ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS
JULY 13 - JULY 19
Young and Freedman - 11th Ed - CHAPTER 23
45. To get any credit for this problem, you MUST prove
any result that you take from problem 23.44.
72. In part (a) of this question, Y&F ask "What will a
voltmeter read ....". This is not a serious question
as asked. The shell is insulating and all voltmeters
measure current (as you will learn in section 26.3).
No current will flow in this case, so the voltmeter
will always read zero. So please change the wording
of this phrase to "What is the absolute value of the
potential difference between the following points?"
In part (b), there should be four parts rather than
three; compare (i) a and b, (ii) b and c, (iii) c
and infinity, and (iv) a and c. Part (c) should read,
"Which, if any, of the answers to (b) would change if
the charge were -150 microC?"
Young and Freedman - 11th 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.
Young and Freedman - 11th Ed - CHAPTER 25
46. 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.)
WOLFSON - CHAPTER 25
50. A charge +4q is located at the origin and a charge -q
is on the x axis at x = a. (a) Write an expression
for the potential on the x axis for x > a. (b) Find
a point in this region where V = 0. (c) Use the result
of (a) to find the electric field on the x axis for
x > a, and (d) find a point where E = 0.
58. Two small metal spheres are located 2.0 m apart. One
has radius 0.50 cm and carries 0.20 microC. The other
has radius 1.0 cm and carries 0.080 microC. (a) What
is the potential difference between the spheres?
(b) If they were connected by a thin wire, how much
charge would move along it, and in what direction?
(P prefixes) HRW Problem Supplement #1 - CHAPTER 25
58. Consider a flat, nonconducting ring of outer
radius R and inner radius r = 0.200R; the ring
has a uniform charge per unit area of sigma.
With V = 0 at infinity, find an expression for
the electric potential at point P on the central
axis of the ring, at a distance z = 2.00R from
the center of the ring.
Halliday and Resnick - 2nd Ed - CHAPTER 26
19. A positive charge per unit length lambda is distributed
uniformly along a straight-line segment of length L.
(a) Determine the potential (chosen to be zero at
infinity) at a point P a distance y from one end of
the charged segment and in line with it. (b) Use the
result of (a) to compute the component of the electric
field at P in the y-direction (along the line). (c)
Determine the component of the electric field at P in
a direction perpendicular to the straight line.
- . P
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y
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- + Figure for H 26:19
| +
| +
| + the line of plus marks
L + stands for the line of
| + positive charge
| +
| +
- +
20. On a thin rod of length L lying along the x-axis with one
end at the origin (x=0), there is distributed a positive
charge per unit length given by lambda = cx, where c is a
constant. (a) Taking the electrostatic potential at
infinity to be zero, find V at the point P on the y-axis.
(b) Determine the vertical component E_y of the electric
field at P from the result of part (a). (c) Why cannot
E_x, the horizontal component of the electric field at P,
be found using the result of part (a)?
y axis
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| Figure for H 26:20
P is on the |
y axis, a . P
distance y |
from the | the line of plus marks
origin | stands for the line of
| positive charge
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--------+++++++++++++++++++------ x axis
(0,0)|<------ L ------>
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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.
(P prefixes) HRW Problem Supplement #1 - CHAPTER 26
53. A certain parallel-plate capacitor is filled with
a dielectric for which Kappa = 5.5. The area of
each plate is 0.034 m^2, and the plates are
separated by 2.0 mm. The capacitor will fail
(short out and burn up) if the electric field
between the plates exceeds 200 kN/C. What is the
maximum energy that can be stored in the capacitor?
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.
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 %.
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. 24-28 (p. 939),
except that the width of the slab is now b instead
of a. A slab of copper of thickness b is thrust
into a parallel-plate capacitor of plate area A; it
is exactly halfway between the plates. (a) What is
the capacitance after the slab is introduced?
(b) If a charge q is maintained on the plates, what
is the ratio of the stored energy before to that
after the slab is inserted? (c) How much work is
done on the slab as it is inserted? Is the slab
sucked in or must it be pushed in?
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.
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?
45. The figure for this problem is Fig. 24-28 (p. 939),
except that the slab is a dielectric with kappa = 2.61
instead of a conductor, and a 85.5 V battery is
connected to the capacitor plates while the dielectric
is being inserted. The area A = 115 cm^2, d = 1.24 cm,
and the width of the slab is (0.629)d. Calculate
(a) the capacitance, (b) the charge on the capacitor
plates, (c) the electric field in the gap, and (d) the
electric field in the slab, after the slab is in place.
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?