College Physics

Hugh D. Young Philip W. Adams

Chapter 17

Electric Charge and Electric Field - all with Video Answers

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Chapter Questions

Problem 1

A positively charged glass rod is brought close to a neutral sphere that is supported on a nonconducting plastic stand as shown in Figure $17.44 .$ Sketch the distribution of charges on the sphere if it is made of (a) aluminum, (b) nonconducting plastic.

Prashant Bana

Prashant Bana

Numerade Educator

Problem 2

A positively charged rubber rod is moved close to a neutral copper ball that is resting on a nonconducting sheet of plastic.
(a) Sketch the distribution of charges on the ball. (b) With the rod still close to the ball, a metal wire is briefly connected from the ball to the earth and then removed. After the rubber rod is also removed, sketch the distribution of charges (if any) on the copper ball.

Ryan Hood

Numerade Educator

Problem 3

Two iron spheres contain excess charge, one positive and the other negative. (a) Show how the charges are arranged on these spheres if they are very far from each other. (b) If the spheres are now brought close to each other, but do not touch, sketch how the charges will be distributed on their surfaces. (c) In part (b), show how the charges would be distributed if both spheres were negative.

Prabhu Ramji

Numerade Educator

Problem 4

During an electrical storm, clouds can build up very large amounts of charge, and this charge can induce charges on the earth's surface. Sketch the distribution of charges at the earth's surface in the vicinity of a cloud if the cloud is positively charged and the earth behaves like a conductor.

Prabhu Ramji

Numerade Educator

Problem 5

In ordinary laboratory circuits, charges in the $\mu \mathrm{C}$ and nC range are common. How many excess electrons must you add to an object to give it a charge of (a) $-2.50 \mu \mathrm{C},(\mathrm{b})-2.50 \mathrm{nC} ?$

Prabhu Ramji

Numerade Educator

Problem 6

Neurons are components of the nervous system of the body that transmit signals as electrical impulses travel along their length. These impulses propagate when charge suddenly rushes into and then out of a part of the neuron called an axon. Measurements have shown that, during the inflow part of this cycle, approximately $5.6 \times 10^{11} \mathrm{Na}^{+}$ (sodium ions) per meter, each with charge $+e,$ enter the axon. How many coulombs of charge enter a $1.5 \mathrm{~cm}$ length of the axon during this process?

Prabhu Ramji

Numerade Educator

Problem 7

You have a pure (24-karat) gold ring with mass $17.7 \mathrm{~g}$. Gold has an atomic mass of $197 \mathrm{~g} / \mathrm{mol}$ and an atomic number of $79 .$ (a) How many protons are in the ring, and what is their total positive charge? (b) If the ring carries no net charge, how many electrons are in it?

Prabhu Ramji

Numerade Educator

Problem 8

Two equal point charges of $+3.00 \times 10^{-6} \mathrm{C}$ are placed $0.200 \mathrm{~m}$ apart. What are the magnitude and direction of the force each charge exerts on the other?

Prabhu Ramji

Numerade Educator

Problem 9

The repulsive force between two electrons has a magnitude of $4.00 \mathrm{~N}$.
(a) What is the distance between the electrons? (b) At what distance would the force be $1.00 \mathrm{~N} ?$ (c) Calculate the ratio of the distance you found in (b) to that you found in (a).

Prabhu Ramji

Numerade Educator

Problem 10

A negative charge of $-0.550 \mu \mathrm{C}$ exerts an upward $0.200 \mathrm{~N}$ force on an unknown charge $0.300 \mathrm{~m}$ directly below it. (a) What is the unknown charge (magnitude and sign)? (b) What are the magnitude and direction of the force that the unknown charge exerts on the $-0.550 \mu \mathrm{C}$ charge?

Ryan Hood

Numerade Educator

Problem 11

The particles in the nucleus of an atom are approximately $10^{-15} \mathrm{~m}$ apart, while the electrons in an atom are about $10^{-10} \mathrm{~m}$ from the nucleus. (a) Calculate the electrical repulsion between two protons in a nucleus if they are $1.00 \times 10^{-i 5} \mathrm{~m}$ apart. If you were holding these protons, do you think you could feel the effect of this force? How many pounds would the force be?
(b) Calculate the electrical attraction that a proton in a nucleus exerts on an orbiting electron if the two particles are $1.00 \times 10^{-10} \mathrm{~m}$

Prabhu Ramji

Numerade Educator

Problem 12

Not existing question number in book

Lucas Finney

Numerade Educator

Problem 13

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Lucas Finney

Numerade Educator

Problem 14

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Lucas Finney

Numerade Educator

Problem 15

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Lucas Finney

Numerade Educator

Problem 16

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Lucas Finney

Numerade Educator

Problem 17

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Lucas Finney

Numerade Educator

Problem 18

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Lucas Finney

Numerade Educator

Problem 19

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Lucas Finney

Numerade Educator

Problem 20

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Lucas Finney

Numerade Educator

Problem 21

Not existing question number in book

Lucas Finney

Numerade Educator

Problem 22

Not existing question number in book

Lucas Finney

Numerade Educator

Problem 23

Not existing question number in book

Lucas Finney

Numerade Educator

Problem 24

Not existing question number in book

Lucas Finney

Numerade Educator

Problem 25

Not existing question number in book

Lucas Finney

Numerade Educator

Problem 26

Not existing question number in book

Lucas Finney

Numerade Educator

Problem 27

II Consider the charges in Figure 17.50. Find the magnitude and direction of the net force on $q_2=+5.00 \mu \mathrm{C}$ if (a) $q_1=q_3=+5.00 \mu \mathrm{C}$, (b) $q_1=+5.00 \mu \mathrm{C}$ and $q_3=-5.00 \mu \mathrm{C}$.

Check back soon!

Problem 27

Consider the charges in Figure $17.50 .$ Find the magnitude and direction of the net force on $q_{2}=+5.00 \mu \mathrm{C}$ if (a) $q_{1}=q_{3}=+5.00 \mu \mathrm{C},$ (b) $q_{1}=+5.00 \mu \mathrm{C}$ and $q_{3}=-5.00 \mu \mathrm{C}$

Prabhu Ramji

Numerade Educator

Problem 28

Two unequal charges repel each other with a force $F$. If both charges are doubled in magnitude, what will be the new force in terms of $F$ ?

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Problem 28

Two unequal charges repel each other with a force $F$. If both charges are doubled in magnitude, what will be the new force in terms of $F ?$

Prabhu Ramji

Numerade Educator

Problem 29

In an experiment in space, one proton is held fixed and another proton is released from rest a distance of $2.50 \mathrm{~mm}$ away. (a) What is the initial acceleration of the proton after it is released? (b) Sketch qualitative (no numbers!) acceleration-time and velocity-time graphs of the released proton's motion.

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Problem 29

In an experiment in space, one proton is held fixed and another proton is released from rest a distance of $2.50 \mathrm{~mm}$ away. (a) What is the initial acceleration of the proton after it is released?
(b) Sketch qualitative (no numbers!) acceleration-time and velocity-time graphs of the released proton's motion.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 30

A charge $+Q$ is located at the origin, and a second charge, $+4 Q$. is at distance $d$ on the $x$ axis. Where should a third charge, $q$, be placed, and what should be its sign and magnitude, so that all three charges will be in equilibrium?

Ryan Hood

Numerade Educator

Problem 31

A small object carrying a charge of $-8.00 \mathrm{nC}$ is acted upon by a downward force of $20.0 \mathrm{nN}$ when placed at a certain point in an electric field. (a) What are the magnitude and direction of the electric field at the point in question? (b) What would be the magnitude and direction of the force acting on a proton placed at this same point in the electric field?

Surjit Tewari

Numerade Educator

Problem 32

(a) What must the charge (sign and magnitude) of a $1.45 \mathrm{~g}$ particle be for it to remain balanced against gravity when placed in a downward-directed electric field of magnitude $650 \mathrm{~N} / \mathrm{C} ?$ (b) What is the magnitude of an electric field in which the electric force it exerts on a proton is equal in magnitude to the proton's weight?

Prabhu Ramji

Numerade Educator

Problem 33

A uniform electric field exists in the region between two oppositely charged plane parallel plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate, $3.20 \mathrm{~cm}$ distant from the first, in a time interval of $1.5 \times 10^{-8} \mathrm{~s}$. (a) Find the magnitude of this electric field.
(b) Find the speed of the electron when it strikes the second plate.

Prabhu Ramji

Numerade Educator

Problem 34

A particle has a charge of $-3.00 \mathrm{nC}$. (a) Find the magnitude and direction of the electric field due to this particle at a point $0.250 \mathrm{~m}$ directly above it. (b) At what distance from the particle does its electric field have a magnitude of $12.0 \mathrm{~N} / \mathrm{C}$ ?

Rashmi Sinha

Numerade Educator

Problem 35

The electric field caused by a certain point charge has a magnitude of $6.50 \times 10^{3} \mathrm{~N} / \mathrm{C}$ at a distance of $0.100 \mathrm{~m}$ from the charge. What is the magnitude of the charge?

Prabhu Ramji

Numerade Educator

Problem 36

At a distance of $16 \mathrm{~m}$ from a charged particle, the electric field has a magnitude of $100 \mathrm{~N} / \mathrm{C}$. (a) At what distance is the electric field $400 \mathrm{~N} / \mathrm{C} ?$ (b) At what distance is it $10 \mathrm{~N} / \mathrm{C} ?$

Prabhu Ramji

Numerade Educator

Problem 37

Electric fields in the atom. (a) Within the nucleus. What strength of electric field does a proton produce at the distance of another proton, about $5.0 \times 10^{-15} \mathrm{~m}$ away? (b) At the electrons. What strength of electric field does this proton produce at the distance of the electrons, approximately $5.0 \times 10^{-10} \mathrm{~m}$ away?

Prabhu Ramji

Numerade Educator

Problem 38

A proton is traveling horizontally to the right at $4.50 \times 10^{6} \mathrm{~m} / \mathrm{s}$.
(a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of $3.20 \mathrm{~cm}$.
(b) How much time does it take the proton to stop after entering the field? (c) What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 39

Two point charges are separated by $25.0 \mathrm{~cm}$ (see Figure 17.51 ). Find the net electric field these charges produce at (a) point $A,$ (b) point $B$.
(c) What would be the magnitude and direction of the electric force this combination of charges would produce on a proton at $A ?$

Prabhu Ramji

Numerade Educator

Problem 40

A point charge of $-4.00 \mathrm{nC}$ is at the origin, and a second point charge of $+6.00 \mathrm{nC}$ is on the $x$ axis at $x=0.800 \mathrm{~m} .$ Find the magnitude and direction of the electric field at each of the following points on the $x$ axis:
(a) $x=20.0 \mathrm{~cm}$
(b) $x=1.20 \mathrm{~m}$
(c) $x=-20.0 \mathrm{~cm}$

Ajay Singhal

Numerade Educator

Problem 41

In a rectangular coordinate system, a positive point charge $q=6.00 \mathrm{nC}$ is placed at the point $x=+0.150 \mathrm{~m}, y=0,$ and an identical point charge is placed at $x=-0.150 \mathrm{~m}, y=0 .$ Find the $x$ and $y$ components and the magnitude and direction of the electric field at the following points: (a) the origin; (b) $x=0.300 \mathrm{~m}, y=0 ;$
(c) $x=0.150 \mathrm{~m}, y=-0.400 \mathrm{~m} ;$ (d) $x=0, y=0.200 \mathrm{~m}$

Ryan Hood

Numerade Educator

Problem 42

Two particles having charges of $+0.500 \mathrm{nC}$ and $+8.00 \mathrm{nC}$ are separated by a distance of $1.20 \mathrm{~m}$. (a) At what point along the line connecting the two charges is the net electric field due to the two charges equal to zero? (b) Where would the net electric field be zero if one of the charges were negative?

Surjit Tewari

Numerade Educator

Problem 43

Three negative point charges lie along a line as shown in Figure 17.52 . Find the magnitude and direction of the electric field this combination of charges produces at point $P$, which lies $6.00 \mathrm{~cm}$ from the $-2.00 \mu \mathrm{C}$ charge measured perpendicular to the line connecting the three charges.

Sheh Lit Chang

University of Washington

Problem 44

An electric dipole is in a uniform external electric field $\vec{E}$ as shown in Figure $17.53 .$ (a) What is the net force this field exerts on the dipole? (b) Find the orientations of the dipole for which the torque on it about an axis through its center perpendicular to the plane of the figure is zero. (c) Which of the orientations in part (b) is stable, and which is unstable? (Hint: Consider a small displacement away from the equilibrium position, and see what happens.) (d) Show that, for the stable orientation in part (c), the dipole's own electric field opposes the external field for points between the charges.

Prabhu Ramji

Numerade Educator

Problem 45

(a) An electron is moving east in a uniform electric field of $1.50 \mathrm{~N} / \mathrm{C}$ directed to the west. At point $A,$ the velocity of the electron is $4.50 \times 10^{5} \mathrm{~m} / \mathrm{s}$ toward the east. What is the speed of the electron when it reaches point $B, 0.375 \mathrm{~m}$ east of point $A ?$ (b) $\mathrm{A}$ proton is moving in the uniform electric field of part (a). At point A, the velocity of the proton is $1.90 \times 10^{4} \mathrm{~m} / \mathrm{s}$, east. What is the speed of the proton at point $B ?$

Ryan Hood

Numerade Educator

Problem 46

$\mathrm{A}+20 \mathrm{nC}$ point charge is placed at the origin, and a $+5 \mathrm{nC}$ charge is placed on the $x$ axis at $x=1 \mathrm{~m} .$ At what position on the $x$ axis is the net electric field zero? (Be careful to keep track of the direction of the electric field of each particle.)

Prabhu Ramji

Numerade Educator

Problem 47

For the dipole shown in Figure $17.54,$ show that the electric field at points on the $x$ axis points vertically downward and has magnitude $k q(2 a) /\left(a^{2}+x^{2}\right)^{3 / 2}$. What does this expression reduce to when the distance between the two charges is much less than $x ?$

Prabhu Ramji

Numerade Educator

Problem 48

Figure 17.55 shows some of the electric field lines due to three point charges arranged along the vertical axis. All three charges have the same magnitude. (a) What are the signs of the three charges? Explain your reasoning. (b) At what point(s) is the magnitude of the electric field the smallest? Explain your reasoning. Explain how the fields produced by each individual point charge combine to give a small net field at this point or points.

Vishal Gupta

Numerade Educator

Problem 49

A proton and an electron are separated as shown in Figure $17.56 .$ Points $A, B,$ and $C$ lie on the perpendicular bisector of the line connecting these two charges. Sketch the direction of the net electric field due to the two charges at (a) point $A,$ (b) point $B$, and (c) point $C$.

Prabhu Ramji

Numerade Educator

Problem 50

Sketch electric field lines in the vicinity of two charges, $Q$ and $-4 Q$, located a small distance apart on the $x$ axis.

Vishal Gupta

Numerade Educator

Problem 51

Two point charges $Q$ and $+q$ (where $q$ is positive) produce the net electric field shown at point $P$ in Figure $17.57 .$ The field points parallel to the line connecting the two charges. (a) What can you conclude about the sign and magnitude of $Q$ ? Explain your reasoning. (b) If the lower charge were negative instead, would it be possible for the field to have the direction shown in the figure? Explain your reasoning.

Sheh Lit Chang

University of Washington

Problem 52

Two very large parallel sheets of the same size carry equal magnitudes of charge spread uniformly over them, as shown in Figure $17.58 .$ In each of the cases that follow, sketch the net pattern of electric field lines in the region between the sheets, but far from their edges. (Hint: First sketch the field lines due to each sheet, and then add these fields to get the net field.) (a) The top sheet is positive and the bottom sheet is negative, as shown,
(b) both sheets are positive, (c) both sheets are negative.

Prabhu Ramji

Numerade Educator

Problem 53

(a) A closed surface encloses a net charge of $2.50 \mu \mathrm{C}$. What is the net electric flux through the surface? (b) If the electric flux through a closed surface is determined to be $1.40 \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C},$ how much charge is enclosed by the surface?

Ryan Hood

Numerade Educator

Problem 54

Figure 17.59 shows cross sections of five closed surfaces $S_{1}, S_{2},$ and $\mathrm{so}$ on. Find the net electric flux passing through each of these surfaces.

Prabhu Ramji

Numerade Educator

Problem 55

A point charge $8.00 \mathrm{nC}$ is at the center of a cube with sides of length $0.200 \mathrm{~m}$. What is the electric flux through (a) the surface of the cube, (b) one of the six faces of the cube?

Ryan Hood

Numerade Educator

Problem 56

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter $12.0 \mathrm{~cm},$ giving it a charge of $-15.0 \mu \mathrm{C}$. Find the electric field
(a) just inside the paint layer, (b) just outside the paint layer, and (c) $5.00 \mathrm{~cm}$ outside the surface of the paint layer.

Prabhu Ramji

Numerade Educator

Problem 57

(a) How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere $30.0 \mathrm{~cm}$ in diameter to produce an electric field of $1150 \mathrm{~N} / \mathrm{C}$ just outside the surface of the sphere? (b) What is the electric field at a point $10.0 \mathrm{~cm}$ outside the surface of the sphere?

Prabhu Ramji

Numerade Educator

Problem 58

An electric dipole consists of charges $q$ and $-q$ separated by a distance $3 R .$ The dipole lies on the negative $x$ axis and is moving in the positive $x$ direction as shown in Figure $17.60 .$ The dipole passes through a sphere of radius $R$ centered at the origin. Make a sketch of the electric flux through the sphere as a function of time.

Vishal Gupta

Numerade Educator

Problem 59

A total charge of magnitude $Q$ is distributed uniformly within a thick spherical shell of inner radius $a$ and outer radius $b$. (a) Use Gauss's law to find the electric field within the cavity $(r \leq a) .(\mathrm{b})$ Use Gauss's law to prove that the electric field outside the shell $(r \geq b)$ is exactly the same as if all the charge were concentrated as a point charge $Q$ at the center of the sphere. (c) Explain why the result in part (a) for a thick shell is the same as that found in Example 17.10 for a thin shell. (Hint: A thick shell can be viewed as infinitely many thin shells.)

Anna Wirth-Singh

Anna Wirth-Singh

Numerade Educator

Problem 60

During a violent electrical storm, a car is struck by a falling highvoltage wire that puts an excess charge of $-850 \mu \mathrm{C}$ on the metal car. (a) How much of this charge is on the inner surface of the car?
(b) How much is on the outer surface?

Prabhu Ramji

Numerade Educator

Problem 61

A neutral conductor completely encloses a hole inside of it. You observe that the outer surface of this conductor carries a charge of $-12 \mu \mathrm{C}$. (a) Can you conclude that there is a charge inside the hole? If so, what is this charge? (b) How much charge is on the inner surface of the conductor?

Surjit Tewari

Numerade Educator

Problem 62

An irregular neutral conductor has a hollow cavity inside of it and is insulated from its surroundings. An excess charge of $+16 \mathrm{nC}$ is sprayed onto this conductor. (a) Find the charge on the inner and outer surfaces of the conductor. (b) Without touching the conductor, a charge of $-11 \mathrm{nC}$ is inserted into the cavity through a small hole in the conductor. Find the charge on the inner and outer surfaces of the conductor in this case.

Prabhu Ramji

Numerade Educator

Problem 63

Three point charges are arranged along the $x$ axis. Charge $q_{1}=-4.50 \mathrm{nC} \quad$ is $\quad$ located $\quad$ at $\quad x=0.200 \mathrm{~m}, \quad$ and $\quad$ charge $q_{2}=+2.50 \mathrm{nC}$ is at $x=-0.300 \mathrm{~m}$. A positive point charge $q_{3}$ is located at the origin. (a) What must the value of $q_{3}$ be for the net force on this point charge to have magnitude $4.00 \mu \mathrm{N}$ ? (b) What is the direction of the net force on $q_{3} ?$ (c) Where along the $x$ axis can $q_{3}$ be placed and the net force on it be zero, other than the trivial answers of $x=+\infty$ and $x=-\infty ?$

Vishal Gupta

Numerade Educator

Problem 64

An electron is released from rest in a uniform electric field. The electron accelerates vertically upward, traveling $4.50 \mathrm{~m}$ in the first $3.00 \mu \mathrm{s}$ after it is released. (a) What are the magnitude and direction of the electric field? (b) Are we justified in ignoring the effects of gravity? Justify your answer quantitatively.

Ze-Han Lee

Numerade Educator

Problem 65

A charge $q_{1}=+5.00 \mathrm{nC}$ is placed at the origin of an $x-y$ coordinate system, and a charge $q_{2}=-2.00 \mathrm{nC}$ is placed on the positive $x$ axis at $x=4.00 \mathrm{~cm} .$ (a) If a third charge $q_{3}=+6.00 \mathrm{nC}$ is now placed at the point $x=4.00 \mathrm{~cm}, y=3.00 \mathrm{~cm},$ find the $x$ and $y$ components of the total force exerted on this charge by the other two charges. (b) Find the magnitude and direction of this force.

Linda Winkler

Numerade Educator

Problem 66

A charge of $-3.00 \mathrm{nC}$ is placed at the origin of an $x-y$ coordinate system, and a charge of $2.00 \mathrm{nC}$ is placed on the $y$ axis at $y=4.00 \mathrm{~cm} .$ (a) If a third charge, of $5.00 \mathrm{nC},$ is now placed at the point $x=3.00 \mathrm{~cm}, y=4.00 \mathrm{~cm},$ find the $x$ and $y$ components of the total force exerted on this charge by the other two charges.
(b) Find the magnitude and direction of this force.

Meghan Miholics

Meghan Miholics

Numerade Educator

Problem 67

Point charges of $3.00 \mathrm{nC}$ are situated at each of three corners of a square whose side is $0.200 \mathrm{~m}$. What are the magnitude and direction of the resultant force on a point charge of $-1.00 \mu \mathrm{C}$ if it is placed
(a) at the center of the square, (b) at the vacant corner of the square?

Vishal Gupta

Numerade Educator

Problem 68

An electron is projected with an initial speed $v_{0}=5.00 \times 10^{6} \mathrm{~m} / \mathrm{s}$ into the uniform field between the parallel plates in Figure $17.61 .$ The direction of the field is vertically downward, and the field is zero except in the space between the two plates. The electron enters the field at a point midway between the plates. If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.

Vishal Gupta

Numerade Educator

Problem 69

A small 12.3 g plastic ball is tied to a very light $28.6 \mathrm{~cm}$ string that is attached to the vertical wall of a room. (See Figure $17.62 .)$ A uniform horizontal electric field exists in this room. When the ball has been given an excess charge of $-1.11 \mu \mathrm{C},$ you observe that it remains suspended, with the string making an angle of $17.4^{\circ}$ with the wall. Find the magnitude and direction of the electric field in the room.

Prabhu Ramji

Numerade Educator

Problem 70

$\mathrm{A}-5.00 \mathrm{nC}$ point charge is on the $x$ axis at $x=1.20 \mathrm{~m}$. A second point charge $Q$ is on the $x$ axis at $-0.600 \mathrm{~m}$. What must be the sign and magnitude of $Q$ for the resultant electric field at the origin to be (a) $45.0 \mathrm{~N} / \mathrm{C}$ in the $+x$ direction,
(b) $45.0 \mathrm{~N} / \mathrm{C}$ in the $-x$ direction?

Maria Gabriela Cota Moreira

Maria Gabriela Cota Moreira

Numerade Educator

Problem 71

A physics student uses induction to give two small spheres the same charge $q$. He then proceeds to measure the magnitude of the repulsive force between the spheres as a function of their separation. The findings are given in the table. Make a linearized plot of the data, in which force is on the $y$ axis. Using a "best fit" to the data, determine the charge on each of the spheres.

Linda Winkler

Numerade Educator

Problem 72

A $9.60 \mu \mathrm{C}$ point charge is at the center of a cube with sides of length $0.500 \mathrm{~m}$. (a) What is the electric flux through one of the six faces of the cube? (b) How would your answer to part (a) change if the sides were $0.250 \mathrm{~m}$ long? Explain.

Prabhu Ramji

Numerade Educator

Problem 73

Two point charges $q_{1}$ and $q_{2}$ are held $4.00 \mathrm{~cm}$ apart. An electron released at a point that is equidistant from both charges (see Figure 17.63 ) undergoes an initial acceleration of $8.25 \times 10^{18} \mathrm{~m} / \mathrm{s}^{2}$ directly upward in the figure, parallel to the line connecting $q_{1}$ and $q_{2} .$ Find the magnitude and sign of $q_{1}$ and $q_{2}$

Linda Winkler

Numerade Educator

Problem 74

An early model of the hydrogen atom viewed it as an electron orbiting a proton in a circular path with a radius of $5.29 \times 10^{-11} \mathrm{~m} .$ What would be the centripetal acceleration of the electron in this model? How does this number compare with the acceleration of gravity, $g ?$ (You may need to review Chapter 6 on circular motion.)

Prabhu Ramji

Numerade Educator

Problem 75

Consider a bee with the mean electric charge found in the experiment. This charge represents roughly how many missing electrons?
A. $1.9 \times 10^{8}$
B. $3.0 \times 10^{8}$
C. $1.9 \times 10^{18}$
D. $3.0 \times 10^{18}$

Ze-Han Lee

Numerade Educator

Problem 76

What is the best explanation for the observation that the electric charge on the stem became positive as the charged bee approached (before it landed)?
A. Because air is a good conductor, the positive charge on the bee's surface flowed through the air from bee to plant.
B. Because the earth is a reservoir of large amounts of charge, positive ions were drawn up the stem from the ground toward the charged bee.
C. The plant became electrically polarized as the charged bee approached.
D. Bees that visited the plant earlier deposited a positive charge on the stem.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 77

After one bee left a flower with a positive charge, that bee flew away and another bee with the same amount of positive charge flew close to the plant. Which diagram in Figure 17.64 best represents the electric field lines between the bee and the flower?

Prabhu Ramji

Numerade Educator

Problem 78

In a follow-up experiment, a charge of $+40 \mathrm{pC}$ was placed at the center of an artificial flower at the end of a $30-\mathrm{cm}$ -long stem. Bees were observed to approach no closer than $15 \mathrm{~cm}$ from the center of this flower before they flew away. This observation suggests that the smallest external electric field to which bees may be sensitive is closest to which of these values?
A. $2.4 \mathrm{~N} / \mathrm{C}$
B. $16 \mathrm{~N} / \mathrm{C}$
C. $2.7 \times 10^{-10} \mathrm{~N} / \mathrm{C}$
D. $4.8 \times 10^{-10} \mathrm{~N} / \mathrm{C}$

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 79

One of the hazards facing humans in space is space radiation: high-energy charged particles emitted by the sun. During a solar flare, the intensity of this radiation can reach lethal levels. One proposed method of protection for astronauts on the surface of the moon or Mars is an array of large, electrically charged spheres placed high above areas where people live and work. The spheres would produce a strong electric field $\vec{E}$ to deflect the charged particles that make up space radiation. The spheres would be similar in construction to a Mylar balloon, with a thin, electrically conducting layer on the outside surface on which a net positive or negative charge would be placed. A typical sphere might be $5 \mathrm{~m}$ in diameter.
Suppose that to repel electrons in the radiation from a solar flare, each sphere must produce an electric field $\vec{E}$ of magnitude $1 \times 10^{6} \mathrm{~N} / \mathrm{C}$ at $25 \mathrm{~m}$ from the center of the sphere. What net charge on each sphere is needed?
A. $-0.07 \mathrm{C}$
B. $-8 \mathrm{mC}$
C. $-80 \mu$ C
D. $-1 \times 10^{-20} \mathrm{C}$

Prabhu Ramji

Numerade Educator

Problem 80

What is the magnitude of $\boldsymbol{E}$ just outside the surface of such a sphere?
A. 0
B. $10^{6} \mathrm{~N} / \mathrm{C}$
C. $10^{7} \mathrm{~N} / \mathrm{C}$
D. $10^{8} \mathrm{~N} / \mathrm{C}$

Mohit Khurana

Texas A&M University

Problem 81

What is the direction of $\vec{E}$ just outside the surface of such a sphere?
A. Tangent to the surface of the sphere
B. Perpendicular to the surface, pointing toward the sphere
C. Perpendicular to the surface, pointing away from the sphere
D. There is no electric field just outside the surface.

Averell Hause

Carnegie Mellon University

Problem 82

Which of the following is true about $\vec{E}$ inside a negatively charged sphere as described here?
A. It points from the center of the sphere to the surface and is largest at the center.
B. It points from the surface to the center of the sphere and is largest at the surface.
C. It is zero.
D. It is constant but is not zero.

Prabhu Ramji

Numerade Educator