ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS
JULY 28 - AUG 5
YOUNG 11e - CHAPTER 24
32. A parallel-plate, air-filled capacitor has plates of
area 0.00260 square meters. The magnitude of charge
on each plate is 8.20 pC, and the potential difference
between the plates is 2.40 V. What is the electric
field energy density in the volume between the plates?
FISHBANE PROBLEMS - CHAPTER 28
57. Show how to use Kirchhoff's loop rule (write a clear and
concise explanation for each term) to find a differential
equation which can be solved for Q(t), the charge as a
function of time, on a discharging capacitor. The figure for
this problem is Fig. 26.23 (page 898), with an initial charge
of Q_0 on capacitor C when the switch is closed at t = 0.
Let positive current represent a charging capacitor, i.e.
i = (dQ/dt). Show BY DIRECT SUBSTITUTION that
Q(t) = (Q_0)e^(-t/RC) is a solution of your differential
equation.
Young and Freedman - 12th Ed - CHAPTER 29
28. Please add the following parts:
(c) What is the magnitude of the induced electric
field at a point just outside the center of the
solenoid (lengthwise) and 4.00 cm from the axis of
the solenoid? (d) Using Figure 29.54 (p. 1027),
and applying that figure to the situation of this
problem, what would be the direction of the induced
electric field in part (a) of this problem?
33. Please add the following part:
(b) What is the mutual inductance of this two-coil
geometry? (Note that, in part (a), the question
is asking only for the average induced EMF in the
second winding due to the change of current in the
first winding; in other words, you are to ignore
the back EMF in the second winding due to its
self inductance.)
63. The rod in this problem is intended to be the moving
part in a simple DC generator. Here is a figure
of such a generator; the connecting wires are not
shown. This problem is most straightforwardly done
by integrating vcrossBdotdl over the length of the
moving rod (note that v in this integral will not
be constant). Here is a pdf version of the figure.
77. Note that the metal rails in the figure for this
problem are drawn in gray; the thin black lines
represent a non-metal frame. For part (b), remember
that the terminal speed is the maximum speed, i.e.
the speed at which the acceleration becomes zero.
Halliday and Resnick - 2nd Ed - CHAPTER 29
22. An initially uncharged capacitor C is fully charged by a
device of constant EMF in series with a resistor R.
(a) Show that the final energy stored in the capacitor is
half the energy supplied by the EMF device. (b) By direct
integration of (i^2)R over the charging time, show that the
thermal energy dissipated by the resistor is also half the
energy supplied by the EMF device.
Young and Freedman - 12th Ed - CHAPTER 30
48. The main purpose of this problem is to calculate
the inductance of a length of coaxial cable (i.e.
part (d)). The problem assumes (but does not
state) that the cable is being used to carry high
frequency alternating currents (like a cable carrying
a TV signal); in such a case the currents would be
largely confined to the outer surface of the inner
wire and the inner surface of the outer tube (i.e.
the magnetic field is confined to the nonconducting
space between the two metal pieces). So the flux
calculated in part (c) is in fact the total flux.
Part (b) is asking you to turn the 2D flux integral
into a 1D integral (the integral over dl being
done implicitly); you may just ignore part (b).
And in part (c), the words "over the volume" are
silly; flux is always an integral over an area, so
the integral is over a rectangular area perpendicular
to the magnetic field between the two pieces of metal.
73. There is a misprint in this problem. The power series
expansion for ln(1+z) = z - z^2/2 + higher order terms.
Y&F mistakenly have a plus sign between the first
and second terms of the expansion.
YOUNG 11e - CHAPTER 30
18. An air-filled toroidal solenoid has 600 turns and a mean
radius of 6.90 cm. Each winding has a cross-sectional area
of 0.0350 square cm. Assume that the magnetic field is
uniform over the cross section of the windings.
(a) When the current in the solenoid is 2.50 A, what is the
magnetic field within the solenoid? (b) Calculate the
energy density in the solenoid directly from the magnetic
field strength. (c) What is the total volume enclosed by
the windings? (d) Use the volume from part c and the
energy density from part b to calculate the total energy
stored in the solenoid. (e) Use the geometry of the
solenoid to calculate its inductance. (f) Use 0.5LI^2
to calculate the energy stored in the solenoid. Compare
your answer to what you obtained in part d.
66. The figure for this problem is here. Switch S is closed
at time t=0 with no charge initially on the capacitor.
(a) What is the reading of each meter just after S is closed?
(b) What does each meter read long after S is closed?
(c) What is the maximum charge on the capacitor and when does
it occur? Here is a pdf version of the same figure.
68. The figure for this problem is here. The capacitor is
originally uncharged. The switch starts in the open position
and is then flipped to position 1 for 0.500 s. It is then
flipped to position 2 and left there. (a) If the resistance
r is very small, what is the upper limit for the amount of
charge the capacitor could receive? (b) Even if r is very
small, how much electrical energy will be dissipated in it?
(c) Sketch a graph showing the reading of the ammeter as a
function of time after the switch is in position 2, assuming
that r is very small and that current from left to right
through the ammeter is positive. (d) Sketch a graph showing
the charge on the right-hand plate of the capacitor as a
function of time after the switch is in position 2, assuming
that r is very small. Here is a pdf version of the
same figure.
Young and Freedman - 12th Ed - CHAPTER 31
36. Please add the following parts:
(d) Assume the circuit elements are arranged as shown
in Figure 31.25 on page 1088. What are the readings
from voltmeters V4 and V5? Remember that AC meters
give RMS values, not peak values. (e) If the
circuit elements are not changed but the angular
frequency of the source is changed to 645 rad/s,
what are the readings on the five voltmeters,
V1-V5? (f) Repeat part e. for 1245 rad/s.
YOUNG 11e - CHAPTER 31
60. You enjoy listening to KONG-FM, which broadcasts at 94.1 MHz.
You destest listening to KRUD-FM, which broadcasts at 94.0 MHz.
You live the same distance from both stations and both
transmitters are equally powerful, so both radio signals
produce the same 1.0 V source voltage as measured at your
house. Your goal is to design an LRC radio circuit with
the following properties: i) It gives the maximum power
response to the signal from KONG-FM; ii) the average power
delivered to the resistor in response to KRUD-FM is 1.00%
of the average power in response to KONG-FM. This limits
the power received from the unwanted station, making it
inaudible. You are required to use an inductor with
L = 1.00 microH. Find the capacitance C and resistance
R that satisfy the design requirements. NOTE: To get R,
you will need to save C in your calculator and use that
saved answer; this is because R depends on the small
DIFFERENCE between X_C and X_L, which magnifies any
rounding error in X_C. GBA
WOLFSON - CHAPTER 31
33. The figure for this problem is Y&F figure 29.36 on
page 1022. The distance between the rails is 10 cm,
the magnetic field strength is 0.50 T, the resistance
is 4.0 Ohms, and the bar is being pulled to the right
at a constant speed of 2.0 m/s. (a) Show carefully
how to use the principle of motional EMF to find the
absolute value of the EMF induced between the points
a and b. Find (b) the current in the resistor and
(c) the magnetic force on the bar. (d) Calculate
directly the rate of energy dissipation in the
resistor. (e) Calculate directly the rate at which
work is being done by the agent pulling the bar.
Young and Freedman - 12th Ed - CHAPTER 32
49. Hint for Problem 32.49: This is a Faraday's Law problem, but
with a radiated B field that is varying sinusoidally (so you
can write B(t) as Bmax*sin(omega*t) and differentiate to get
the maximum value of dB/dt).
Halliday and Resnick - 2nd Ed - CHAPTER 32
7. An elastic conducting material is stretched into a
circular loop of 12.0 cm radius. It is placed with
its plane perpendicular to a uniform 0.800 T
magnetic field. When released, the radius of the
loop starts to shrink at an instantaneous rate of
75.0 cm/s. What EMF is induced in the loop at
that instant? Hint: this problem is most easily
(and most correctly) done as a motional EMF
problem, but it is also instructive to do the
problem using Faraday's Law (remember to use the
chain rule properly).
20. A stiff wire bent into a semicircle of radius 0.700 m
is rotated with frequency 80 Hz in a uniform magnetic
field of 0.400 T, as suggested in the figure
(pdf version). By means of the two pivots on which it
rotates, the stiff wire is connected to a long wire
of resistance 3.4 Ohms; the stiff wire combined with
the long wire forms a conducting loop. When the stiff
wire is in the position shown in the figure, the
absolute value of the magnetic flux through the
non-circular part of the loop is 1.20 Wb. (a) Find
the absolute value of the total flux through the loop
when the stiff wire is in the position shown in the
figure. (b) When the stiff wire has been rotated
first by 90 degrees, and then by 180 degrees from the
position shown in the figure, what is the absolute
value of the total flux through the loop? (c) With
respect to the position shown in the figure, at what
point or points during the rotation of the stiff wire
is the absolute value of the flux through the loop a
maximum? (d) With respect to the position shown in
the figure, at what point or points during the
rotation of the stiff wire is the absolute value of
the flux changing with time at a maximum rate?
(e) What is the maximum rate at which the flux
through the loop is changing with time?
(f) What is the amplitude of the varying EMF induced
in the loop? (You must clearly show your logic to
get full credit.)
27. At a certain place, Earth's magnetic field has
magnitude B = 0.590 gauss and is inclined downward at
an angle of 70.0 degrees to the horizontal. A flat
horizontal circular coil of wire with a radius of
10.0 cm has 1000 turns and a total resistance of
85.0 Ohms. It is connected to a meter with 140 Ohm
resistance. The coil is flipped through a half-
revolution about a diameter, so that it is again
horizontal. (a) What is the absolute value of the
change in magnetic flux through the coil as a result
of the flip? (b) How much charge flows through the
meter during the flip? (HINT: You aren't given enough
information to find the induced current, and you don't
know the amount of time required for the flip; however,
you can solve for the product of current -- assumed
constant -- and time.)
(P prefixes) HRW Problem Supplement #1 - CHAPTER 32
28. Suppose that a parallel-plate capacitor has circular plates
with radius R = 30 mm and a plate separation of 5.0 mm.
Suppose also that sinusoidal potential difference with a
maximum value of 150 V and a frequency of 60 Hz is applied
across the plates; that is V = (150 V)sin[2pi(60 Hz)t].
(a) Find B_max(R), the maximum value of the induced magnetic
field that occurs at r = R.
(b) Plot B_max(r) for 0 < r < 10 cm.
38. A capacitor with parallel circular plates of radius R is
discharging via a current of 12.0 A. Consider a loop of
radius R/3 that is centered on the central axis between the
plates. (a) How much displacement current is encircled by
the loop? The maximum induced magnetic field has a magnitude
of 12.0 mT. (b) At what radial distance, or distances, from
the central axis of the plate is the magnitude of the induced
magnetic field 3.00 mT?
WOLFSON - CHAPTER 32
9. A rectangular loop of length L and width w is
located a distance a from a long, straight wire.
What is the mutual inductance of this arrangement?
The picture for this problem is Y&F Figure 29.27 on
page 1021, with b-a in that figure equal to w in
this problem statement.
Halliday and Resnick - 2nd Ed - CHAPTER 33
11. A coil with an inductance of 2.0 H and a resistance of
10 Ohms is suddenly connected to a resistanceless battery
with EMF = 100 V. At 0.10 s after the connection is made,
what are the rates at which (a) energy is being stored in
the magnetic field, (b) thermal energy is appearing in the
resistance, and (c) energy is being delivered by the battery?
12. The figure for this problem is Figure 30.11 on page 1041 with
EMF = 10.0 V, R = 6.70 Ohms, and L = 5.50 H. With S2 open,
S1 was closed at time t = 0. (a) How much energy is
delivered by the battery during the first 2.00 s? (b) How
much of this energy is stored in the magnetic field of
the inductor? (c) How much of this energy is dissipated
in the resistor?
FISHBANE PROBLEMS - CHAPTER 33
46. The figure for this problem is Fig. 30.11. After being
closed for a long time, S1 is suddenly opened while, at
the same instant, S2 is suddenly closed. Show how to
use Kirchhoff's loop rule to find the differential equation
which can be solved for the resulting I(t), and show that
I(t) = (EMF/R)e^(-tR/L) is a solution of that differential
equation.
(P prefixes) HRW Problem Supplement #1 - CHAPTER 33
5. The frequency of oscillation of a certain LC circuit is
200 kHz. At time t = 0, plate A of the capacitor has maximum
positive charge. At what times t > 0 will (a) plate A again
have maximum positive charge, (b) the other plate of the
capacitor have maximum positive charge, and (c) the inductor
have maximum magnetic field?
12. In an oscillating LC circuit in which C = 4.00 microF, the
maximum potential difference across the capacitor during
the oscillations is 1.50 V and the maximum current through
the inductor is 50.0 mA. (a) What is the inductance L?
(b) What is the frequency of the oscillations? (c) How
much time is required for the charge on the capacitor to
rise from zero to its maximum value?
44. An AC generator with EMF_max = 220 V and operating at
400 Hz causes oscillations is a series RLC circuit having
R = 220 Ohms, L = 150 mH, and C = 24.0 microF. Find (a)
the capacitive reactance X_C, (b) the impedance Z, and (c)
the current amplitude I. A second capacitor of the same
capacitance is then connected in series with the other
components. Determine whether the values of (d) X_C,
(e) Z, and (f) I increase, decrease, or remain the same.
50. An AC voltmeter with large impedance is connected in turn
across the inductor, the capacitor, and the resistor in a
series circuit having an alternating EMF of 100 V (rms);
it gives the same reading in volts in each case. What is
the reading? (To get any credit for your answer to this
problem, you must very carefully explain the logic that
you used to obtain that answer.)
WOLFSON - CHAPTER 34
6. An electric field points into the page and occupies a
circular region of radius 1.0 m. There is a magnetic field
forming circular closed loops centered on the circular region
and pointing clockwise. The magnetic field strength 50 cm
from the center of the region is 2.0 microT. (a) What is the
rate of change of the electric field? (b) Is the electric
field increasing or decreasing?
KNIGHT 2nd Ed - CHAPTER 35
24. A sinuosoidal radio wave of frequency 1.0 MHz is traveling
in the negative z direction. The electric field of the
radio wave oscillates in the plus or minus y direction.
The maximum electric field strength is 1000 V/m. What are
(a) the maximum radiated magnetic field strength,
(b) the radiated magnetic field strength and direction
at a point where the radiated electric field is
500 V/m in the negative y direction, and
(c) the smallest distance between a point on the wave
having the magnetic field of part b and a point where
the magnetic field is at maximum strength?
Halliday and Resnick - 2nd Ed - CHAPTER 36
1. An AC generator has EMF = (EMF_max)sin((w_d)t); it is
connected to an inductor of inductance L. (a) Write
Kirchhoff's Loop Rule for this circuit at a particular
instant of time. (b) Find the current as a function of
time. Hint: the result of (a) should be a simple
differential equation that can be solved easily by
integration. In this case, it is simplest to use
indefinite integration (antiderivatives); eliminate the
possible constant by an argument that the current should
be purely AC, with no DC contribution. Now assume
EMF_max = 25.0 V, w_d = 377 rad/s (w stands for omega),
and L=12.7 H. (c) What is the maximum value of the
current? (d) When the current is a maximum, what is the
EMF of the generator? (e) When the EMF of the generator
is -12.5 V and increasing in magnitude, what is the
current? (f) For the conditions of part (e), is the
generator supplying or taking energy from the circuit?
2. The AC generator of problem 1 is connected to a
capacitor of capacitance C. (a) Write Kirchhoff's Loop
Rule for this circuit at a particular instant of time.
Is your result a differential equation? (b) Find the
current as a function of time. Now assume
EMF_max = 25.0 V, w_d = 377 rad/s (w stands for omega),
and C=4.15 microF. (c) What is the maximum value of the
current? (d) When the current is a maximum, what is the
EMF of the generator? (e) When the EMF of the generator
is -12.5 V and increasing in magnitude, what is the
current? (f) For the conditions of part (e), is the
generator supplying or taking energy from the circuit?
4. A resistor of resitance R is connected to an AC
generator with EMF(t)=(EMF_max)sin((w_d)t). (a) Write
Kirchhoff's Loop Rule for this circuit at a particular
instant of time. Is your result a differential equation?
(b) Find the current as a function of time. Now assume
R=50 Ohm and EMF_max = 30.0 V. (c) What is the amplitude
of the resulting alternating current if the frequency of
the EMF is 1.00 kHz and (d) if the frequency of the EMF
is 8.00 kHz?
17. A typical "light dimmer" used to dim the stage lights in a
theater consists of a variable inductor L (the inductance
of which is adjustable between zero and L_{max}) connected
in series with a lightbulb (a lightbulb is a non-ohmic
resistor, but assume it is ohmic for the purpose of this
problem). The electrical supply for this series circuit is
120 V (rms) at 60.0 Hz; the lightbulb is rated as "120 V,
1000 W". (a) What L_{max} is required if the rate of energy
dissipation in the lightbulb is to be varied by a factor of
five from its upper limit of 1000 W? (b) Could one use a
variable resistor (adjustable between zero and R_{max})
instead of an inductor? If so, what R_{max} is required?
Why isn't this done?
KNIGHT 2nd Ed - CHAPTER 36
67. The figure for this problem is here. The figure shows
voltage and current graphs for a series LRC circuit with a
generator. The voltage curve first crosses the time axis
at t=25 microseconds; the current curve first crosses the
time axis at t=41.67 microseconds. (a) What is the
resistance in the circuit? (b) If L=200 microH, what is
the capacitance in the circuit? (c) What is the resonant
angular frequency for the circuit? Here is a pdf
version of the same figure.
A Prefixes
A:10 The figure shows a graph of the output voltage
versus time for an AC generator, and also the
current versus time for an attached resistor.
(a) Assuming the generator consists of a single
coil of many turns being rotated in a uniform
magnetic field, how many times per second is
the coil being rotated? (b) If the coil is
rectangular with sides 7.5 cm and 13 cm, and
if the magnetic field strength is 14 mT, at
least how many turns must the coil contain?
(c) What is the resistance of the circuit
containing the generator and the resistor?
(d) What is the maximum possible flux through
the generator coil as it is spinning? (e) For
the times shown on the graph, at which times is
the flux through the coil a maximum? Here is
a pdf version of the figure.
A:11 An LC circuit has an inductance of 0.360 H and a
capacitance of 0.280 nF. During the current oscillations,
the maximum current in the inductor is 1.50 A. (a) What
is the maximum energy stored in the capacitor at any time
during the current oscillations? (b) How many times per
second does the capacitor contain the amount of energy
found in part A? (c) At an instant in time when the
current in the inductor is 0.75 A, what is the amount of
energy stored in the capacitor? (d) If the cycle begins
(t=0) when the maximum energy is stored in the capacitor,
when is the first instant in time that the energy stored
in the capacitor is equal to the energy stored in the
inductor? (e) What is the current in the inductor at the
instant referred to in part (d)?
A:12 An LRC series circuit with L=0.125 H, R=242 Ohms, and
C=7.26 microF carries an RMS current of 0.452 A with a
frequency of 402 Hz. (a) What is the phase constant?
(b) What is the power factor? (c) What is the
impedance of this circuit? (d) What is the RMS EMF
of the source? (e) What is the average power delivered
by the source? (f) What is the average rate at which
electrical energy is converted to thermal energy in
the resistor? (g) What is the average rate at which
electrical energy is converted to other forms in the
capacitor and in the inductor? (h) If the driving
frequency were changed to the resonant frequency of
this circuit, what would be the resulting RMS current
(instead of 0.452 A)? (i) If the driving frequency
were changed to the resonant frequency of this circuit,
what would be the resulting average power delivered by
the source (instead of your answer to part (e))?
A:13 A satellite in geostationary orbit is used to transmit
data via electromagnetic radiation. The satellite is
at a height of 35000 km above the surface of the Earth,
and we assume it has an isotropic power output of
4.00 kW (in practice, satellite antennas transmit
signals that are less powerful but more directional).
The satellite dish which will receive the signal sent
from the satellite is located on the surface of the
Earth directly below the satellite. (a) What is the
intensity of the signal from the satellite at the
location of the antenna? (b) What is the energy
density of the electromagnetic radiation from the
satellite which is being received by the antenna?
(c) The satellite dish detects the variation in the
radiated electric field from the satellite. What is
the amplitude of the radiated electric field vector
of the satellite broadcast at the location of the dish?