Physics: Principles with Applications

Douglas C. Giancoli

Chapter 16

ELECTRIC CHARGE AND ELECTRIC FIELD - all with Video Answers

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Chapter Questions

Problem 1

(I) What is the magnitude of the electric force of attraction between an iron nucleus $(q= + 26e)$ electron if the distance between them is 1.5 $\times$ 10$^{-12}$m?

Katie Mcalpine

Katie Mcalpine

Numerade Educator

Problem 2

(I) How many electrons make up a charge of -48.0$\mu$C?

Chasen Shaw

Numerade Educator

Problem 3

(I) What is the magnitude of the force a +a25$\mu$C charge exerts on a +2.5mC charge 16 cm away?

Dading Chen

Numerade Educator

Problem 4

(I) What is the repulsive electrical force between two protons 4.0 $\times$ 10$^{-15}$ apart from each other in an atomic nucleus?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 5

(II) When an object such as a plastic comb is charged by rubbing it with a cloth, the net charge is typically a few microcoulombs. If that charge is 3.0 $\mu$C, by what percentage does the mass of a 9.0-g comb change during charging?

Katie Mcalpine

Numerade Educator

Problem 6

(II) Two charged dust particles exert a force of 4.2 $\times$ 10$^{-2}$ on each other. What will be the force if they are moved so they are only one-eighth as far apart?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 7

(II) Two small charged spheres are 6.52 cm apart. They are moved, and the force each exerts on the other is found to have tripled. How far apart are they now?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 8

(II) A person scuffing her feet on a wool rug on a dry day accumulates a net charge of -28$\mu$C. How many excess electrons does she get, and by how much does her mass increase?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 9

(II) What is the total charge of all the electrons in a 12-kg bar of gold? What is the net charge of the bar? (Gold has 79 electrons per atom and an atomic mass of 197 u.)

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 10

(II) Compare the electric force holding the electron in orbit ($r =$ 0.53 $\times$ 10$^{-10}$ m) around the proton nucleus of the hydrogen atom, with the gravitational force between the same electron and proton. What is the ratio of these two forces?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 11

(II) Particles of charge +65, + 48, and -95$\mu$C are placed in a line (Fig. 16-52). The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two.
FIGURE 16-52 Problem 11. (CANT COPY FIGURE)

Katie Mcalpine

Numerade Educator

Problem 12

(II) Three positive particles of equal charge, +17.0$\mu$C, are located at the corners of an equilateral triangle of side 15.0 cm (Fig. 16-53). Calculate the magnitude and direction of the net force on each particle due to the other two.
FIGURE 16-53 Problem 12. (CANT COPY FIGURE)

Donald Albin

Numerade Educator

Problem 13

(II) A charge $Q$ is transferred from an initially uncharged plastic ball to an identical ball 24 cm away.The force of attraction is then 17 mN. How many electrons were transferred from one ball to the other?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 14

(II) A charge of 6.15 mC is placed at each corner of a square 0.100 m on a side. Determine the magnitude and directio of the force on each charge.

Suzanne W.

Numerade Educator

Problem 15

(II) At each corner of a square of side there are point charges of magnitude $Q, 2Q, 3Q,$ and 4$Q$ (Fig. 16-54). Determine the magnitude and direction of the force on the charge 2$Q$.
FIGURE 16-54 Problem 15. (CANT COPY FIGURE)

Donald Albin

Numerade Educator

Problem 16

(II) A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 21-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26$^\circ$ angle with the vertical (Fig. 16-55), what total charge $Q$ must have been applied to the electroscope? Ignore the mass of the wires.
FIGURE 16-55 Problem 16. (CANT COPY FIGURE)

Nicholas Mogoi

Numerade Educator

Problem 17

(III) Two small nonconducting spheres have a total charge of 90.0$\mu$C ($a$) When placed 28.0 cm apart, the force each exerts on the other is 12.0 N and is repulsive. What is the charge on each? ($b$) What if the force were attractive?

Keshav Singh

Numerade Educator

Problem 18

(III) Two charges, $-Q$ and $-3Q$ are a distance $\ell$ apart. These two charges are free to move but do not because there is a third (fixed) charge nearby. What must be the magnitude of the third charge and its placement in order for the first two to be in equilibrium?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 19

(I) Determine the magnitude and direction of the electric force on an electron in a uniform electric field of strength 2460N/C that points due east.

Katie Mcalpine

Numerade Educator

Problem 20

(I) A proton is released in a uniform electric field, and it experiences an electric force of 1.86 $\times$ 10$^{-14}$ toward the south. Find the magnitude and direction of the electric field.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 21

(I) Determine the magnitude and direction of the electric field 21.7 cm directly above an isolated 33.0 $\times$ 10$^{-6}$ charge.

Katie Mcalpine

Numerade Educator

Problem 22

(I) A downward electric force of 6.4 N is exerted on a -7.3$\mu$C charge. Find the magnitude and direction of the electric field at the position of this charge.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 23

(II) Determine the magnitude of the acceleration experienced by an electron in an electric field of 756N/C. How does the direction of the acceleration depend on the direction of the field at that point?

Katie Mcalpine

Numerade Educator

Problem 24

(II) Determine the magnitude and direction of the electric field at a point midway between a -8.0$\mu$C and a +5.8$\mu$C charge 6.0 cm apart. Assume no other charges are nearby.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 25

(II) Draw, approximately, the electric field lines about two point charges, $+Q$ and $-3Q$, which are a distance $\ell$ apart.

Katie Mcalpine

Numerade Educator

Problem 26

(II) What is the electric field strength at a point in space where a proton experiences an acceleration of 2.4 million "g's"?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 27

(II) An electron is released from rest in a uniform electric field and accelerates to the north at a rate of 105m/s$^2$. Find the magnitude and direction of the electric field.

Katie Mcalpine

Numerade Educator

Problem 28

(II) The electric field midway between two equal but opposite point charges is 386 N/C, and the distance between the charges is 16.0 cm.What is the magnitude of the charge on each?

Katie Mcalpine

Numerade Educator

Problem 29

(II) Calculate the electric field at one corner of a square 1.22 m on a side if the other three corners are occupied by 3.25 $\times$ 10$^{-6}$C charges.

Suzanne W.

Numerade Educator

Problem 30

(II) Calculate the electric field at the center of a square 42.5 cm on a side if one corner is occupied by a -38.6$\mu$C charge and the other three are occupied by -27.0$\mu$C charges.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 31

(II) Determine the direction and magnitude of the electric field at the point P in Fig. 16-56. The charges are separated by a distance 2$a$, and point P is a distance $x$ from the midpoint between the two charges. Express your answer in terms of $Q, x, a,$ and $k$.
FIGURE 16-56 Problem 31. (CANT COPY FIGURE)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 32

(II) Two point charges, $Q_1 = -32\mu$C and $Q_2 = +45\mu$C are separated by a distance of 12 cm. The electric field at the point P (see Fig. 16-57) is zero. How far from $Q_1$ is P?
FIGURE 16-57 Problem 32. (CANT COPY FIGURE)

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 33

(II) Determine the electric field $\overrightarrow{E}$ at the origin 0 in Fig. 16-58 due to the two charges at A and B.
FIGURE 16-58 Problem 33. (CANT COPY FIGURE)

Prabhu Ramji

Numerade Educator

Problem 34

(II) You are given two unknown point charges, $Q_1$ and $Q_2$. At a point on the line joining them, one third of the way from $Q_1$ to $Q_2$ the electric field is zero (Fig. 16-59). What is the ratio $Q_1/Q_2$?
FIGURE 16-59 Problem 34. (CANT COPY FIGURE)

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 35

(III) Use Coulomb's law to determine the magnitude and direction of the electric field at points A and B in Fig. 16-60 due to the two positive charges ($Q = 4.7\mu$C) shown. Are your results consistent with Fig. 16-32b?
FIGURE 16-60 Problem 35. (CANT COPY FIGURE)

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 36

(III) An electron (mass m = 9.11 $\times$ 10$^{-31}$) is accelerated in the uniform field $\overrightarrow{E}$ ($E =$ 1.45 $\times$ 10$^4$N/C) between two thin parallel charged plates. The separation of the plates is 1.60 cm.The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate, Fig. 16-61. ($a$) With what speed does it leave the hole? ($b$) Show that the gravitational force can be ignored.
FIGURE 16-61 Problem 36. (CANT COPY FIGURE)

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 37

(III) The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in Fig. 16-39. Assume that the net average charge (due to electron sharing) indicated on H and N atoms has magnitude 0.2$e$ and on the indicated C and O atoms is 0.4$e$. Assume also that atoms on each molecule are separated by 1.0 $\times$ 10$^{-10}$ Estimate the net force between ($a$) a thymine and an adenine; and ($b$) a cytosine and a guanine. For each bond (red dots) consider only the three atoms in a line (two atoms on one molecule, one atom on the other). ($c$) Estimate the total force for a DNA molecule containing 10$^5$pairs of such molecules. Assume half are A-T pairs and half are C-G pairs.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 38

(I) The total electric flux from a cubical box of side 28.0 cm is 1.85 $\times$ 10$^3$ N $\cdot$ m$^2$/C What charge is enclosed by the box?

Vishal Gupta

Numerade Educator

Problem 39

(II) In Fig. 16-62, two objects, O$_1$ and O$_2$, have charges +1.0$\mu$C and -2.0$\mu$C, respectively, and a third object, O$_3$ is electrically neutral. ($a$) What is the electric flux through the surface $A_1$ that encloses all three objects? ($b$) What is the electric flux through the surface $A_2$ that encloses the third object only?
FIGURE 16-62 Problem 39. (CANT COPY FIGURE)

Katie Mcalpine

Numerade Educator

Problem 40

(II) A cube of side 8.50 cm is placed in a uniform field $E =$ 7.50 $\times$ 10$^3$N/C with edges parallel to the field lines. (a) What is the net flux through the cube? ($b$) What is the flux through each of its six faces?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 41

(II) The electric field between two parallel square metal plates is 130 N/C. The plates are 0.85 m on a side and are separated by 3.0 cm. What is the charge on each plate (assume equal and opposite)? Neglect edge effects.

Dading Chen

Numerade Educator

Problem 42

(II) The field just outside a 3.50-cm-radius metal ball is 3.75 $\times$ 10$^2$ N/C and points toward the ball. What charge resides on the ball?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 43

(III) A point charge $Q$ rests at the center of an uncharged thin spherical conducting shell. (See Fig. 16-34.) What is the electric field $E$ as a function of $r$ ($a$) for $r$ less than the inner radius of the shell, ($b$) inside the shell, and ($c$) beyond the shell? ($d$) How does the shell affect the field due to $Q$ alone? How does the charge $Q$ affect the shell?

Katie Mcalpine

Numerade Educator

Problem 44

How close must two electrons be if the magnitude of the electric force between them is equal to the weight of either at the Earth's surface?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 45

Given that the human body is mostly made of water, estimate the total amount of positive charge in a 75-kg person.

Katie Mcalpine

Numerade Educator

Problem 46

A 3.0-g copper penny has a net positive charge of 32$\mu$C. What fraction of its electrons has it lost?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 47

Measurements indicate that there is an electric field surrounding the Earth. Its magnitude is about 150 N/C at the Earth's surface and points inward toward the Earth's center. What is the magnitude of the electric charge on the Earth? Is it positive or negative? [$Hint:$ The electric field outside a uniformly charged sphere is the same as if all the charge were concentrated at its center.]

Katie Mcalpine

Numerade Educator

Problem 48

(a) The electric field near the Earth's surface has magnitude of about 150 N/C. What is the acceleration experienced by an electron near the surface of the Earth? ($b$) What about a proton? ($c$) Calculate the ratio of each acceleration to $g = 9.8\mathrm{m/s}^2$.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 49

A water droplet of radius 0.018 mm remains stationary in the air. If the downward-directed electric field of the Earth is 150 N/C, how many excess electron charges must the water droplet have?

Katie Mcalpine

Numerade Educator

Problem 50

Estimate the net force between the CO group and the HN group shown in Fig. 16-63. The C and O have charges $\pm$ 0.40$e$, and the H and N have charges $\pm$ 0.20$e$, where $e = 1.6 \times 10^{-19}$ [Hint: Do not include the "internal" forces between C and O, or between H and N.]
FIGURE 16-63 Problem 50. (CANT COPY FIGURE)

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 51

In a simple model of the hydrogen atom, the electron revolves in a circular orbit around the proton with a speed of 2.2 $\times$ 10$^6$m/s. Determine the radius of the electron's orbit. [$Hint:$ See Chapter 5 on circular motion.]

Katie Mcalpine

Numerade Educator

Problem 52

Two small charged spheres hang from cords of equal length $\ell$ as shown in Fig. 16-64 and make small angles $\theta_1$ and $\theta_2$ with the vertical. ($a$) If $Q_1 = Q, Q_2 = 2Q$ and $m_1 = m_2 = m$, determine the ratio $\theta_1/\theta_2$. ($b$) Estimate the distance between the spheres.
FIGURE 16-64 Problem 52. (CANT COPY FIGURE)

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 53

A positive point charge $Q_1 = 2.5 \times 10^{-5}$C is fixed at the origin of coordinates, and a negative point charge $Q_1 = -5.0 \times 10^{-6}$C is fixed to the $x$ axis at $x = +2.4$m. Find the location of the place(s) along the $x$ axis where the electric field due to these two charges is zero.

Katie Mcalpine

Numerade Educator

Problem 54

Dry air will break down and generate a spark if the electric field exceeds about 3 $\times$ 10$^6$N/C. How much charge could be packed onto a green pea (diameter 0.75 cm) before the pea spontaneously discharges? [$Hint:$ Eqs. 16-4 work outside a sphere if $r$ is measured from its center.]

Audrey Fleming

Numerade Educator

Problem 55

Two point charges, $Q_1 = -6.7\mu$C and $Q_2 = 1.8\mu$C are located between two oppositely charged parallel plates, as shown in Fig. 16-65. The two charges are separated by a distance of $x =$ 0.47m. Assume that the electric field produced by the charged plates is uniform and equal to $E =$ 53,000 N/C. Calculate the net electrostatic force on $Q_1$ and give its direction.
FIGURE $16-65$ Problem 55. (CANT COPY FIGURE)

Katie Mcalpine

Numerade Educator

Problem 56

Packing material made of pieces of foamed polystyrene can easily become charged and stick to each other. Given that the density of this material is about 35 kg/m$^3$, estimate how much charge might be on a 2.0-cm-diameter foamed polystyrene sphere, assuming the electric force between two spheres stuck together is equal to the weight of one sphere.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 57

A point charge ($m =$ 1.0 gram) at the end of an insulating cord of length 55 cm is observed to be in equilibrium in a uniform horizontal electric field of 9500 N/C, when the pendulum's position is as shown in Fig. 16-66, with the charge 12 cm above the lowest (vertical) position. If the field points to the right in Fig. 16-66, determine the magnitude and sign of the point charge.
FIGURE 16-66 Problem 57. (CANT COPY FIGURE)

Katie Mcalpine

Numerade Educator

Problem 58

Two small, identical conducting spheres A and B are a distance $R$ apart; each carries the same charge $Q$. ($a$) What is the force sphere B exerts on sphere A? ($b$) An identical sphere with zero charge, sphere C, makes contact with sphere B and is then moved very far away. What is the net force now acting on sphere A? ($c$) Sphere C is brought back and now makes contact with sphere A and is then moved far away. What is the force on sphere A in this third case?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 59

For an experiment, a colleague of yours says he smeared toner particles uniformly over the surface of a sphere 1.0 m in diameter and then measured an electric field of 5000 N/C near its surface. ($a$) How many toner particles (Example 16-6) would have to be on the surface to produce these results? ($b$) What is the total mass of the toner particles?

Katie Mcalpine

Numerade Educator

Problem 60

A proton ($m =$ 1.67 $\times$ 10$^{-27}$kg) is suspended at rest in a uniform electric field $\overrightarrow{E}$. Take into account gravity at the Earth's surface, and determine $\overrightarrow{E}$.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 61

A point charge of mass 0.185 kg, and net charge +0.340$\mu$C hangs at rest at the end of an insulating cord above a large sheet of charge. The horizontal sheet of fixed uniform charge creates a uniform vertical electric field in the vicinity of the point charge. The tension in the cord is measured to be 5.18 N. Calculate the magnitude and direction of the electric field due to the sheet of charge (Fig. 16-67).
FIGURE 16-67 Problem 61. (CANT COPY FIGURE)

Katie Mcalpine

Numerade Educator

Problem 62

An electron with speed $v_0 =$ 5.32 $\times$ 10$^6$m/s is traveling parallel to an electric field of magnitude $E =$ 9.45 $\times$ 10$^3$ N/C. ($a$) How far will the electron travel before it stops? ($b$) How much time will elapse before it returns to its starting point?

Justin Swantek

Numerade Educator

Problem 63

Given the two charges shown in Fig. 16-68, at what position(s) $x$ is the electric field zero?
FIGURE 16-68 Problem 63. (CANT COPY FIGURE)

Prashant Bana

Numerade Educator

Problem 64

What is the total charge of all the electrons in a 25-kg bar of aluminum? (Aluminum has 13 electrons per atom and an atomic mass of 27 u.)

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 65

Two point charges, $+Q$ and $-Q$ of mass m, are placed on the ends of a massless rod of length $\ell$, which is fixed to a table by a pin through its center. If the apparatus is then subjected to a uniform electric field $E$ parallel to the table and perpendicular to the rod, find the net torque on the system of rod plus charges.

Katie Mcalpine

Numerade Educator

Problem 66

Determine the direction and magnitude of the electric field at point P, Fig. 16-69. The two charges are separated by a distance of 2$a$. Point P is on the perpendicular bisector of the line joining the charges, a distance x from the midpoint between them. Express your answers in terms of $Q, x, a,$ and $k$.
FIGURE 16-69 Problem 66.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 67

A mole of carbon contains 7.22 $\times$ 10$^{24}$ electrons. Two electrically neutral carbon spheres, each containing 1 mole of carbon, are separated by 15.0 cm (center to center). What fraction of electrons would have to be transferred from one sphere to the other for the electric force and the gravitational force between the spheres to be equal?

Katie Mcalpine

Numerade Educator