• Home
  • Textbooks
  • Fundamentals of Physics, Volume 2
  • Coulomb's Law

Fundamentals of Physics, Volume 2

David Halliday & Robert Resnick & Jearl Walker

Chapter 21

Coulomb's Law - all with Video Answers

Educators

Chapter Questions

01:03

Problem 1

Of the charge $Q$ initially on a tiny sphere, a portion $q$ is to be transferred to a second, nearby sphere. Both spheres can be treated as particles and are fixed with a certain separation. For what value of $q / Q$ will the electrostatic force between the two spheres be maximized?

Anand Jangid
Anand Jangid
Numerade Educator
03:55

Problem 2

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Fig. 21.12a). The electrostatic force acting on sphere 2 due to sphere 1 is $\vec{F}$. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Fig. 21.12b), then to sphere 2 (Fig. $21.12 c$ ), and finally removed (Fig. 21.12d). The electrostatic force that now acts on sphere 2 has magnitude $F^{\prime}$. What is the ratio $F^{\prime} F^{\prime}$ ?
(Figure Cant Copy)
Figure 21.12 Problem 2.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:20

Problem 3

What must be the distance between point charge $q_1=26.0 \mu \mathrm{C}$ and point charge $q_2=-47.0 \mu \mathrm{C}$ for the electrostatic force between them to have a magnitude of $5.70 \mathrm{~N}$ ?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:03

Problem 4

In the return stroke of a typical lightning bolt, a current of $2.5 \times 10^4 \mathrm{~A}$ exists for $20 \mu \mathrm{s}$. How much charge is transferred in this event?

Narayan Hari
Narayan Hari
Numerade Educator
00:57

Problem 5

A particle of charge $+3.00 \times 10^{-6} \mathrm{C}$ is $12.0 \mathrm{~cm}$ distant from a second particle of charge $-1.50 \times 10^{-6} \mathrm{C}$. Calculate the magnitude of the electrostatic force between the particles.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
05:19

Problem 6

Two equally charged particles are held $3.2 \times 10^{-3} \mathrm{~m}$ apart and then released from rest. The initial acceleration of the first particle is observed to be $7.0 \mathrm{~m} / \mathrm{s}^2$ and that of the second to be $9.0 \mathrm{~m} / \mathrm{s}^2$. If the mass of the first particle is $6.3 \times 10^{-7} \mathrm{~kg}$, what are (a) the mass of the second particle and (b) the magnitude of the charge of each particle?

Salamat Ali
Salamat Ali
Numerade Educator
02:49

Problem 7

In Fig. 21.13, three charged particles lie on an $x$ axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero. If $L_{23}=L_{12}$, what is the ratio $q_1 / q_2$ ?
(Figure Cant Copy)

Sheh Lit Chang
Sheh Lit Chang
University of Washington
04:32

Problem 8

In Fig. 21.14, three identical conducting spheres initially have the following charges: sphere $A$, $4 Q$; sphere $B,-6 Q$; and sphere $C, 0$. Spheres $A$ and $B$ are fixed in place, with a center-to-center separation that is much larger than the spheres. Two experiments are conducted. In experiment 1 , sphere $C$ is touched to sphere $A$ and then (separately) to sphere $B$, and then it is removed. In experiment 2 , starting with the same initial states, the procedure is reversed: Sphere $C$ is touched to sphere $B$ and then (separately) to sphere $A$, and then it is removed. What is the ratio of the electrostatic force between $A$ and $B$ at the end of experiment 2 to that at the end of experiment 1 ?
Figure 21.14 Problem 8.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
05:52

Problem 9

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of $0.108 \mathrm{~N}$ when their center-to-center separation is $50.0 \mathrm{~cm}$. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of $0.0360 \mathrm{~N}$. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
16:35

Problem 10

In Fig. 21.15, four particles form a square. The charges are $q_1=q_4=Q$ and $q_2=q_3=q$. (a) What is $Q / q$ if the net electrostatic force on particles 1 and 4 is zero? (b) Is there any value of $q$ that makes the net electrostatic force on each of the four particles zero? Explain.
(Figure Cant Copy)
Figure 21.15 Problems 10 and 11 .

Brandy Heflin
Brandy Heflin
Numerade Educator
01:11

Problem 11

In Fig. 21.15, the particles have charges $q_1=-q_2=100 \mathrm{nC}$ and $q_3=-q_4=200 \mathrm{nC}$, and distance $a=5.0 \mathrm{~cm}$. What are the (a) $x$ and (b) $y$ components of the net electrostatic force on particle 3 ?
(Figure Cant Copy)
Figure 21.15 Problems 10 and 11 .

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
11:08

Problem 12

Two particles are fixed on an $x$ axis. Particle 1 of charge $40 \mu \mathrm{C}$ is located at $x=-2.0 \mathrm{~cm}$; particle 2 of charge $Q$ is located at $x=3.0 \mathrm{~cm}$. Particle 3 of charge magnitude $20 \mu \mathrm{C}$ is released from rest on the $y$ axis at $y=2.0 \mathrm{~cm}$. What is the value of $Q$ if the initial acceleration of particle 3 is in the positive direction of (a) the $x$ axis and (b) the $y$ axis?

Thembuluwo Radzilani
Thembuluwo Radzilani
Numerade Educator
08:52

Problem 13

In Fig. 21.16, particle 1 of charge $+1.0 \mu \mathrm{C}$ and particle 2 of charge $-3.0 \mu \mathrm{C}$ are held at separation $L=10.0 \mathrm{~cm}$ on an $x$ axis. If particle 3 of unknown charge $q_3$ is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) $x$ and (b) $y$ coordinates of particle 3 ?
(Figure Cant Copy)
Figure 21.16 Problems $13,19,30$, and 58 .

Morgan Cheatham
Morgan Cheatham
Numerade Educator
02:45

Problem 14

Three particles are fixed on an $x$ axis. Particle 1 of charge $q_1$ is at $x=-a$, and particle 2 of charge $q_2$ is at $x=+a$. If their net electrostatic force on particle 3 of charge $+Q$ is to be zero, what must be the ratio $q_1 / q_2$ when particle 3 is at (a) $x=+0.500 a$ and (b) $x=+1.50 a$ ?

Salamat Ali
Salamat Ali
Numerade Educator
13:16

Problem 15

The charges and coordinates of two charged particles held fixed in an $x y$ plane are $q_1=+3.0 \mu \mathrm{C}, x_1=3.5 \mathrm{~cm}$, $y_1=0.50 \mathrm{~cm}$, and $q_2=-4.0 \mu \mathrm{C}, x_2=-2.0 \mathrm{~cm}, y_2=1.5 \mathrm{~cm}$. Find the (a) magnitude and (b) direction of the electrostatic force on particle 2 due to particle 1 . At what (c) $x$ and (d) $y$ coordinates should a third particle of charge $q_3=+4.0 \mu \mathrm{C}$ be placed such that the net electrostatic force on particle 2 due to particles 1 and 3 is zero?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:36

Problem 16

In Fig. 21.17a, particle 1 (of charge $q_1$ ) and particle 2 (of charge $q_2$ ) are fixed in place on an $x$ axis, $8.00 \mathrm{~cm}$ apart. Particle 3 (of charge $q_3=+8.00 \times 10^{-19} \mathrm{C}$ ) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force $\vec{F}_{3 \text {, net }}$ on it. Figure $21.17 b$ gives the $x$ component of that force versus the coordinate $x$ at which particle 3 is placed.
(Figure Cant Copy)
Figure 21.17 Problem 16.
The scale of the $x$ axis is set by $x_s=8.0 \mathrm{~cm}$. What are (a) the sign of charge $q_1$ and (b) the ratio $q_2 / q_1$ ?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
03:44

Problem 17

In Fig. 21.18a, particles 1 and 2 have charge $20.0 \mu \mathrm{C}$ each and are held at separation distance $d=1.50 \mathrm{~m}$. (a) What is the magnitude of the electrostatic force on particle 1 due to particle 2? In Fig. $21.18 b$, particle 3 of charge $20.0 \mu \mathrm{C}$ 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 ?
(Figure Cant Copy)
Figure 21.18 Problem 17.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:59

Problem 18

In Fig. 21.19a, 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 $2.014 \times 10^{-23} \mathrm{~N}$ in the negative direction of the $x$ axis. In Fig. $21.19 b$, 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 $2.877 \times 10^{-24} \mathrm{~N}$ in the negative direction of the $x$ axis. What is the ratio $q_C / q_B$ ?
(Figure Cant Copy)
Figure 21.19 Problem 18.

Eduard Sanchez
Eduard Sanchez
Numerade Educator
04:29

Problem 19

In Fig. 21.16, particle 1 of charge $+q$ and particle 2 of charge $+4.00 q$ are held at separation $L=9.00 \mathrm{~cm}$ 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 $q_3 / q$ ?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
08:11

Problem 20

Figure $21.20 a$ 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 $\theta$ relative to the positive direction of the $x$ axis (Fig. 21.20b). The curves in Fig. 21.20c give, for two situations, the magnitude $F_{\text {net }}$ of the net electrostatic force on particle $A$ due to the other particles. That net force is given as a function of angle $\theta$ and as a multiple of a basic amount $F_0$. For example on curve 1 , at $\theta=180^{\circ}$, we see that $F_{\text {net }}=2 F_0$. (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?
(Figure Cant Copy)
Figure 21.20 Problem 20.

Salamat Ali
Salamat Ali
Numerade Educator
03:31

Problem 21

A nonconducting spherical shell, with an inner radius of $4.0 \mathrm{~cm}$ and an outer radius of $6.0 \mathrm{~cm}$, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density $\rho$ is the charge per unit volume, with the unit coulomb per cubic meter. For this shell $\rho=b / r$, where $r$ is the distance in meters from the center of the shell and $b=3.0 \mu \mathrm{C} / \mathrm{m}^2$. What is the net charge in the shell?

Bettina Hanlon
Bettina Hanlon
Numerade Educator
09:50

Problem 22

Figure 21.21 shows an arrangement of four charged particles, with angle $\theta=30.0^{\circ}$ and distance $d=2.00 \mathrm{~cm}$. Particle 2 has charge $q_2=+8.00 \times 10^{-19} \mathrm{C}$; particles 3 and 4 have charges $q_3=q_4=-1.60 \times 10^{-19} \mathrm{C}$. (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)?
(Figure Cant Copy)
Figure 21.21 Problem 22.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
09:59

Problem 23

In Fig. 21.22, particles 1 and 2 of charge $q_1=q_2=+3.20 \times 10^{-19} \mathrm{C}$ are on a $y$ axis at distance $d=17.0 \mathrm{~cm}$ from the origin. Particle 3 of charge $q_3=+6.40 \times 10^{-19} \mathrm{C}$ is moved gradually along the $x$ axis from $x=0$ to $x=+5.0 \mathrm{~m}$. 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?
(Figure Cant Copy)
Figure 21.22 Problem 23.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
02:57

Problem 24

Two tiny, spherical water drops, with identical charges of $-1.00 \times 10^{-16} \mathrm{C}$, have a center-to-center separation of $1.00 \mathrm{~cm}$. (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?

Salamat Ali
Salamat Ali
Numerade Educator
00:43

Problem 25

How many electrons would have to be removed from a coin to leave it with a charge of $+1.0 \times 10^{-7} \mathrm{C}$ ?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
02:18

Problem 26

What is the magnitude of the electrostatic force between a singly charged sodium ion $\left(\mathrm{Na}^{+}\right.$, of charge $\left.+e\right)$ and an adjacent singly charged chlorine ion $\left(\mathrm{Cl}^{-}\right.$, of charge $\left.-e\right)$ in a salt crystal if their separation is $2.82 \times 10^{-10} \mathrm{~m}$ ?

Salamat Ali
Salamat Ali
Numerade Educator
02:02

Problem 27

The magnitude of the electrostatic force between two identical ions that are separated by a distance of $5.0 \times$ $10^{-10} \mathrm{~m}$ is $3.7 \times 10^{-9} \mathrm{~N}$. (a) What is the charge of each ion? (b) How many electrons are "missing" from each ion (thus giving the ion its charge imbalance)?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
01:01

Problem 28

A current of $0.300 \mathrm{~A}$ through your chest can send your 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 $2.00 \mathrm{~min}$, how many conduction electrons pass through your chest?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
08:41

Problem 29

In Fig. 21.23, particles 2 and 4 , of charge $-e$, are fixed in place on a $y$ axis, at $y_2=-10.0 \mathrm{~cm}$ and $y_4=5.00 \mathrm{~cm}$. Particles 1 and 3 , of charge $-e$, can be moved along the $x$ axis. Particle 5, of charge $+e$, is fixed at the origin. Initially particle 1 is at $x_1=-10.0 \mathrm{~cm}$ and particle 3 is at $x_3=10.0 \mathrm{~cm}$. (a) To what $x$ value must particle 1 be moved to rotate the direction of the net electric force $\vec{F}_{\text {net }}$ on particle 5 by $30^{\circ}$ counterclockwise? (b) With particle 1 fixed at its new position, to what $x$ value must you move particle 3 to rotate $\vec{F}_{\text {net }}$ back to its original direction?
(Figure Cant Copy)
Figure 21.23 Problem 29.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
06:03

Problem 30

In Fig. 21.16, particles 1 and 2 are fixed in place on an $x$ axis, at a separation of $L=8.00 \mathrm{~cm}$. Their charges are $q_1=+e$ and $q_2=-27 e$. Particle 3 with charge $q_3=+4 e$ is to be placed on the line between particles 1 and 2, so that they produce a net electrostatic force $\vec{F}_{3, \text { net }}$ on it. (a) At what coordinate should particle 3 be placed to minimize the magnitude of that force? (b) What is that minimum magnitude?

Morgan Cheatham
Morgan Cheatham
Numerade Educator
01:16

Problem 31

Earth's atmosphere is constantly bombarded by cosmic ray protons that originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth's surface would intercept protons at the average rate of 1500 protons per second. What would be the electric current intercepted by the total surface area of the planet?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
05:51

Problem 32

Figure 21.24a shows charged particles 1 and 2 that are fixed in place on an $x$ axis. Particle 1 has a charge with a magnitude of $\left|q_1\right|=8.00 e$. Particle 3 of charge $q_3=+8.00 e$ is initially on the $x$ axis near particle 2 . Then particle 3 is gradually moved in the positive direction of the $x$ axis. As a result, the magnitude of the net electrostatic force $\vec{F}_{2 \text {, net }}$ on particle 2 due to particles 1 and 3 changes. Figure $21.24 b$ gives the $x$ component of that net force as a function of the position $x$ of particle 3 . The scale of the $x$ axis is set by $x_s=0.80 \mathrm{~m}$. The plot has an asymptote of $F_{2, \text { net }}=1.5 \times 10^{-25} \mathrm{~N}$ as $x \rightarrow \infty$. As a multiple of $e$ and including the sign, what is the charge $q_2$ of particle 2 ?
(Figure Cant Copy)
Figure 21.24 Problem 32.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:35

Problem 33

Calculate the number of coulombs of positive charge in $250 \mathrm{~cm}^3$ of (neutral) water.

Manish Kumar ( Iit K )
Manish Kumar ( Iit K )
Numerade Educator
05:16

Problem 34

Figure 21.25 shows electrons 1 and 2 on an $x$ axis and charged ions 3 and 4 of identical charge $-q$ and at identical angles $\theta$. Electron 2 is free to move; the other three particles are fixed in place at horizontal distances $R$ from electron 2 and are intended to hold electron 2 in place. For physically possible values of $q \leq 5 e$, what are the (a) smallest, (b) second smallest, and (c) third smallest values of $\theta$ for which electron 2 is held in place?
(Figure Cant Copy)
Figure 21.25 Problem 34.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:21

Problem 35

In crystals of the salt cesium chloride, cesium ions $\mathrm{Cs}^{+}$form the eight corners of a cube and a chlorine ion $\mathrm{Cl}^{-}$is at the cube's center (Fig. 21.26). The edge length of the cube is $0.40 \mathrm{~nm}$. The $\mathrm{Cs}^{+}$ions are each deficient by one electron (and thus each has a charge of $+e$ ), and the $\mathrm{Cl}^{-}$ion has one excess electron (and thus has a charge of $-e$ ). (a) What is the magnitude of the net electrostatic force exerted on the $\mathrm{Cl}^{-}$ion by the eight $\mathrm{Cs}^{+}$ions at the corners of the cube? (b) If one of the $\mathrm{Cs}^{+}$ions is missing, the crystal is said to have a defect, what is the magnitude of the net electrostatic force exerted on the $\mathrm{Cl}^{-}$ion by the seven remaining $\mathrm{Cs}^{+}$ions?
(Figure Cant Copy)
Figure 21.26 Problem 35.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
01:26

Problem 36

Electrons and positrons are produced by the nuclear transformations of protons and neutrons known as beta decay. (a) If a proton transforms into a neutron, is an electron or a positron produced? (b) If a neutron transforms into a proton, is an electron or a positron produced?

Salamat Ali
Salamat Ali
Numerade Educator
03:11

Problem 37

Identify $\mathrm{X}$ in the following nuclear reactions:
(a) ${ }^1 \mathrm{H}+{ }^9 \mathrm{Be} \rightarrow \mathrm{X}+\mathrm{n}$; (b) ${ }^{12} \mathrm{C}+{ }^1 \mathrm{H} \rightarrow \mathrm{X}$; (c) ${ }^{15} \mathrm{~N}+{ }^1 \mathrm{H} \rightarrow$ ${ }^4 \mathrm{He}+\mathrm{X}$. Appendix F will help.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
05:59

Problem 38

Figure 21.27 shows four identical conducting spheres that are actually well separated from one another. Sphere $W$ (with an initial charge of zero) is touched to sphere $A$ and then they are separated. Next, sphere $W$ is touched to sphere $B$ (with an initial charge of $-32 e$ ) and then they are separated. Finally, sphere $W$ is touched to sphere $C$ (with an initial charge of $+48 e$ ), and then they are separated. The final charge on sphere $W$ is $+18 e$. What was the initial charge on sphere $A$ ?
(Figure Cant Copy)
Figure 21.27 Problem 38.

Eduard Sanchez
Eduard Sanchez
Numerade Educator
02:57

Problem 39

n Fig. 21.28, particle 1 of charge $+4 e$ is above a floor by distance $d_1=2.00 \mathrm{~mm}$ and particle 2 of charge $+6 e$ is on the floor, at distance $d_2=6.00 \mathrm{~mm}$ horizontally from particle 1 . What is the $x$ component of the electrostatic force on particle 2 due to particle 1?
(Figure Cant Copy)
Figure 21.28 Problem 39.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
03:46

Problem 40

In Fig. 21.13, particles 1 and 2 are fixed in place, but particle 3 is free to move. If the net electrostatic force on particle 3 due to particles 1 and 2 is zero and $L_{23}=2.00 L_{12}$, what is the ratio $q_1 / q_2$ ?

Salamat Ali
Salamat Ali
Numerade Educator
04:57

Problem 41

(a) What equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction? (b) Why don't you need to know the lunar distance to solve this problem? (c) How many kilograms of hydrogen ions (that is, protons) would be needed to provide the positive charge calculated in (a)?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
14:14

Problem 42

In Fig. 21.29, two tiny conducting balls of identical mass $m$ and identical charge $q$ hang from nonconducting threads of length L. Assume that $\theta$ is so small that $\tan \theta$ can be replaced by its approximate equal, $\sin \theta$. (a) Show that
$$
x=\left(\frac{q^2 L}{2 \pi \varepsilon_0 m g}\right)^{1 / 3}
$$
gives the equilibrium separation $x$ of the balls. (b) If $L=120 \mathrm{~cm}, m=10 \mathrm{~g}$, and $x=5.0 \mathrm{~cm}$, what is $|q|$ ?
(Figure Cant Copy)
Figure 21.29 Problems 42 and 43.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:59

Problem 43

(a) Explain what happens to the balls of Problem 42 if one of them is discharged (loses its charge $q$ to, say, the ground). (b) Find the new equilibrium separation $x$, using the given values of $L$ and $m$ and the computed value of $|q|$.
(Figure Cant Copy)
Figure 21.29 Problems 42 and 43.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
02:58

Problem 44

How far apart must two protons be if the magnitude of the electrostatic force acting on either one due to the other is equal to the magnitude of the gravitational force on a proton at Earth's surface?

Salamat Ali
Salamat Ali
Numerade Educator
02:16

Problem 45

How many megacoulombs of positive charge are in 1.00 mol of neutral molecular-hydrogen gas $\left(\mathrm{H}_2\right)$ ?

Bettina Hanlon
Bettina Hanlon
Numerade Educator
04:45

Problem 46

In Fig. 21.30, four particles are fixed along an $x$ axis, separated by distances $d=2.00 \mathrm{~cm}$. The charges are $q_1=+2 e, q_2=-e, q_3=+e$, and $q_4=+4 e$, with $e=1.60 \times 10^{-19} \mathrm{C}$. In unit-vector notation, what is the net electrostatic force on (a) particle 1 and (b) particle 2 due to the other particles?
(Figure Cant Copy)
Figure 21.30 Problem 46.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
02:45

Problem 47

Point charges of $+6.0 \mu \mathrm{C}$ and $-4.0 \mu \mathrm{C}$ are placed on an $x$ axis, at $x=8.0 \mathrm{~m}$ and $x=16 \mathrm{~m}$, respectively. What charge must be placed at $x=24 \mathrm{~m}$ so that any charge placed at the origin would experience no electrostatic force?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
10:19

Problem 48

In Fig. 21.31, three identical conducting spheres form an equilateral triangle of side length $d=20.0 \mathrm{~cm}$. The sphere radii are much smaller than $d$, and the sphere charges are $q_A=-2.00 \mathrm{nC}, \quad q_B=-4.00 \mathrm{nC}$, and $q_C=+8.00 \mathrm{nC}$. (a) What is the magnitude of the electrostatic force between spheres $A$ and $C$ ? The following steps are then taken: $A$ and $B$ are connected by a thin wire and then disconnected; $B$ is grounded by the wire, and the wire is then removed; $B$ and $C$ are connected by the wire and then disconnected. What now are the magnitudes of the electrostatic force (b) between spheres $A$ and $C$ and (c) between spheres $B$ and $C$ ?
(Figure Cant Copy)
Figure 21.31 Problem 48.

Eduard Sanchez
Eduard Sanchez
Numerade Educator
01:20

Problem 49

A neutron consists of one "up" quark of charge $+2 e / 3$ and two "down" quarks each having charge $-e / 3$. If we assume that the down quarks are $2.6 \times 10^{-15} \mathrm{~m}$ apart inside the neutron, what is the magnitude of the electrostatic force between them?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
07:55

Problem 50

Figure 21.32 shows a long, nonconducting, massless rod of length $L$, pivoted at its center and balanced with a block of weight $W$ at a distance $x$ from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges $q$ and $2 q$, respectively. A distance $h$ directly beneath each of these spheres is a fixed sphere with positive charge $Q$. (a) Find the distance $x$ when the rod is horizontal and balanced. (b) What value should $h$ have so that the rod exerts no vertical force on the bearing when the rod is horizontal and balanced?
(Figure Cant Copy)
Figure 21.32 Problem 50.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
03:29

Problem 51

A charged nonconducting rod, with a length of $2.00 \mathrm{~m}$ and a cross-sectional area of $4.00 \mathrm{~cm}^2$, lies along the positive side of an $x$ axis with one end at the origin. The volume charge density $\rho$ is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if $\rho$ is (a) uniform, with a value of $-4.00 \mu \mathrm{C} / \mathrm{m}^3$, and (b) nonuniform, with a value given by $\rho=b x^2$, where $b=-2.00 \mu \mathrm{C} / \mathrm{m}^5$ ?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
03:09

Problem 52

A particle of charge $Q$ is fixed at the origin of an $x y$ coordinate system. At $t=0$ a particle ( $m=0.800 \mathrm{~g}, q=4.00 \mu \mathrm{C}$ ) is located on the $x$ axis at $x=20.0 \mathrm{~cm}$, moving with a speed of $50.0 \mathrm{~m} / \mathrm{s}$ in the positive $y$ direction. For what value of $Q$ will the moving particle execute circular motion? (Neglect the gravitational force on the particle.)

Bettina Hanlon
Bettina Hanlon
Numerade Educator
01:46

Problem 53

What would be the magnitude of the electrostatic force between two $1.00 \mathrm{C}$ point charges separated by a distance of (a) $1.00 \mathrm{~m}$ and (b) $1.00 \mathrm{~km}$ if such point charges existed (they do not) and this configuration could be set up?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
01:27

Problem 54

A charge of $6.0 \mu \mathrm{C}$ is to be split into two parts that are then separated by $3.0 \mathrm{~mm}$. What is the maximum possible magnitude of the electrostatic force between those two parts?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:38

Problem 55

Of the charge $Q$ on a tiny sphere, a fraction $\alpha$ is to be transferred to a second, nearby sphere. The spheres can be treated as particles. (a) What value of $\alpha$ maximizes the magnitude $F$ of the electrostatic force between the two spheres? What are the (b) smaller and (c) larger values of $\alpha$ that put $F$ at half the maximum magnitude?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
04:45

Problem 56

If a cat repeatedly rubs against your cotton slacks on a dry day, the charge transfer between the cat hair and the cotton can leave you with an excess charge of $-2.00 \mu \mathrm{C}$. (a) How many electrons are transferred between you and the cat?
You will gradually discharge via the floor, but if instead of waiting, you immediately reach toward a faucet, a painful spark can suddenly appear as your fingers near the faucet. (b) In that spark, do electrons flow from you to the faucet or vice versa? (c) Just before the spark appears, do you induce positive or negative charge in the faucet? (d) If, instead, the cat reaches a paw toward the faucet, which way do electrons flow in the resulting spark? (e) If you stroke a cat with a bare hand on a dry day, you should take care not to bring your fingers near the cat's nose or you will hurt it with a spark. Considering that cat hair is an insulator, explain how the spark can appear.

Salamat Ali
Salamat Ali
Numerade Educator
02:21

Problem 57

We know that the negative charge on the electron and the positive charge on the proton are equal. Suppose, however, that these magnitudes differ from each other by $0.00010 \%$. With what force would two copper coins, placed $1.0 \mathrm{~m}$ apart, repel each other? Assume that each coin contains $3 \times 10^{22}$ copper atoms. (Hint: A neutral copper atom contains 29 protons and 29 electrons.) What do you conclude?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
08:10

Problem 58

In Fig. 21.16, particle 1 of charge $-80.0 \mu \mathrm{C}$ and particle 2 of charge $+40.0 \mu \mathrm{C}$ are held at separation $L=20.0 \mathrm{~cm}$ on an $x$ axis. In unit-vector notation, what is the net electrostatic force on particle 3 , of charge $q_3=20.0 \mu \mathrm{C}$, if particle 3 is place at (a) $x=40.0 \mathrm{~cm}$ and (b) $x=80.0 \mathrm{~cm}$ ? What should be the (c) $x$ and (d) $y$ coordinates of particle 3 if the net electrostatic force on it due to particles 1 and 2 is zero?

Salamat Ali
Salamat Ali
Numerade Educator
01:02

Problem 59

What is the total charge in coulombs of $75.0 \mathrm{~kg}$ of electrons?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
04:21

Problem 60

In Fig. 21.33, six charged particles surround particle 7 at radial distances of either $d=1.0 \mathrm{~cm}$ or $2 d$, as drawn. The charges are $q_1=+2 e, q_2=+4 e, q_3=+e, q_4=+4 e, q_5=+2 e, q_6=+8 e$, $q_7=+6 e$, with $e=1.60 \times 10^{-19} \mathrm{C}$. What is the magnitude of the net electrostatic force on particle 7?
(Figure Cant Copy)
Figure 21.33 Problem 60.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
06:40

Problem 61

Three charged particles form a triangle: Particle 1 with charge $Q_1=80.0 \mathrm{nC}$ is at $x y$ coordinates $(0,3.00 \mathrm{~mm})$, particle 2 with charge $Q_2$ is at $(0,-3.00 \mathrm{~mm})$, and particle 3 with charge $q=18.0 \mathrm{nC}$ is at ( $4.00 \mathrm{~mm}, 0$ ). In unit-vector notation, what is the electrostatic force on particle 3 due to the other two particles if $Q_2$ is equal to (a) $80.0 \mathrm{nC}$ and (b) $-80.0 \mathrm{nC}$ ?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
11:36

Problem 62

In Fig. 21.34, what are the (a) magnitude and (b) direction of the net electrostatic force on particle 4 due to the other three particles? All four particles are fixed in the $x y$ plane, and $q_1$ $=-3.20 \times 10^{-19} \mathrm{C}, q_2=+3.20 \times 10^{-19} \mathrm{C}, q_3=+6.40 \times 10^{-19} \mathrm{C}, q_4$ $=+3.20 \times 10^{-19} \mathrm{C}, \theta_1=35.0^{\circ}, d_1=3.00 \mathrm{~cm}$, and $d_2=d_3=2.00 \mathrm{~cm}$ $=+3.20 \times 10^{-19} \mathrm{C}, \theta_1=35.0^{\circ}, d_1=3.00 \mathrm{~cm}$, and $d_2=d_3=2.00 \mathrm{~cm}$.
(Figure Cant Copy)
Figure 21.34 Problem 62.

Salamat Ali
Salamat Ali
Numerade Educator
01:28

Problem 63

Charge of a penny. A U.S. penny has mass $m=3.11 \mathrm{~g}$ and contains equal amounts of positive and negative charge. Assume the coin is made entirely of copper (molar mass $M=63.5 \mathrm{~g} / \mathrm{mol}$, atomic number $Z=29$ ). (a) What is the magnitude $q$ of these charges? (b) If the charges could be concentrated into two separate bundles held $100 \mathrm{~m}$ apart, what would be the attractive force between the bundles?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
06:35

Problem 64

What is the quark composition of (a) a proton, (b) a neutron, and (c) an antiproton? (The symbols can be in any order.) (d) When a nucleon undergoes beta-minus emission (see problem 67), what is the change in the quark composition?

Daniel Sneed
Daniel Sneed
Numerade Educator
02:45

Problem 65

The average distance $r$ between the electron and the central proton in the hydrogen atom is $5.3 \times 10^{-11} \mathrm{~m}$. What are the magnitudes of (a) the electrostatic force and (b) the gravitational force acting between the particles? (c) Can the latter account for holding the atom together?

Narayan Hari
Narayan Hari
Numerade Educator
01:15

Problem 66

Certain radionuclides can decay by electron capture,
$$
\mathrm{p}+\mathrm{e}^{-} \rightarrow \mathrm{n}+\nu,
$$
and then the daughter nuclei can release Auger-Meitner electrons. If the radionuclides are placed next to cancer cells, those released electrons can lethally damage the cells. What is the daughter atom if the parent atom is (a) iodine ${ }_{53}^{123} I$, (b) iodine ${ }_{53}^{125} \mathrm{I}$, and (c) gallium ${ }_{31}^{67} \mathrm{Ga}$ ?

David Collins
David Collins
Numerade Educator
01:15

Problem 67

Certain radionuclides undergo beta-minus decay, in which a neutron transforms into a proton (which remains in the nucleus) and releases an electron and a neutrino:
$$
\mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+\nu .
$$
If the radionuclides are placed next to a tumor, the released electrons can lethally damage the tumor. What is the daughter atom if the parent atom is (a) iodine ${ }_{53}^{131} \mathrm{I}$, (b) copper ${ }_{29}^{67} \mathrm{Cu}$, and (c) yttrium ${ }_{39}^{90} \mathrm{Y}$ ? The first two are used for smaller tumors, the third for larger tumors.

David Collins
David Collins
Numerade Educator
05:26

Problem 68

Many household smoke detectors (Fig. 21.35) contain radioactive americium-241 ${ }_{95}^{241} \mathrm{Am}$, which is an alpha emitter. The alpha particles ionize the air (they strip electrons from the air molecules) between two charged plates. The freed electrons then flow to the positively charged plate. Thus, there is an electrical current between the plates. If smoke particles enter the air, they reduce that current, which triggers an alarm. What is the daughter nucleus produced by the alpha decay?
(Figure Cant Copy)
Figure 21.35 Problem 68.

Crystal Wang
Crystal Wang
Numerade Educator
02:08

Problem 69

Certain radionuclides decay by emitting an alpha particle. To treat bone cancer, an alpha emitter such as radium ${ }_{8 \leqslant}^{223} \mathrm{Ra}$ is attached to a carrier molecule that is then taken up by bone as though it were calcium. What is the daughter atom if the parent atom is (a) radium $\underset{{ }_8^{223}}{\mathrm{2}} \mathrm{Ra}$, (b) radium ${ }_{89}^{226} \mathrm{Ra}$, and (c) actinium ${ }_{89}^{225} \mathrm{Ac}$ ?

Nicholas Majtenyi
Nicholas Majtenyi
Numerade Educator
02:06

Problem 70

Some radionuclides can undergo either beta-plus decay or electron capture. What is the resulting daughter when carbon ${ }_6^{11} \mathrm{C}$ undergoes (a) beta-plus decay and (b) electron capture? What is the daughter when ${ }_9^{18} \mathrm{~F}$ undergoes (c) beta-plus decay and (d) electron capture?

David Collins
David Collins
Numerade Educator
02:59

Problem 71

If a slow neutron is captured by a uranium-235 nucleus (a large nucleus), the nucleus can fission (split) into two intermediate-size nuclei and release two or three neutrons. Here is one possibility:
$$
{ }_{92}^{235} \mathrm{U}+\mathrm{n} \rightarrow{ }_{56}^{144} \mathrm{Ba}+\underset{(\mathrm{b})}{(\mathrm{a})}(\mathrm{c})+3 \mathrm{n} .
$$
What numbers go into superscript (a) and subscript (b), and what chemical symbol goes into position (c)? (d) The intermediate-size nuclei have too many neutrons to be stable and so they decay by beta-minus decays, in which a neutron becomes a proton and the nucleus emits an electron and a neutrino (which has no charge). See Problem 67. What daughter nucleus results from the decay of ${ }_{56}^{144} \mathrm{Ba}$ ?

Supratim Pal
Supratim Pal
Numerade Educator
01:43

Problem 72

To image organs in a patient's body, the patient is injected with a substance containing radioactive molybdenum ${ }_{42}^{99} \mathrm{Mo}$, which decays to technetium ${ }_{43}^{99} \mathrm{Tc}$, and then slid into a gamma camera (Fig. 21.36). The technetium is produced in a higher energy state but while in the gamma camera it reduces its energy by emitting a gamma ray. The patient is partially surrounded by an array of gamma-ray detectors that function much like a conventional camera capturing an image with visible light. The detection system produces an image of the patient showing the emission sites of the gamma rays. (Radionuclides that emit electrons, positrons, or alpha particles are not useful in deep imaging because those particles travel only a short distance through the body whereas the gamma rays can escape and reach the detectors.) In the decay of ${ }_{42}{ }^{99} \mathrm{Mo}$ to ${ }_{43}^{99} \mathrm{Tc}$, what particle is emitted in addition to a neutrino?
(Figure Cant Copy)
Figure 21.36 Problem 72.

Narayan Hari
Narayan Hari
Numerade Educator