cle 2 of charge ϩ4.00q are held at separation L ϭ 9.00 cm on an
x axis. If particle 3 of charge q 3 is to be located such that the
three particles remain in place when released, what must be the (a)
x and (b) y coordinates of particle 3, and (c) the ratio q 3 /q?
•••20
Figure 21-30a shows an arrangement of three charged
particles separated by distance d. Particles A and C are fixed on
the x axis, but particle B can be moved along a circle centered on
particle A. During the movement, a radial line between A and B
makes an angle u relative to the positive direction of the x axis
(Fig. 21-30b). The curves in Fig. 21-30c give, for two situations, the
magnitude F net of the net electrostatic force on particle A due to the
other particles. That net force is given as a function of angle u and as
a multiple of a basic amount F 0 . For example on curve 1, at u ϭ 180Њ,
we see that F net ϭ 2F 0 . (a) For the situation corresponding to curve 1,
what is the ratio of the charge of particle C to that of particle B (including sign)? (b) For the situation corresponding to curve 2, what is
that ratio?
626
CHAPTE R 21 COU LOM B’S L AW
charge q 3 ϭ ϩ8.00 ϫ 10
Ϫ19
C) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force
on it.
Figure 21-27b gives the x component of that force versus the coordinate x at which particle 3 is placed.The scale of the x axis is set by x s ϭ
8.0 cm.What are (a) the sign of charge q 1 and (b) the ratio q 2 /q 1 ?
••17 In Fig. 21-28a, particles 1 and
2 have charge 20.0 mC each and are
held at separation distance d ϭ 1.50
m. (a) What is the magnitude of the
electrostatic force on particle 1 due
to particle 2? In Fig. 21-28b, particle
3 of charge 20.0 mC is positioned so
as to complete an equilateral triangle. (b) What is the magnitude of
the net electrostatic force on particle 1 due to particles 2 and 3?
••18 In Fig. 21-29a, three positively
charged particles are fixed on an x
axis. Particles B and C are so close
to each other that they can be considered to be at the same distance
from particle A. The net force on
particle A due to particles B and
C is 2.014 ϫ 10
Ϫ23
N in the negative
direction of the x axis. In Fig. 2129b, particle B has been moved to the opposite side of A but is still
at the same distance from it. The net force on A is now 2.877 ϫ
10
Ϫ24
N in the negative direction of the x axis. What is the ratio
q C /q B ?
••19
In Fig. 21-26, particle 1 of charge ϩq and partiWWW
SSM
F
:
3,net
•••21
A nonconducting spherical shell, with an inner radius of
4.0 cm and an outer radius of 6.0 cm, has charge spread nonuniformly through its volume between its inner and outer surfaces.
The volume charge density r is the charge per unit volume, with the
unit coulomb per cubic meter. For this shell r ϭ b/r, where r is the distance in meters from the center of the shell and b ϭ 3.0 mC/m
2
.What
is the net charge in the shell?
•••22
Figure 21-31 shows an
2 of charge q 1 ϭ q 2 ϭ ϩ3.20 ϫ 10
Ϫ19
C
are on a y axis at distance d ϭ 17.0 cm
from the origin. Particle 3 of charge
q 3 ϭ ϩ6.40 ϫ 10
Ϫ19
C is moved gradually along the x axis from x ϭ 0 to x ϭ
ϩ5.0 m. At what values of x will the
magnitude of the electrostatic force on
the third particle from the other two
particles be (a) minimum and (b)
maximum? What are the (c) minimum and (d) maximum magnitudes?
Module 21-2 Charge Is Quantized
•24 Two tiny, spherical water drops, with identical charges
of Ϫ1.00 ϫ 10
Ϫ16
C, have a center-to-center separation of 1.00 cm.
(a) What is the magnitude of the electrostatic force acting between
them? (b) How many excess electrons are on each drop, giving it
its charge imbalance?
•25
How many electrons would have to be removed from a
ILW
Figure 21-28 Problem 17.
d
(a )
( b )
1
2
d
d
3
A
A
B
C
B C
x
x
(a)
(b)
Figure 21-29 Problem 18.
•27
The magnitude of the electrostatic force between two idenSSM
F
net
2
1
0
90°
0°
θ
θ
180°
1
2
(a)
(b)
(c)
x
x
A
C
B
B
A
C
d
d
d
Figure 21-30 Problem 20.
arrangement of four charged particles, with angle u ϭ 30.0Њ and distance d ϭ 2.00 cm. Particle 2 has
charge q 2 ϭ ϩ8.00 ϫ 10
Ϫ19
C; particles 3 and 4 have charges q 3 ϭ q 4
ϭ Ϫ1.60 ϫ 10
Ϫ19
C. (a) What is distance D between the origin and
particle 2 if the net electrostatic
force on particle 1 due to the other particles is zero? (b) If particles 3 and 4 were moved closer to the x axis but maintained their
symmetry about that axis, would the required value of D be
greater than, less than, or the same as in part (a)?
•••23
In Fig. 21-32, particles 1 and
x
y
1
2
d
D
3
4
θ
θ
Figure 21-31 Problem 22.
Figure 21-32 Problem 23.
x
1
3
d
d
2
y
coin to leave it with a charge of ϩ1.0 ϫ 10
Ϫ7
C?
•26 What is the magnitude of the electrostatic force between a
singly charged sodium ion (Na
ϩ
, of charge ϩe) and an adjacent
singly charged chlorine ion (Cl
Ϫ
, of charge Ϫe) in a salt crystal if
their separation is 2.82 ϫ 10
Ϫ10
m?
tical ions that are separated by a distance of 5.0 ϫ 10
Ϫ10
m is 3.7 ϫ 10
Ϫ9
N. (a) What is the charge of each ion? (b) How many electrons are
“missing” from each ion (thus giving the ion its charge imbalance)?
•28
A current of 0.300 A through your chest can send your
x
y
1
3
4
2
Figure 21-33 Problem 29.
heart into fibrillation, ruining the
normal rhythm of heartbeat and
disrupting the flow of blood (and
thus oxygen) to your brain. If that
current persists for 2.00 min, how
many conduction electrons pass
through your chest?
••29
In Fig. 21-33, particles 2
and 4, of charge Ϫe, are fixed in
place on a y axis, at y 2 ϭ Ϫ10.0 cm
x axis. If particle 3 of charge q 3 is to be located such that the
three particles remain in place when released, what must be the (a)
x and (b) y coordinates of particle 3, and (c) the ratio q 3 /q?
•••20
Figure 21-30a shows an arrangement of three charged
particles separated by distance d. Particles A and C are fixed on
the x axis, but particle B can be moved along a circle centered on
particle A. During the movement, a radial line between A and B
makes an angle u relative to the positive direction of the x axis
(Fig. 21-30b). The curves in Fig. 21-30c give, for two situations, the
magnitude F net of the net electrostatic force on particle A due to the
other particles. That net force is given as a function of angle u and as
a multiple of a basic amount F 0 . For example on curve 1, at u ϭ 180Њ,
we see that F net ϭ 2F 0 . (a) For the situation corresponding to curve 1,
what is the ratio of the charge of particle C to that of particle B (including sign)? (b) For the situation corresponding to curve 2, what is
that ratio?
626
CHAPTE R 21 COU LOM B’S L AW
charge q 3 ϭ ϩ8.00 ϫ 10
Ϫ19
C) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force
on it.
Figure 21-27b gives the x component of that force versus the coordinate x at which particle 3 is placed.The scale of the x axis is set by x s ϭ
8.0 cm.What are (a) the sign of charge q 1 and (b) the ratio q 2 /q 1 ?
••17 In Fig. 21-28a, particles 1 and
2 have charge 20.0 mC each and are
held at separation distance d ϭ 1.50
m. (a) What is the magnitude of the
electrostatic force on particle 1 due
to particle 2? In Fig. 21-28b, particle
3 of charge 20.0 mC is positioned so
as to complete an equilateral triangle. (b) What is the magnitude of
the net electrostatic force on particle 1 due to particles 2 and 3?
••18 In Fig. 21-29a, three positively
charged particles are fixed on an x
axis. Particles B and C are so close
to each other that they can be considered to be at the same distance
from particle A. The net force on
particle A due to particles B and
C is 2.014 ϫ 10
Ϫ23
N in the negative
direction of the x axis. In Fig. 2129b, particle B has been moved to the opposite side of A but is still
at the same distance from it. The net force on A is now 2.877 ϫ
10
Ϫ24
N in the negative direction of the x axis. What is the ratio
q C /q B ?
••19
In Fig. 21-26, particle 1 of charge ϩq and partiWWW
SSM
F
:
3,net
•••21
A nonconducting spherical shell, with an inner radius of
4.0 cm and an outer radius of 6.0 cm, has charge spread nonuniformly through its volume between its inner and outer surfaces.
The volume charge density r is the charge per unit volume, with the
unit coulomb per cubic meter. For this shell r ϭ b/r, where r is the distance in meters from the center of the shell and b ϭ 3.0 mC/m
2
.What
is the net charge in the shell?
•••22
Figure 21-31 shows an
2 of charge q 1 ϭ q 2 ϭ ϩ3.20 ϫ 10
Ϫ19
C
are on a y axis at distance d ϭ 17.0 cm
from the origin. Particle 3 of charge
q 3 ϭ ϩ6.40 ϫ 10
Ϫ19
C is moved gradually along the x axis from x ϭ 0 to x ϭ
ϩ5.0 m. At what values of x will the
magnitude of the electrostatic force on
the third particle from the other two
particles be (a) minimum and (b)
maximum? What are the (c) minimum and (d) maximum magnitudes?
Module 21-2 Charge Is Quantized
•24 Two tiny, spherical water drops, with identical charges
of Ϫ1.00 ϫ 10
Ϫ16
C, have a center-to-center separation of 1.00 cm.
(a) What is the magnitude of the electrostatic force acting between
them? (b) How many excess electrons are on each drop, giving it
its charge imbalance?
•25
How many electrons would have to be removed from a
ILW
Figure 21-28 Problem 17.
d
(a )
( b )
1
2
d
d
3
A
A
B
C
B C
x
x
(a)
(b)
Figure 21-29 Problem 18.
•27
The magnitude of the electrostatic force between two idenSSM
F
net
2
1
0
90°
0°
θ
θ
180°
1
2
(a)
(b)
(c)
x
x
A
C
B
B
A
C
d
d
d
Figure 21-30 Problem 20.
arrangement of four charged particles, with angle u ϭ 30.0Њ and distance d ϭ 2.00 cm. Particle 2 has
charge q 2 ϭ ϩ8.00 ϫ 10
Ϫ19
C; particles 3 and 4 have charges q 3 ϭ q 4
ϭ Ϫ1.60 ϫ 10
Ϫ19
C. (a) What is distance D between the origin and
particle 2 if the net electrostatic
force on particle 1 due to the other particles is zero? (b) If particles 3 and 4 were moved closer to the x axis but maintained their
symmetry about that axis, would the required value of D be
greater than, less than, or the same as in part (a)?
•••23
In Fig. 21-32, particles 1 and
x
y
1
2
d
D
3
4
θ
θ
Figure 21-31 Problem 22.
Figure 21-32 Problem 23.
x
1
3
d
d
2
y
coin to leave it with a charge of ϩ1.0 ϫ 10
Ϫ7
C?
•26 What is the magnitude of the electrostatic force between a
singly charged sodium ion (Na
ϩ
, of charge ϩe) and an adjacent
singly charged chlorine ion (Cl
Ϫ
, of charge Ϫe) in a salt crystal if
their separation is 2.82 ϫ 10
Ϫ10
m?
tical ions that are separated by a distance of 5.0 ϫ 10
Ϫ10
m is 3.7 ϫ 10
Ϫ9
N. (a) What is the charge of each ion? (b) How many electrons are
“missing” from each ion (thus giving the ion its charge imbalance)?
•28
A current of 0.300 A through your chest can send your
x
y
1
3
4
2
Figure 21-33 Problem 29.
heart into fibrillation, ruining the
normal rhythm of heartbeat and
disrupting the flow of blood (and
thus oxygen) to your brain. If that
current persists for 2.00 min, how
many conduction electrons pass
through your chest?
••29
In Fig. 21-33, particles 2
and 4, of charge Ϫe, are fixed in
place on a y axis, at y 2 ϭ Ϫ10.0 cm