College Physics

Roger A. Freedman; Todd Ruskell; Philip R. Kesten

Chapter 16

Electrostatics I: Electric Charge - all with Video Answers

Educators

Chapter Questions

Problem 1

How, if at all, would the physical universe be different if the proton were negatively charged and the electron were positively charged?

Prabhu Ramji

Prabhu Ramji

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Problem 2

How, if at all, would the physical universe be different if the proton's charge was very slightly larger in magnitude than the electron's charge?

Prabhu Ramji

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Problem 3

When an initially electrically neutral object acquires a net positive charge, does its mass increase or decrease? Why? SSM

Prabhu Ramji

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Problem 4

When you remove socks from a hot dryer, they tend to cling to everything. Two identical socks, however, usually repel. Why?

Prabhu Ramji

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Problem 5

Describe a set of experiments that might be used to determine if you have discovered a third type of charge other than positive and negative.

Prabhu Ramji

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Problem 6

How does a person become "charged" as he or she shuffles across a carpet, wearing cloth slippers, on a dry winter day?

Prabhu Ramji

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Problem 7

After combing your hair with a plastic comb, you find that when you bring the comb near a small bit of paper, the bit of paper moves toward the comb. Then, shortly after the paper touches the comb, it moves away from the comb. Explain these observations. SSM

Prabhu Ramji

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Problem 8

After combing your hair with a plastic comb, you find that when you bring the comb near an empty aluminum soft-drink can that is lying on its side on a nonconducting tabletop, the can rolls toward the comb. After being touched by the comb, the can is still attracted by the comb. Explain these observations.

Keshav Singh

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Problem 9

(a) A positively charged glass rod attracts a lighter object suspended by a thread. Does it follow that the object is negatively charged? (b) If, instead, the rod repels it, does it follow that the suspended object is positively charged?

Prabhu Ramji

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Problem 10

Some days it can be frustrating to attempt to demonstrate electrostatic phenomena for a physics class. An experiment that works beautifully one day may fail the next day if the weather has changed. Air-conditioning helps a lot while demonstrating the phenomena during the summer. Why?

Keshav Singh

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Problem 11

Discuss the similarities and differences between the gravitational and electric forces.

Prabhu Ramji

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Problem 12

Why is the gravitational force usually ignored in problems on the scale of particles such as electrons and protons?

Prabhu Ramji

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Problem 13

(a) What are the advantages of thinking of the force on a charge at a point $P$ as being exerted by an electric field at $P$, rather than by other charges at other locations? (b) Is the convenience of the field as a calculation device worth inventing a new physical quantity? Or is there more to the field concept than that? SSM

Ze-Han Lee

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Problem 14

Do electric field lines point along the trajectory of positively charged particles? Why or why not?

Prabhu Ramji

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Problem 15

An electron and a proton are released in a region of space where the electric field is vertically downward. How do the electric forces acting on the electron and proton compare?

Prabhu Ramji

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Problem 16

Inside a uniform spherical charge distribution, why is it that as one moves out from the center, the electric field increases as $r$ rather than decreases as $1 / r^{2} ?$

Prabhu Ramji

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Problem 17

Is the electric field $\mathrm{E} \rightarrow \overrightarrow{\boldsymbol{E}}$ in Gauss's law only the electric field due to the charge inside the Gaussian surface, or is it the total electric field due to all charges both inside and outside the surface? Explain your answer. SSM

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Problem 18

If the net electric flux out of a closed surface is zero, does that mean the charge density must be zero everywhere inside the surface? Explain your answer.

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Problem 19

Electric charges of the opposite sign
A. exert no force on each other.
B. attract each other.
C. repel each other.
D. repel and attract each other.
E. repel and attract each other depending on the magnitude of the charges.

Prabhu Ramji

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Problem 20

If two uncharged objects are rubbed together and one of them acquires a negative charge, then the other one
A. remains uncharged.
B. also acquires a negative charge.
C. acquires a positive charge.
D. acquires a positive charge equal to twice the negative charge.
E. acquires a positive charge equal to half the negative charge.

Prabhu Ramji

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Problem 21

Metal sphere $A$ has a charge of $-Q$. An identical metal sphere $B$ has a charge of $+2 Q$. The magnitude of the electric force on $B$ due to $A$ is $F$. The magnitude of the electric force on $A$ due to $B$ is
A. $F / 4$.
B. F/2.
C. F.
D. $2 F$.
E. $4 F .$ SSM

Prabhu Ramji

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Problem 22

A balloon can be charged by rubbing it with your sleeve while holding it in your hand. You can conclude from this that the balloon is a(n)
A. conductor.
B. insulator.
C. neutral object.
D. Gaussian surface.
E. semiconductor.

Prabhu Ramji

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Problem 23

A positively charged rod is brought near one end of an uncharged metal bar. The end of the metal bar farthest from the charged rod will be charged
A. positively.
B. negatively.
C. neutral.
D. twice as much as the end nearest the rod.
E. none of the above ways. SSM

Hubert Agamasu

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Problem 24

A free positive charge released in an electric field will
A. remain at rest.
B. accelerate in the direction opposite to the electric field.
C. accelerate in the direction perpendicular to the electric field.
D. accelerate in the same direction as the electric field.
E. accelerate in a circular path.

Prabhu Ramji

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Problem 25

Consider a point charge $+Q$ located outside a closed surface such as a sphere bound by the black circle in Figure $16-24$. What is the net electric flux through the closed surface?
A. $+\mathrm{Q} \varepsilon 0^{\frac{+Q}{\varepsilon_{0}}}$
B. $-\mathrm{Q} \varepsilon 0^{\frac{-Q}{\varepsilon_{0}}}$
C. 0
D. $+2 \mathrm{Q} \varepsilon 0^{\frac{+2 Q}{\varepsilon_{0}}}$
E. $-2 \mathrm{Q} \varepsilon 0^{\frac{-2 Q}{\varepsilon_{0}}}$

Prabhu Ramji

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Problem 26

If a charge is located at the center of a spherical volume and the electric flux through the surface of the sphere is $\Phi$, what would be the flux through the surface if the radius of the sphere were tripled?
A. $3 \Phi$
B. $9 \Phi$
C. $\Phi$
D. $\Phi / 3$
E. $\Phi / 9$

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Problem 27

A point charge $+Q$ is at the center of a spherical conducting shell of inner radius $R_{1}$ and outer radius $R_{2}$, as shown in $\underline{\text { Figure } 16-25 . \text { The charge on }}$ the inner surface of the shell is
A. $+Q$.
B. $-Q$.
C. 0 .
D. $+Q / 2$.
E. $-Q / 2 .$ SSM

Prabhu Ramji

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Problem 28

(a) Estimate the positive charge in you due to the protons in the molecules present in your body. (b) What is the net charge in your body?

Keshav Singh

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Problem 29

Estimate the amount of charge needed on both a comb and on a bit of tissue paper in order to generate an electric force of sufficient magnitude to support the weight of the paper.

Keshav Singh

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Problem 30

A cylindrical jar $10 \mathrm{~cm}$ in diameter and $15 \mathrm{~cm}$ tall is full of old copper pennies. Estimate the number of valence electrons in the jar.

Supratim Pal

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Problem 31

The electrical breakdown of an insulator occurs when an electric field becomes large enough to ionize the insulator, allowing electrical current to flow-lightning is an example of the electrical breakdown of air. The electrical breakdown of air occurs when the electric field reaches about $3 \times 106 \mathrm{~N} / \mathrm{C}^{3} \times 10^{6} \mathrm{~N} / \mathrm{C}$. Estimate the total static charge on your body when you generate a static spark with your fingertip when getting out of your car.

Narayan Hari

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Problem 32

Suppose two people are standing near each other having a conversation. If both people carry the same amount of static charge, estimate how much charge each person would have to carry in order for the repulsive electric force to cancel the attractive gravitational force between them.

Prabhu Ramji

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Problem 33

Estimate the electric flux passing through the passenger window of your car when you become charged up after sliding into your vehicle.

Keshav Singh

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Problem 34

The magnitude of the repulsive force $(F)$ between two $+2.5-\mu \mathrm{C}$ charges as a function of the distance of separation $(r)$ is listed in the following table. Empirically derive a relationship between $F$ and $r$ by doing a curve fit to find the power $n$ of $r$ in the following formula:
F=kq1q2rn $F=\frac{k q_{1} q_{2}}{r^{n}}$
Use a graphing calculator or spreadsheet.
$$
\begin{array}{cccc}
r(\mathrm{~m}) & F(\mathrm{~N}) & r(\mathrm{~m}) & F(\mathrm{~N}) \\
\hline 0.003 & 5500 & 0.080 & 6 \\
0.004 & 3000 & 0.100 & 5 \\
0.005 & 2000 & 0.200 & 1 \\
0.010 & 600 & 0.300 & 0.5 \\
0.020 & 175 & 0.400 & 0.35 \\
0.040 & 30 & 0.500 & 0.25 \\
0.050 & 10 & 0.600 & 0.15 \\
\hline
\end{array}
$$

Keshav Singh

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Problem 35

The nucleus of a copper atom has 29 protons and 35 neutrons. What is the total charge of the nucleus? Example $16-1$

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Problem 36

Five electrons are added to $1.00 \mathrm{C}$ of positive charge. What is the net charge of the system? Example $16-1$

Prabhu Ramji

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Problem 37

How many coulombs of negative charge are there in $0.500$ kg of water? SSM Example $16-1$

Prabhu Ramji

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Problem 38

An ion has 17 protons, 18 neutrons, and 18 electrons. What is the net charge of the ion? Example $16-1$

Prabhu Ramji

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Problem 39

The charge per unit length on a glass rod is $0.00500 \mathrm{C} / \mathrm{m}$. If the rod is 1 $\mathrm{mm}$ long, how many electrons have been removed from the glass rod? $\underline{\text { Example } 16-1}$

Prabhu Ramji

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Problem 40

How many electrons must be transferred from an object to produce a charge of $1.60$ C? Example $16-1$

Prabhu Ramji

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Problem 41

Suppose $2.00 \mathrm{C}$ of positive charge are distributed evenly throughout a solid sphere of $1.27$ -cm radius. (a) What is the charge per unit volume for this situation? (b) Is the sphere insulating or conducting? How do you know?

Prabhu Ramji

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Problem 42

The maximum amount of charge that can be collected on a Van de Graaff generator's conducting sphere (30-cm diameter) is about $30 \mu \mathrm{C}$. Calculate the surface charge density, $\sigma$, of the sphere in $\mathrm{C} / \mathrm{m}^{2}$

Prabhu Ramji

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Problem 43

Biology Most workers in nanotechnology are actively monitored for excess static charge buildup. The human body acts like an insulator as one walks across a carpet, collecting $-50 \mathrm{nC}$ per step. (a) What charge buildup will a worker in a manufacturing plant accumulate if she walks 25 steps? (b) How many electrons are present in that amount of charge? (c) If a delicate manufacturing process can be damaged by an electrical discharge of greater than $10^{12}$ electrons, what is the maximum number of steps that any worker should be allowed to take before touching the components? SSM

Prabhu Ramji

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Problem 44

Two point charges are separated by a distance of $20.0 \mathrm{~cm}$. The numerical value of one charge is twice that of the other. If each charge exerts a force of magnitude $45.0 \mathrm{~N}$ on the other, find the magnitude of the charges. $\underline{\text { Example } 16-2}$

Prabhu Ramji

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Problem 45

The mass of an electron is $9.11 \times 10-31 \mathrm{~kg} 9.11 \times 10^{-31} \mathrm{~kg}$. How far apart would two electrons have to be in order for the electric force exerted by each on the other to be equal to the weight of an electron? SSM Example $16-2$

Prabhu Ramji

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Problem 46

Charge $A$, $+5.00 \mu \mathrm{C}$, is positioned at the origin of a coordinate system.
Charge $B,-3.00 \mu \mathrm{C}$, is fixed on the $x$ axis at $x=3.00 \mathrm{~m}$. (a) Determine the magnitude and direction of the force that charge $B$ exerts on charge $A$. (b) What is the magnitude and direction of the force that charge $A$ exerts on charge $B$ ? Example $16-2$

Prabhu Ramji

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Problem 47

Point charge $A$ with charge $\mathrm{qA}=+3.00 \mu \mathrm{C}^{q_{A}}=+3.00 \mu \mathrm{C}$ is located at the origin. Point charge $B$ with charge $\mathrm{qB}=-4.00 \mu \mathrm{C}^{q}_{B}=-4.00 \mu \mathrm{C}$ is on the $x$ axis at $x=3.00 \mathrm{~m} x=3.00 \mathrm{~m}$. Point charge $C$ with charge $\mathrm{qC}=-2.00 \mu \mathrm{C}$ $q_{C}=-2.00 \mu \mathrm{C}$ is on the $x$ axis at $\mathrm{x}=6.00 \mathrm{~m} x=6.00 \mathrm{~m}$. And point charge $D$ with charge $\mathrm{qD}=+6.00 \mu \mathrm{C}^{q_{D}}=+6.00 \mu \mathrm{C}$ is on the $x$ axis at $\mathrm{x}=8.00 \mathrm{~m}$
$x=8.00 \mathrm{~m}$. What is the net electric force on point charge $A$ due to the other three charges? Example $16-3$

Prabhu Ramji

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Problem 48

A charge of $+3.00 \mu \mathrm{C}$ is located at the origin, and a second charge of $-2.00 \mu \mathrm{C}$ is located on the $x^{-} y$ plane at the point $(30.0 \mathrm{~cm}, 20.0 \mathrm{~cm})$. Determine the electric force exerted by the $-2.00 \mu \mathrm{C}$ charge on the $3.00 \mu \mathrm{C}$ charge. Example $16-4$

Prabhu Ramji

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Problem 49

A point charge with charge $q 1=+5.00 \mathrm{nC} q_{1}=+5.00 \mathrm{nC}$ is fixed at the origin. A second point charge with charge $\mathrm{q} 2=-7.00 \mathrm{nC} q_{2}=-7.00 \mathrm{nC}$ is located on the $x$ axis at $x=5.00 \mathrm{~m} x=5.00 \mathrm{~m}$. Where along the $x$ axis will a third point charge of $\mathrm{q}=+2.00 \mathrm{nC}^{q}=+2.00 \mathrm{n} \mathrm{C}$ charge need to be for the net electric force on it due to the two fixed charges to be equal to zero? SSM $\underline{\text { Example } 16-3}$

Prabhu Ramji

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Problem 50

Two charges lie on the $x$ axis, a $-2.00-\mu$ C charge at the origin and a $+3.00-\mu \mathrm{C}$ charge at $\mathrm{x}=0.100 \mathrm{~m} x=0.100 \mathrm{~m}$. At what position along the $x$ axis, if any, should a third $+4.00-\mu \mathrm{C}$ charge be placed so that the net force on the third charge is equal to zero? Example $16-3$

Keshav Singh

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Problem 51

Point charge $A$ with a charge of $+3.00 \mu \mathrm{C}$ is located at the origin. Point charge $B$ with a charge of $+6.00 \mu \mathrm{C}$ is located on the $x$ axis at $\mathrm{x}=7.00 \mathrm{~cm}$ $x=7.00 \mathrm{~cm}$. And point charge $C$ with a charge of $+2.00 \mu \mathrm{C}$ is located on the $y$ axis at $\mathrm{y}=6.00 \mathrm{~cm}^{y}=6.00 \mathrm{~cm} .$ What is the net force (magnitude and direction) exerted on each charge by the others? SSM Example $16-4$

Meghan Miholics

Meghan Miholics

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Problem 52

A charge $q_{1}$ equal to $0.600 \mu \mathrm{C}$ is at the origin, and a second charge $q_{2}$ equal to $0.800 \mu \mathrm{C}$ is on the $x$ axis at $5.00 \mathrm{~cm}$. (a) Find the force (magnitude and direction) that each charge exerts on the other. (b) How would your answer change if $a_{7}$ were $-0.800 \mu \mathrm{C}$ ? Example $16-2$

Keshav Singh

Numerade Educator

Problem 53

A charge $\mathrm{Q} 1=+7.00 \mu \mathrm{C}^{Q_{1}}=+7.00 \mu \mathrm{C}$ is located on the $y$ axis at $y=$ $4.00 \mathrm{~cm}$. A second charge $\mathrm{Q} 2=-4.00 \mu \mathrm{C}^{Q} 2=-4.00 \mu \mathrm{C}$ is located on the $x-y$
plane at the point $(-3.00 \mathrm{~cm}, 4.00 \mathrm{~cm})$. And a third charge $\mathrm{Q} 3=+6.00 \mu \mathrm{C}$ $Q_{3}=+6.00 \mu \mathrm{C}$ is located on the $x$ axis at $\mathrm{x}=-3.00 \mathrm{~cm}^{x}=-3.00 \mathrm{~cm}$
Determine the $x$ and $y$ components of the net electric force that acts on the third charge $Q_{3} .$ Example $16-4$

Surjit Tewari

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Problem 54

At point $P$ in Figure $16-26$ the electric field is zero. (a) What are the signs of $q_{1}$ and $q_{2}$ ? (b) Describe their magnitudes. Example 16-6

Prabhu Ramji

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Problem 55

Near the surface of Earth an electric field points radially downward and has a magnitude of approximately $100 \mathrm{~N} / \mathrm{C}$. What charge (magnitude and sign) would have to be placed on a penny that has a mass of $3.11 \mathrm{~g}$ to cause it to rise into the air with an upward acceleration of $0.190 \mathrm{~m} / \mathrm{s}^{2} ?$ Example $16-5$

Prabhu Ramji

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Problem 56

Two charges are placed on the $x$ axis, $+5.00 \mu \mathrm{C}$ at the origin and $-10.0$ $\mu \mathrm{C}$ at $\mathrm{x}=10.0 \mathrm{~cm} x=10.0 \mathrm{~cm}$. (a) Find the electric field on the $x$ axis at $\mathrm{x}=6.00 \mathrm{~cm} x=6.00 \mathrm{~cm}$. (b) At what point(s) on the $x$ axis is the electric field zero? Example 16-6

Prabhu Ramji

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Problem 57

In Figure 16-27 the electric field at the origin is zero. If $q_{1}$ is $1.00 \times 10-7 \mathrm{C}, 1.00 \times 10^{-7} \mathrm{C}$, what is $q_{2} ? \underline{\text { Example } 16-6}$

Prabhu Ramji

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Problem 58

In Figure 16-27 if $q 1=1.00 \times 10-7$ C $q_{1}=1.00 \times 10^{-7} \mathrm{C}$ and
$\mathrm{q} 2=2.00 \times 10^{-7} \mathrm{C}, q_{2}=2.00 \times 10^{-7} \mathrm{C},(\mathrm{a})$ what is the electric field $\mathrm{E} \rightarrow \overrightarrow{\boldsymbol{E}}$ at the
point $(\mathrm{x}, \mathrm{y})=(0.00 \mathrm{~cm}, 3.00 \mathrm{~cm})^{(x, y)}=(0.00 \mathrm{~cm}, 3.00 \mathrm{~cm}) ?$ (b) What is the
force $\mathrm{F} \rightarrow \overrightarrow{\boldsymbol{F}}$ acting on an electron at that position? Example $16-7$

Keshav Singh

Numerade Educator

Problem 59

In Figure 16-27 if $\mathrm{q} 1=1.00 \times 10-7 \mathrm{C} q_{1}=1.00 \times 10^{-7} \mathrm{C}$ and
$\mathrm{q} 2=2.00 \times 10-7 \mathrm{C}, q_{2}=2.00 \times 10^{-7} \mathrm{C},(\mathrm{a})$ what is the electric field $\mathrm{E} \rightarrow \overrightarrow{\boldsymbol{E}}$ at the
point $(\mathrm{x}, \mathrm{y})=(6.00 \mathrm{~m}, 3.00 \mathrm{~m})^{(x, y)}=(6.00 \mathrm{~m}, 3.00 \mathrm{~m})$ ? (b) What is the force
$\mathrm{F} \rightarrow \overrightarrow{\boldsymbol{F}}$ acting on a proton at that position? Example $16-7$

Keshav Singh

Numerade Educator

Problem 60

In the Bohr model the hydrogen atom consists of an electron in a circular orbit of radius $a 0=5.29 \times 10-11 \mathrm{~m} a_{0}=5.29 \times 10^{-11} \mathrm{~m}$ around the nucleus. Using this model, and ignoring relativistic effects, what is the speed of the electron? Example $16-5$

Prabhu Ramji

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Problem 61

Biology The cockroach Periplaneta americana can detect a static electric field of $8.0 \mathrm{kN} / \mathrm{C}$ using its long antennae. If we model the excess static charge on a cockroach as a point charge located at the end of each antenna, what magnitude of charge would each antenna possess in order for each antennae to experience a force of $3.0 \mu \mathrm{N}$ from the external electric field? Example 16-5

Prabhu Ramji

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Problem 62

A rectangular area is rotated in a uniform electric field, from a position where the maximum electric flux goes through it to an orientation where only half the maximum flux goes through it. What is the angle of rotation?

Prabhu Ramji

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Problem 63

A point charge of $4.00 \times 10^{-12} \mathrm{C} 4.00 \times 10^{-12} \mathrm{C}$ is located at the center of a cubical Gaussian surface. What is the electric flux through each face of the cube?

Prabhu Ramji

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Problem 64

The net electric flux through a cubic box with sides that are $20.0 \mathrm{~cm}$ long is $4.80 \times 103 \mathrm{~N} \cdot \mathrm{m} 2 / \mathrm{C}^{4.80 \times 10^{3} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}}$. What charge is enclosed by
the box?

Prabhu Ramji

Numerade Educator

Problem 65

A $10.0$ -cm-long uniformly charged plastic rod is sealed inside a plastic bag. The net electric flux through the bag is $7.50 \times 105 \mathrm{~N} \cdot \mathrm{m} 2 / \mathrm{C}$ $7.50 \times 10^{5} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}$. What is the linear charge density (charge per unit length) on the rod? SSM

Prabhu Ramji

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Problem 66

Figure $16-28$ shows a prism-shaped object that is $40.0 \mathrm{~cm}$ high, $30.0$ $\mathrm{cm}$ deep, and $80.0 \mathrm{~cm}$ long. The prism is immersed in a uniform electric field of $500 \mathrm{~N} / \mathrm{C}$ directed parallel to the $x$ axis. (a) Calculate the electric flux out of each of its five faces and (b) the net electric flux out of the entire closed surface. (c) If in addition to the given electric field the prism also enclosed a point charge of $-2.00 \mu \mathrm{C}$, qualitatively how would your answers above change, if at all?

Prabhu Ramji

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Problem 67

Use Gauss's law to find an expression for the electric field just outside the surface of a sphere carrying a uniform surface charge density $\sigma$ (charge per unit area). SSM $\underline{\text { Example } 16-8}$

Prabhu Ramji

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Problem 68

Determine the charge density for each of the following cases (assume that all densities are uniform): (a) a solid cylinder that has a length $L$, has a radius $R$, and carries a charge $Q$ throughout its volume; (b) a flat plate (very thin) that has a width $W$, has a length $L$, and carries a charge $Q$ on its surface area; (c) a solid sphere of radius $R$ carrying a charge $Q$ throughout its volume; and (d) a hollow sphere of radius $R$ carrying a charge $Q$ over its surface area.

Prabhu Ramji

Numerade Educator

Problem 69

An electric field of magnitude $4.00 \times 102 \mathrm{~N} / \mathrm{C}^{4.00 \times 10^{2} \mathrm{~N} / \mathrm{C} \text { exists at all }}$ points just outside the surface of a 2.00-cm-diameter steel ball bearing. Assuming the ball bearing is in electrostatic equilibrium, (a) what is the total charge on the ball? (b) What is the surface charge density on the ball? $\underline{\text { Example } 16-8}$

Prabhu Ramji

Numerade Educator

Problem 70

Consider an infinite plane with a uniform charge distribution \sigma. (a) Use Gauss's law to find an expression for the electric field due to the plane. (b) What field would be created by two equal but oppositely charged parallel planes? Consider the region between the planes as well as the two regions outside the planes. The simplest way to express your answers is in terms of the surface charge density $\sigma$ (the charge per unit area) on the plane.

Prabhu Ramji

Numerade Educator

Problem 71

A $-3.20-\mu \mathrm{C}$ charge sits in static equilibrium in the center of a conducting spherical shell that has an inner radius of $2.50 \mathrm{~cm}$ and an outer radius of $3.50 \mathrm{~cm}$. The shell has a net charge of $-5.80 \mu \mathrm{C}$. Determine the charge on each surface of the shell and the electric field just outside the shell. $\underline{\text { Example } 16-8}

Prabhu Ramji

Numerade Educator

Problem 72

A spherical party balloon on Earth's surface that is $25 \mathrm{~cm}$ in diameter contains helium at room temperature $\left(20^{\circ} \mathrm{C}\right)$ and at a pressure of $1.3$ atm. If one electron could be stripped from every helium atom in the balloon and removed to a satellite orbiting Earth $22,000 \mathrm{mi}(32,187 \mathrm{~km})$ above the planet, with what force would the balloon and the satellite attract each other when the satellite is directly above the balloon? Example $16-2$

Keshav Singh

Numerade Educator

Problem 73

A plutonium- 242 atom has a nucleus of 94 protons and 148 neutrons and has 94 electrons. The diameter of its nucleus is approximately $15 \times 10-15 \mathrm{~m} 15 \times 10^{-15} \mathrm{~m}$. (a) Make a reasonable physical argument as to why we can treat the nucleus as a point charge for points outside of it. (b)

Keshav Singh

Numerade Educator

Problem 74

When a test charge of $+5.00 \mathrm{nC}$ is placed at a certain point, the force that acts on it has a magnitude of $0.0800 \mathrm{~N}$ and is directed northeast. (a) If the test charge were $-2.00 \mathrm{nC}$ instead, what force would act on it? (b) What is the electric field at the point in question? Example $16-5$

Prabhu Ramji

Numerade Educator

Problem 75

Biology A red blood cell may carry an excess charge of about $-2.5 \times 10-12 \mathrm{C}^{-2.5 \times 10^{-12} \mathrm{C}}$ distributed uniformly over its surface. The cells, modeled as spheres, are approximately $7.5 \mu \mathrm{m}$ in diameter and have a mass of $9.0 \times 10-14 \mathrm{~kg}^{9.0 \times 10^{-14} \mathrm{~kg} \text { . (a) How many excess electrons does a }}$ typical red blood cell carry? (b) What is the surface charge density $\sigma$ on the red blood cell? Express your answer in $\mathrm{C} / \mathrm{m}^{2}$ and in electrons $/ \mathrm{m}^{2}$. SSM Example 16-1

Keshav Singh

Numerade Educator

Problem 76

Three point charges are placed on the $x-y$ plane: $a+50.0-n C$ charge at the origin, a $-50.0-\mathrm{n} \mathrm{C}$ charge on the $x$ axis at $10.0 \mathrm{~cm}$, and $\mathrm{a}+150 \mathrm{n} \mathrm{C}$ charge at the point $(10.0 \mathrm{~cm}, 8.00 \mathrm{~cm})$. (a) Find the total electric force on the $+150$ $\mathrm{n} \mathrm{C}$ charge due to the other two. (b) What is the electric field at the location of the $+150-\mathrm{n} \mathrm{C}$ charge due to the presence of the other two charges? Example $16-4$

Keshav Singh

Numerade Educator

Problem 77

Two small spheres each have a mass $m$ of $0.100 \mathrm{~g}$ and are suspended as pendulums by light insulating strings from a common point, as shown in Figure $16-29 .$ The spheres are given the same electric charge, and the two come to equilibrium when each string is at an angle of $\theta=3.00^{\circ} \theta=3.00^{\circ}$ with the vertical. If each string is $1.00 \mathrm{~m}$ long, what is the magnitude of the charge on each sphere? Example $16-2$

Keshav Singh

Numerade Educator

Problem 78

A small 1.00-g plastic ball that has a charge $q$ of $1.00$ C is suspended by a string that has a length $L$ of $1.00 \mathrm{~m}$ in a uniform electric field, as shown in Figure 16-30. If the ball is in equilibrium when the string makes a $9.80^{\circ}$ angle with the vertical as indicated by $\theta$, what is the electric field strength? Example 16-5

Keshav Singh

Numerade Educator

Problem 79

79. - Biology The 9-inch-long elephant nose fish in the Congo River generates a weak electric field around its body using an organ in its tail. When small prey (or even potential mates) swim within a few feet of the fish, they perturb the electric field. The change in the field is picked up by electric sensor cells in the skin of the elephant nose. These remarkable fish can detect changes in the electric field as small as $3.0 \mu \mathrm{N} / \mathrm{C}$. (a) How much charge (modeled as a point charge) in the fish would be needed to produce such a change in the electric field at a distance of $75 \mathrm{~cm}$ ? (b) How many electrons would be required to create the charge? SSM Example $16-1$

Keshav Singh

Numerade Educator

Problem 80

Three charges $\left(q_{A}, q_{B}\right.$, and $q_{C}$ ) are placed at the vertices of the equilateral triangle that has sides of length $s$ in Figure 16-31. Derive expressions for the electric field at (a) $X$ (at the center of the triangle), (b) $Y$ (at the midpoint of the side between $q_{\mathrm{B}}$ and $\left.q_{\mathrm{C}}\right)$, and (c) $Z$ (at the midpoint of the side between $q_{A}$ and $q_{C}$ ). (d) Now use the following numerical values and calculate the electric field at those same points: $\mathrm{s}=10.0 \mathrm{~cm},^{s}=10.0 \mathrm{~cm}$, $\mathrm{qA}=+20.0 \mathrm{nC}, q_{\mathrm{A}}=+20.0 \mathrm{nC}, \mathrm{qB}=-8.00 \mathrm{nC}, q_{\mathrm{B}}=-8.00 \mathrm{nC}$, and $\mathrm{qC}=-10.0 \mathrm{nC}$
$q_{\mathrm{C}}=-10.0 \mathrm{nC}_{\underline{ }}$ Example $16-7$

Keshav Singh

Numerade Educator

Problem 81

Calculate the electric field at the center of the hexagon shown in Figure 16-32. Assume the sides of the hexagon are all $5.00 \mathrm{~cm}$ long. SSM Example $\underline{16-7}$

Keshav Singh

Numerade Educator

Problem 82

Electric fields up to $2.00 \times 105 \mathrm{~N} / \mathrm{C}^{2.00 \times 10^{5} \mathrm{~N} / \mathrm{C}}$ have been measured inside of clouds during electrical storms. Neglect the drag force due to the air in the cloud and any collisions with air molecules. (a) What acceleration does the maximum electric field produce for protons in the cloud? Express your answer in SI units and as a fraction of $g .$ (b) If the electric field remains constant, how far will the proton have to travel to reach $10 \%$ of the speed of light $(3.00 \times 108 \mathrm{~m} / \mathrm{s})^{\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}$ if it started with negligible speed? (c) Can you neglect the effects of gravity? Explain your answer. Example $16-5$

Keshav Singh

Numerade Educator

Problem 83

An electron with an initial speed of $5.00 \times 105 \mathrm{~m} / \mathrm{s}^{5.00 \times 10^{5} \mathrm{~m} / \mathrm{s} \text { enters }}$ a region in which there is an electric field directed along its direction of motion. If the electron travels $5.00 \mathrm{~cm}$ in the field before being stopped, what are the magnitude and direction of the electric field? Example $16-5$

Daniel Alva

Numerade Educator

Problem 84

An electron, released in a region where the electric field is uniform, is observed to have an acceleration of $3.00 \times 1014 \mathrm{~m} / \mathrm{s} 2^{3.00} \times 10^{14} \mathrm{~m} / \mathrm{s}^{2}$ in the
positive $x$ direction. (a) Determine the electric field producing the acceleration. (b) Assuming the electron is released from rest, determine the time required for it to reach a speed of $11,200 \mathrm{~m} / \mathrm{s}$, the escape speed from Earth's surface. Example $16-5$

Keshav Singh

Numerade Educator

Problem 85

Chemistry The iron atom (Fe) has 26 protons, 30 neutrons, and 26 electrons. The diameter of the atom is approximately $1.0 \times 10-10 \mathrm{~m}$, $1.0 \times 10^{-10} \mathrm{~m}$, while the diameter of its nucleus is about $9.2 \times 10-15 \mathrm{~m}$ $9.2 \times 10^{-15} \mathrm{~m}$. (You can reasonably model the nucleus as a uniform sphere of charge.) What are the magnitude and direction of the electric field that the nucleus produces (a) just outside the surface of the nucleus and (b) at the

Keshav Singh

Numerade Educator

Problem 86

An electron with kinetic energy $K$ is traveling along the $+x$ axis, which is along the axis of a cathode-ray tube as shown in Figure 16 - 33 . There is an electric field $\mathrm{E}=12.00 \times 104 \mathrm{~N} / \mathrm{C}^{E}=12.00 \times 10^{4} \mathrm{~N} / \mathrm{C}$ pointed in the $+y$
direction between the deflection plates, which are $0.0600 \mathrm{~m}$ long and are separated by $0.0200 \mathrm{~m}$. Determine the minimum initial kinetic energy the electron can have and still avoid colliding with one of the plates. Example $16-5$

Keshav Singh

Numerade Educator

Problem 87

In the famous Millikan oil-drop experiment, tiny spherical droplets of oil are sprayed into a uniform vertical electric field. The drops get a very small charge (just a few electrons) due to friction with the atomizer as they are sprayed. The field is adjusted until the drop (which is viewed through a small telescope) is just balanced against gravity and therefore remains stationary. Using the measured value of the electric field, we can calculate the charge on the drop and from this calculate the charge $e$ of the electron. In one apparatus the drops are $1.10 \mu \mathrm{m}$ in diameter, and the oil has a density of $0.850 \mathrm{~g} / \mathrm{cm}^{3}$.(a) If the drops are negatively charged, which way should the electric field point to hold them stationary (up or down)? (b) Why? (c) If a certain drop contains four excess electrons, what magnitude electric field is needed to hold it stationary? (d) You measure a balancing field of $5183 \mathrm{~N} / \mathrm{C}$ for another drop. How many excess electrons are on this drop? Example $16-5$

Keshav Singh

Numerade Educator

Problem 88

Biology There is a naturally occurring vertical electric field near Earth's surface, pointing toward the ground. In fair weather conditions and in an open field, the strength of the electric field is $1.00 \times 102 \mathrm{~N} / \mathrm{C}$ $1.00 \times 10^{2} \mathrm{~N} / \mathrm{C}$. A spherical pollen grain, with a radius of $12 \mu \mathrm{m}$, is released from its parent plant by a light breeze, giving it a net charge of $-0.80 \mathrm{fC}$ (where $1 \mathrm{fC}=1 \times 10-15 \mathrm{CfC}=1 \times 10^{-15} \mathrm{C}$ ). What is the ratio of the
magnitudes of the electric force to the gravitational force, $F_{\text {electric }} / F_{\text {gravitational }}$, acting on the pollen? Assume the volume mass density of the pollen is the same as water, $1.00 \times 103 \mathrm{~kg} / \mathrm{m} 3,1.00 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, which is a primary
constituent of pollen. Example $16-5$

Dading Chen

Numerade Educator

Problem 89

Two hollow, concentric, spherical shells are covered with charge (Figure 16-34). The inner sphere has a radius $R_{\mathrm{i}}$ and a surface charge density of $+\sigma_{i}$, while the outer sphere has a radius $R_{0}$ and a surface charge density of $-\sigma_{0}$. Derive an expression for the electric field in the following three radial
regions: (a) $\mathrm{r}<\mathrm{Ri}, r<R_{i}$, (b) $\mathrm{Ri}<\mathrm{r}<\mathrm{Ro}, R_{\mathrm{i}}<r<R_{\mathrm{o}}$, and (c) $\mathrm{r}>\mathrm{Ro}^{r}>R_{\mathrm{o}}$.
SSM Example $16-8$

Keshav Singh

Numerade Educator

Problem 90

A charge $q 1=+2 q^{q_{1}}=+2 q$ is at the origin, and a charge $q 2=-q^{q_{2}}=-q$ is on the $x$ axis at $x=a$. Find expressions for the total electric field on the $x$ axis in each of the regions (a) $x<0 x<0$ (b) $0<x<a 0<x<a$ and (c) $a<x a<x$
(d) Determine all points on the $x$ axis where the electric field is zero. (e) Use a graphing calculator or spreadsheet to make a plot of $E_{x}$ versus $x$ for all points on the $x$ axis, and (f) qualitatively discuss what happens for $-\infty<x<\infty$. $-\infty<x<\infty$. Example 16-6

Keshav Singh

Numerade Educator

Problem 91

Two point charges are enclosed by a spherical conducting shell that has an inner and outer radius of $13.0$ and $15.2 \mathrm{~cm}$, respectively. One point charge has a charge of $\mathrm{q} 1=8.30 \mu \mathrm{C}, q_{1}=8.30 \mu \mathrm{C}$, while the second point charge has an unknown charge $q_{2}$. The conducting shell is known to have a net electric charge of $-2.40 \mu \mathrm{C}$, but measurements find that the charge on the outer shell is $+3.70 \mu \mathrm{C}$. Determine the charge $q_{2}$ of the second point charge. Example $\underline{16-8}$

Daniel Alva

Numerade Educator