare to the available kinetic
energy in 1.0 cm^3 due the the drift speed?
WOLFSON - CHAPTER 26
10. Two square conducting plates measure 5.0 cm on a
side. The plates are parallel, spaced 1.2 mm
apart, and initially uncharged. (a) How much work
is required to transfer 7.2 microC from one plate
to the other? (b) How much work is required to
transfer a second 7.2 microC?
15. Two conducting spheres of radius a are separated
by a distance L >> a; since the distance is large,
neither sphere affects the other's electric field
significantly, and the fields remain spherically
symmetric. (a) If the spheres carry equal but
opposite charges +-q, show that the potential
difference between them is 2kq/a. (b) Write an
expression for the work dW involved in moving an
infinitesimal charge dq from the negative to the
positive sphere. (c) Integrate your expression
to find the work involved in transferring a
charge Q from one sphere to the other, assuming
both are initially uncharged.
52. You have three capacitors: capacitors 1 and 3 each
have a capacitance of 0.02 microF and capacitor 2
has a capacitance of 0.01 microF. You first
connect capacitors 2 and 3 in parallel; then you
construct a series capacitor circuit consisting of
a 100 V battery, capacitor 1, and the combination
of capacitors 2 and 3. (a) Draw a circuit diagram
for your capacitor circuit. (b) What is the
equivalent capacitance of your three capacitors
connected in this fashion? (c) What is the charge
on each capacitor in the circuit? (d) What is the
voltage across each capacitor in the circuit?
(P prefixes) HRW Problem Supplement #1 - CHAPTER 26
66. Two parallel-plate capacitors A and B are connected
in parallel across a 600 V battery. Each plate has
area 80.0 cm^2 and the plate separations are 3.0 mm.
Capacitor A is filled with air; capacitor B is
filled with a dielectric of dielectric constant
Kappa = 2.60. Find the magnitude of the electric
field within (a) the dielectric of capacitor B and
(b) the air of capacitor A. What are the free
charge densities sigma on the higher-potential
plate of (c) capacitor A and (d) capacitor B?
(e) What is the induced charge density sigma' on
the surface of the dielectric which is nearest to
the higher-potential plate of capacitor B.
Young and Freedman - 12th Ed - CHAPTER 27
76. Please add the following part:
(d) For each of the above magnetic fields, what
will be the maximum kinetic energy of the loop if
it is released from rest from the position shown
in Figure 27.66 (you may consider the loop to be
pivoted about the y-axis and you may ignore all
friction)?
WOLFSON - CHAPTER 27
4. The electron beam that "paints" the image on a
computer screen contains 5 million electrons per
cm of its length. If the electrons move toward
the screen at 60 million m/s, how much current
does the beam carry? What is the direction of
this current?
62. A power plant produces 1000 MW to supply a city
40 km away. Current flows from the power plant
on a single wire of resistance 0.050 Ohms/km,
through the city, and returns via the ground,
assumed to have negligible resistance. At the
power plant the voltage between the wire and the
ground is 115 kV. (a) What is the current in
the wire? (b) What fraction of the power is
lost in transmission? (c) What should be the
power line voltage if the transmission loss is
not to exceed 2.0 %.
72. A circular pan of radius b has a plastic bottom and
metallic side wall of height h. It is filled with
solution of resistivity rho. A metal disk of radius
a and height h is placed at the center of the pan,
as shown in the figure (pdf version). Assume that
the side wall and the disk are perfect conductors.
(a) Assume that a current I is flowing between the
metal disk and the metallic side wall. Find an
expression for the electric field strength at a
distance r (a < r < b) from the center of the metal
disk. (b) Find an expression for the voltage
between the metal disk and the metallic side wall
which would be required to produce current I.
(c) Use the definition of resistance with your
results from parts (a) and (b) to show that the
resistance measured from side to disk is given by
rho*ln(b/a)/(2pi*h).
Halliday and Resnick - 2nd Ed - CHAPTER 27
7. Two metal objects, a saw and a wrench, are lying
side-by-side on an non-conducting table; the two
metal objects are not in contact with one another;
they have net charges of +70 pC and -70 pC, and
this results in a 20 V potential difference
between them. (a) What is the capacitance of the
system? (b) If the charges are changed to +200 pC
and -200 pC, what does the capacitance become?
(c) What does the potential difference become?
13. The figure for this problem is Fig. 24-36 (p. 843).
A slab of copper of thickness (0.629)d is thrust
into a parallel-plate capacitor of plate area
115 cm^2 and separation distance d = 1.24 cm; it
is exactly halfway between the plates. Assume that
charges of +-702 pC existed on the two plates
before the slab was introduced, and also that the
battery used to charge the plates was disconnected
before the insertion. (a) What is the electric
field strength in the air gap before and after
insertion of the slab? (b) What is the voltage
between the plates before and after insertion of
the slab? (c) What is the capacitance after the
slab is introduced? (d) What is the stored
electrostatic energy before and after the slab is
inserted? Now suppose that the slab is not made
of copper, but rather of a dieletric material with
kappa = 2.61. Also suppose that an 85.5 V battery
is connected to the capacitor plates while the
dielectric is being inserted. WITHOUT resorting
to a calculation of capacitance, find (e) the
electric field in the gap, and (f) the charge on
the capacitor plates before and after the insertion.
(g) Use your answer to (f) to find the capacitance
after the slab is in place. (h) What is the stored
electrostatic energy before and after the slab is
inserted?
18. Two parallel plates of area 100 cm^2 are given charges
of equal magnitudes 0.89 microC but opposite signs.
The electric field within the dielectric material
filling the space between the plates is 1.4 MV/m.
(a) Calculate the dielectric constant of the material.
(b) Determine the magnitude of the charge induced on
each dielectric surface. (c) The capacitor will fail
(short out and burn up) if the electric field
between the plates exceeds 20 MV/m; as a result the
maximum energy that can be stored in this capacitor
is 0.292 J. Find the separation distance between the
plates.
43. You are asked to construct a capacitor having a
capacitance near 1 nF and a breakdown potential in
excess of 10000 V. You think of using the sides of
a tall Pyrex drinking glass as a dielectric, lining
the inside and outside curved surfaces with aluminum
foil to act as the plates. The glass is 15 cm tall
with an inner radius of 3.6 cm and an outer radius
of 3.8 cm. What are the (a) capacitance and (b)
breakdown potential of this capacitor?
Young and Freedman - 12th Ed - CHAPTER 28
69. To get credit for this problem, you must show
carefully how to use the Biot-Savart Law to arrive
at the answer.
WOLFSON - CHAPTER 28
12. A defective starting motor in a car draws 300 A from
the car's 12 V battery, dropping the battery terminal
voltage to only 6 V. A good starter motor should draw
only 100 A. What will the battery terminal voltage
be with a good starter?
42. You have three resistors: resistors 2 and 3 each
have a resistance of 40 kOhms and resistor 1
has a resistance of 30 kOhms. You first
connect resistors 2 and 3 in parallel; then you
construct a series circuit consisting of a 100 V
battery, resistor 1, and the combination
of resistors 2 and 3. (a) Draw a circuit diagram
for your circuit. You have three voltmeters, each
with a different internal resistance. You will
use each voltmeter, in turn, to measure the voltage
across resistor 1 while the circuit is in operation.
What will be the reading when the voltage is
measured with a (b) 50-kOhm voltmeter,
(c) a 250-kOhm voltmeter, and (d) a digital meter
with a 10-MOhm resistance?
Halliday and Resnick - 2nd Ed - CHAPTER 30
9. A stationary circular wall clock has a face with a
radius of 15 cm. Six turns of wire are wound around
its perimeter; the wire carries a current of 2.0 A in
the clockwise direction. The clock is located where
there is a constant, uniform external magnetic field
of magnitude 70 mT (but the clock still keeps perfect
time). At exactly 1:00 p.m., the hour hand of the
clock points in the direction of the external magnetic
field. (a) After how many minutes will the minute hand
point in the direction of the torque on the winding due
to the magnetic field? (b) Find the torque magnitude.
22. An electric field of 1.50 kV/m and a magnetic field of
0.400 T act on a moving electron to produce no net force.
(a) Calculate the minimum speed v of the electron.
(b) Draw the vectors E, B, and v (E, B, and v are vector
symbols).
29. An alpha particle (q = +2e, m = 4.00 u) travels in a
circular path of radius 4.50 cm in a uniform magnetic
field with B = 1.20 T. Calculate (a) its speed, (b) its
period of revolution, (c) its kinetic energy in electron-
volts, and (d) the potential difference through which it
would have to be accelerated to achieve this energy.
31. An electron has an initial velocity of
(12.0 km/s)j + (15.0 km/s)k and a constant acceleration
of (2.00 Tm/s^2)i in a region in which uniform electric
and magnetic fields are present. If B = (400 microT)i,
find the electric field E (E and B are vectors).
(P prefixes) HRW Problem Supplement #1 - CHAPTER 30
73. A long, hollow cylindrical conductor (inner radius
= 2.0 mm, outer radius = 4.0 mm) carries a current
of 24 A distributed uniformly across its cross
section. A long thin wire that is coaxial with
the cylinder carries a current of 24 A in the
opposite direction. What are the magnitudes of
the magnetic fields (a) 1.0 mm, (b) 3.0 mm, and
(c) 5.0 mm from the central axis of the wire and
cylinder?
FISHBANE PROBLEMS - CHAPTER 30
32. Consider a toroidal solenoid with a square cross
section, each side of which has length 3 cm.
The inner wall of the torus forms a cylinder of
radius 12 cm (figure 28.25(a) on page 976 could
roughly be a toroid of this description -- for a
cutaway view see figure 30.8 on page 1037). The
torus is wound evenly with 200 turns of 0.3 mm-
DIAMETER copper wire. The wire is connected to a
3.0 V battery with negligible internal resistance.
(a) Calculate the largest and smallest magnetic
field across the cross section of the toroid.
(b) Calculate the absolute value of the magnetic
flux through one turn of the toroidal solenoid.
(c) Do you need to cool the solenoid? (Calculate
the heat created per second when current is flowing.)
WOLFSON - CHAPTER 30
24. A 5.0 cm by 10 cm rectangular wire loop is carrying
a current of 500 mA; the plane of the loop is
purely horizontal, with the 5.0 cm sides at the
north and south ends of the loop. A long straight
wire is carrying a current of 20 A due north; the
long straight wire is in the same plane as the loop
and is 2.0 cm to the west of the westernmost side of
the loop. Find the net magnetic force on the loop
by the current in the wire.
42. A conducting slab extends infinitely in the x and y
directions and has thickness h in the z direction.
It carries a uniform current density vecJ = J(veci)
(vec indicates that the first J and the i are vectors,
-- the veci is the unit vector in the x direction).
Find the magnetic field strength (a) inside and
(b) outside the slab, as functions of the distance z
from the center plane of the slab.
48. A long solenoid with n turns per unit lengths carries
a current I. The current returns to its driving
battery along a wire of radius R that passes through
the solenoid, along its axis. Find expressions for
(a) the magnetic field strength at the surface of
the wire, and (b) the angle the field at the wire
surface makes with the solenoid axis.
57. The figure below shows a wire of length L carrying
current fed by other wires that are not shown (the
current direction is to the right). Point A lies
on the perpendicular bisector, a distance y from the
wire. Show how to use the Biot-Savart Law to
demonstrate that the magnetic field at A due to the
straight wire alone has magnitude
(mu_0(I)L)/((2pi)y(sqrt(L^2+4y^2))).
What is the field direction?
_ . B . A
y
- ------------------------------ I -->
|<-- L -->|
58. Point B in the figure above lies a distance y
perpendicular to the end of the wire. Show how to
use the Biot-Savart Law to demonstrate that the
magnetic field at B due to the straight wire alone
has magnitude
(mu_0(I)L)/((4pi)y(sqrt(L^2+y^2))).
What is the field direction?
68. A solid conducting wire of radius R runs parallel
to the z axis and carries a current density given by
vecJ = J_0(1-(r/R))veck, where J_0 is a constant and
r the radial distance from the wire axis (vec
indicates that the first J and the k are vectors,
-- the veck is the unit vector in the z direction).
Find expressions for (a) the total current in the
wire, (b) the magnetic field strength for r > R,
and (c) the magnetic field strength for r < R.
Halliday and Resnick - 2nd Ed - CHAPTER 31
5. A square loop of wire of edge a carries a current i.
Show that the value of B at the center of the square
is given by
B =(2sqrt2)(mu_0)(i)/(pi)a
Hint: You may use the result of Wolfson 30:57.
25. A circular loop of radius 12 cm carries a current of
15 A. A flat coil of radius 0.82 cm, having 50 turns
and a current of 1.3 A, is concentric with the loop.
(a) What magnetic field strength B does the loop
produce at its center? (b) What torque acts on the
coil? Assume that the planes of the loop and coil
are perpendicular and that the magnetic field due to
the loop is essentially uniform throughout the
volume occupied by the coil.
KNIGHT - CHAPTER 33
69. A long, straight wire with linear mass density of
50 g/m is suspended by many fine threads; the
hanging part of the wire is perfectly horizontal.
A long section of the wire is within a constant
and uniform magnetic field; the rest of the wire
is in an ignorably small magnetic field. A 10 A
current in the wire experiences a horizontal
magnetic force; as a result, the wire is deflected
until the threads make a 10 degree angle with the
vertical. The length of the wire within the
magnetic field is not given. (a) Make a drawing
of the situation, showing the directions of the
current and the magnetic field. (b) Make a
free-body diagram for the current-carrying wire.
(c) What is the strength of the magnetic field?
A Prefixes
A6: Consider a circuit (pdf version) containing five
identical light bulbs and an ideal battery. Assume
that the resistance of each light bulb remains
constant. (a) When the switch is closed, rank the
bulbs (A through E) based on their brightness.
(b) If the resistance of each light bulb is
23.5 Ohms, what is the resistance of the entire
network of bulbs when the switch is closed?
(c) If the battery voltage is 11 V, what is the
current through bulb C when the switch is closed?
(d) If the switch were opened, what would be the
resistance of the entire network of bulbs?
(e) What would be the current through bulb C
if the switch were opened? (f) For each of the
bulbs A-E, does it get brighter or dimmer when
the switch is opened?
A7: A particle with a charge of -6.00 nC is moving in a
uniform magnetic field of strength 1.25 T; the field
points in the negative z direction. The magnetic
force on the particle is measured to have an x
component of -0.400 mN and a y component of +7.60 mN.
(a) Calculate the x component of the velocity of the
particle. (b) Calculate the y component of the
velocity of the particle. (c) What can be determined
about the z component of the velocity of the particle?
Explain your answer carefully. (d) What is the scalar
product of the force vector and your velocity vector?
Hint: you must have saved your answers to (a) and (b)
in your calculator to correctly determine part (d) in
the most straightforward manner.
A8: A coil with a magnetic dipole moment of 1.47 A⋅m^2
is within a uniform magnetic field of magnitude
0.835 T. (a) Make a graph of the potential energy of
the coil versus angle in degrees between the magnetic
moment and magnetic field directions; let the angle
vary between -180 and +180 degrees. (b) For each of
zero, +-90, and +180 degrees, make a drawing of the
magnetic field and the coil (assume a single turn),
showing the current in the coil and the resulting
magnetic dipole moment vector (see Y&F figure 27.35
as an example). (c) What is the change in this
orientational potential energy when the coil is
rotated 180 degrees, beginning with its magnetic
dipole moment antiparallel to the field direction?
A9: A beginning physics student has used a two-point
probe to measure the effective electrostatic field
in a shallow pan of water. He reports his results
to you in an xy-coordinate system. He reports that
for all points with x<0, the electrostatic field
is 300 N/C in the +y direction; for all points
with x>0, the reported electrostatic field is
300 N/C in the -y direction; for x=0, the field
is zero. Use the integral form of Kirchhoff's
Loop Rule to double check the feasibility of the
student's report; use a square loop with vertices
(-1,-1), (-1,1), (1,1), and (1,-1) and do the
integral in the CCW direction (as viewed from +z).
(a) State the value of the integral for each side
of the square. (b) Is there any possible
distribution of charges that can produce the field
reported by the student? Explain your answer
carefully.