Holt Physics

Raymond A. Serway, Jerry S. Faughn

Chapter 17

Electric Forces And Fields - all with Video Answers

Educators

Chapter Questions

Problem 1

How are conductors different from insulators?

Timothy Vitale

Timothy Vitale

Numerade Educator

Problem 2

When a conductor is charged by induction, is the induced surface charge on the conductor the same or opposite the charge of the object inducing the surface charge?

Rodger Claar

Numerade Educator

Problem 3

A negatively charged balloon has $3.5 \mu \mathrm{C}$ of charge. How many excess electrons are on this balloon?

Timothy Vitale

Numerade Educator

Problem 4

Which activity does not produce the same results as the other three?
a. sliding over a plastic-covered automobile seat
b. walking across a woolen carpet
c. scraping food from a metal bowl with a metal spoon
d. brushing dry hair with a plastic comb

Surjit Tewari

Numerade Educator

Problem 5

Would life be different if the electron were positively charged and the proton were negatively charged? Explain your answer

Rodger Claar

Numerade Educator

Problem 6

If a suspended object is attracted to another object that is charged, can you conclude that the suspended object is charged?

Surjit Tewari

Numerade Educator

Problem 7

Explain from an atomic viewpoint why charge is usually transferred by electrons.

Timothy Vitale

Numerade Educator

Problem 8

Because of a higher moisture content, air is a better conductor of charge in the summer than in the winter. Would you expect the shocks from static electricity to be more severe in summer or winter? Explain your answer.

Rodger Claar

Numerade Educator

Problem 9

A balloon is negatively charged by rubbing and then clings to a wall, Does this mean that the wall is positively charged?

Timothy Vitale

Numerade Educator

Problem 10

Which effect proves more conclusively that an object is charged, attraction to or repulsion from another object? Explain

Surjit Tewari

Numerade Educator

Problem 11

What determines the direction of the electric force between two charges?

Timothy Vitale

Numerade Educator

Problem 12

In which direction will the electric force from the two equal positive charges pull the negative charge shown in Figure $17-24 ?$

Surjit Tewari

Numerade Educator

Problem 13

The gravitational force is always attractive, while the electric force is both attractive and repulsive. What accounts for this difference?

Timothy Vitale

Numerade Educator

Problem 14

When more than one charged object is present in an area, how can the total electric force on one of the charged objects be found?

Surjit Tewari

Numerade Educator

Problem 15

Identify examples of electric forces in everyday life

Timothy Vitale

Numerade Educator

Problem 16

How does the electric force between two charges change when the distance between them is doubled? How does it change when the distance is halved?

Surjit Tewari

Numerade Educator

Problem 17

According to Newton's third law, every action has an equal and opposite reaction. When a comb is charged and held near small pieces of paper, the comb exerts an electric force on the paper pieces and pulls them toward it. Why don't you observe the comb moving toward the paper pieces as well?

Rodger Claar

Numerade Educator

Problem 18

At the point of fission, a nucleus of $^{235} \mathrm{U}$ that has 92 protons is divided into two smaller spheres. each of which has 46 protons and a radius of $5.9 \times 10^{-15} \mathrm{m} .$ What is the repulsive force pushing these two spheres apart? (See Sample Problem 17A.)

Surjit Tewari

Numerade Educator

Problem 19

What is the electric force between a glass ball that has $+2.5 \mu \mathrm{C}$ of charge and a rubber ball that has $-5.0 \mu \mathrm{C}$ of charge when they are separated by a distance of $5.0 \mathrm{cm} ?$ (See Sample Problem 17A.)

Surjit Tewari

Numerade Educator

Problem 20

An alpha particle (charge $=+2.0 e$ ) is sent at high speed toward a gold nucleus (charge $=+79 e$ ). What is the clectric force acting on the alpha particle when the alpha particle is $2.0 \times 10^{-14} \mathrm{m}$ from the gold nucleus? (See Sample Problem 17A.)

Timothy Vitale

Numerade Educator

Problem 21

Three positive point charges of $3.0 \mathrm{nC}, 6,0 \mathrm{nC},$ and $2.0 \mathrm{nC}$
respectively, are arranged in a triangular pattern, as shown in Figure $17-25 .$ Find the magnitude and direction of the electric force on the 6.0 nC charge (See Sample Problem 17B.

Surjit Tewari

Numerade Educator

Problem 22

Two positive point charges, each of which has a charge of $2.5 \times 10^{-9} \mathrm{C}$, are located at $y=+0.50 \mathrm{m}$ and $y=-0.50 \mathrm{m} .$ Find the magnitude and direction of the resultant electrical force on a charge of $3.0 \times 10^{-9} \mathrm{C}$ located at $x=0.70 \mathrm{m}$ (See Sample Problem 17B.)

Timothy Vitale

Numerade Educator

Problem 23

Three point charges lie in a straight line along the $y$ -axis. A charge of $q_{l}=-9.0 \mu \mathrm{C}$ is at $y=6.0 \mathrm{m}$ and a charge of $q_{2}=-8.0 \mu \mathrm{C}$ is at $y=-4.0 \mathrm{m} .$ The net electric force on the third point charge is zero. Where is this charge located? (See Sample Problem 17C.)

Surjit Tewari

Numerade Educator

Problem 24

A charge of $+3.5 \mathrm{nC}$ and a charge of $+5.0 \mathrm{nC}$ are separated by $40.0 \mathrm{cm} .$ Find the equilibrium position for $a-6.0$ nC charge (See Sample Problem 17C.)

Surjit Tewari

Numerade Educator

Problem 25

What is an electric field?

Rodger Claar

Numerade Educator

Problem 26

Show that the definition of electric field strength $\left(E=F_{\text {elvorrid }} / q_{0}\right)$ is equivalent to the equation $E=k_{C q} / r^{2}$ for point charges.

Surjit Tewari

Numerade Educator

Problem 27

In an irregularly shaped conductor, a corona forms around a sharp end sooner than around a smoother end Explain why.

Surjit Tewari

Numerade Educator

Problem 28

When electric field lines are being drawn, what determines the number of lines originating from a charge? What determines whether the lines originate from or terminate on a charge?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 29

Draw some representative electric field lines for two charges of $+q$ and $-3 q$ separated by a small distance.

Keshav Singh

Numerade Educator

Problem 30

Consider the electric field lines in Figure $17-26$
a. Where is charge density the highest? Where is it the lowest?
b. If an opposite charge were brought into the vicinity, where would charge on the pear shaped object "leak off" most readily?

Surjit Tewari

Numerade Educator

Problem 31

Do electric field lines actually exist?

Rodger Claar

Numerade Educator

Problem 32

Why does the dome of a Van de Graaff generator have a spherical surface?

Surjit Tewari

Numerade Educator

Problem 33

When defining the electric field, why must the magnitude of the test charge be very small?

Timothy Vitale

Numerade Educator

Problem 34

Why can't two field lines from the same field cross one another?

Rodger Claar

Numerade Educator

Problem 35

A student stands on a piece of insulating material. places her hand on a Van de Graaff generator, and then turns on the generator (see Figure $17-21$ on page 651 ). Is she shocked? Why or why not? The student finds that her hair stands on end. Why does this occur?

Surjit Tewari

Numerade Educator

Problem 36

In Figure $17-18$ (page 649 ), where do the extra lines leaving the $+2 q$ charge end?
3

Surjit Tewari

Numerade Educator

Problem 37

A "free" electron and "free" proton are placed in an identical electric field. Compare the electric force on each particle. How do their accelerations compare?

Timothy Vitale

Numerade Educator

Problem 38

Find the electric field at a point midway between two charges of $+30.0 \times 10^{-9} \mathrm{C}$ and $+60.0 \times 10^{-9} \mathrm{C}$ separated by a distance of $30.0 \mathrm{cm}$ (See Sample Problem 17D.)

Surjit Tewari

Numerade Educator

Problem 39

$A+5.7 \mu C$ point charge is on the $x$ -axis at $x=$ $-3.0 \mathrm{m},$ and $\mathrm{a}+2.0 \mu \mathrm{C}$ point charge is on the $x$ -axis at $x=+1.0 \mathrm{m} .$ Determine the net electric field (magnitude and direction on the $y$ -axis at $y=+2.0 \mathrm{m}$ (See Sample Problem 17 D.)

Surjit Tewari

Numerade Educator

Problem 40

Calculate the net charge on a substance consisting of a combination of $7.0 \times 10^{13}$ protons and $4.0 \times 10^{13}$ electrons.

Rodger Claar

Numerade Educator

Problem 41

An electron moving through an electric field experiences an acceleration of $6.3 \times 10^{3} \mathrm{m} / \mathrm{s}^{2}$
a. Find the electric force acting on the electron.
b. What is the strength of the electric field?

Prabhat Tyagi

Numerade Educator

Problem 42

One gram of copper has $9.48 \times 10^{21}$ atoms, and each copper atom has 29 electrons.
a. How many electrons are contained in 1.00 g of copper?
b. What is the total charge of these electrons?

Rodger Claar

Numerade Educator

Problem 43

Consider three charges arranged as shown in Figure $17-27$
a. What is the electric field strength at a point $1.0 \mathrm{cm}$ to the left of the middle charge?
b. What is the magnitude of the force on a $-2.0 \mu \mathrm{C}$ charge placed at this point?

Surjit Tewari

Numerade Educator

Problem 44

Consider three charges arranged in a triangle as shown in Figure $17-28$
a. What is the net electric force on the charge at the origin?
b. What is the net electric field at the position of the charge at the origin?

Surjit Tewari

Numerade Educator

Problem 45

$1.00 \mathrm{g}$ of hydrogen contains $6.02 \times 10^{23}$ atoms, each with one electron and one proton. Suppose that $1.00 \mathrm{g}$ of hydrogen is separated into protons and clectrons, that the protons are placed at Earth's north pole, and that the electrons are placed at Earth's south pole Find the magnitude of the resulting compressional force on Earth. (The radius of Earth is approximately $6.38 \times 10^{6} \mathrm{m}.$

Surjit Tewari

Numerade Educator

Problem 46

Sketch the electric field pattern set up by a positively charged hollow conducting sphere. Include regions both inside and outside the sphere.

Timothy Vitale

Numerade Educator

Problem 47

The moon $\left(m=7.36 \times 10^{22} \mathrm{kg}\right)$ is bound to Earth $\left(m=5.98 \times 10^{24} \mathrm{kg}\right)$ by gravity. If, instead, the force of attraction were the result of each having a charge of the same magnitude but opposite in $\operatorname{sign},$ find the quantity of charge that would have to be placed on cach to produce the required force.

Rodger Claar

Numerade Educator

Problem 48

Two small metallic spheres, each with a mass of $0.20 \mathrm{g}$, are suspended as pendulums by light strings from a common point. They are given the same electric charge, and the two come to equilibrium when each string is at an angle of $5.0^{\circ}$ with the vertical. If the string is $30.0 \mathrm{cm}$ long, what is the magnitude of the charge on each sphere?

Timothy Vitale

Numerade Educator

Problem 49

What are the magnitude and the direction of the electric ficld that will balance the weight of an electron? What are the magnitude and direction of the electric field that will balance the weight of a proton?

Surjit Tewari

Numerade Educator

Problem 50

Three positive charges are arranged as shown in Figure $17-29 .$ Find the electric field at the fourth corner of the rectangle.

Surjit Tewari

Numerade Educator

Problem 51

An electron and a proton are each placed at rest in an external uniform electric field of $520 \mathrm{N} / \mathrm{C}$. Calculate the speed of each particle after 48 ns.

Surjit Tewari

Numerade Educator

Problem 52

The dome of a Van de Graaff generator receives a charge of $2.0 \times 10^{-4} \mathrm{C}$. The radius of the dome is $1.0 \mathrm{m} .$ Find the magnitude of the electric field strength at the following locations:
a. inside the dome
b. at the surface of the dome
c. $4.0 \mathrm{m}$ from the center of the dome

Surjit Tewari

Numerade Educator

Problem 53

Air becomes a conductor when the electric field strength exceeds $3.0 \times 10^{6} \mathrm{N} / \mathrm{C}$. Determine the maximum amount of charge that can be carried by a metal sphere $2.0 \mathrm{m}$ in radius.

Surjit Tewari

Numerade Educator

Problem 54

A Van de Graaff generator is charged so that the electric field at its surface is $3.0 \times 10^{4} \mathrm{N} / \mathrm{C}$
a. What is the electric force on a proton released at the surface of the generator?
b, Find the proton's acceleration at this instant

Rodger Claar

Numerade Educator

Problem 55

Thunderstorms can have an electric field of up to $3.4 \times 10^{5} \mathrm{N} / \mathrm{C}$. What is the magnitude of the electric force on an electron in such a field?

Timothy Vitale

Numerade Educator

Problem 56

Three identical charges $(q=+5.0 \mu \mathrm{C})$ are along a circle with a radius of $2.0 \mathrm{m}$ at angles of $30^{\circ}$ $150^{\circ},$ and $270^{\circ},$ as shown in Figure $17-30$. What is the resultant electric field at the center?

Surjit Tewari

Numerade Educator

Problem 57

$ An object with a net charge of $24 \mu \mathrm{C}$ is placed in a uniform electric field of $610 \mathrm{N} / \mathrm{C}$, directed vertically. What is the mass of this object if it floats in this electric field?

Surjit Tewari

Numerade Educator

Problem 58

A proton accelerates from rest in a uniform electric field of $640 \mathrm{N} / \mathrm{C}$. At some time later, its speed is $1.20 \times 10^{6} \mathrm{m} / \mathrm{s}$
a. What is the magnitude of the acceleration of the proton?
b. How long does it take the proton to reach this speed?
c. How far has it moved in this time interval?
d. What is its kinetic energy at the later time?

Surjit Tewari

Numerade Educator

Problem 59

Three identical point charges, each of mass $m=0.10 \mathrm{kg},$ hang from three strings, as shown in Figure $17-31 .$ If $L=30.0 \mathrm{cm}$ and $\theta=45^{\circ},$ what is the value of $q ?$

Surjit Tewari

Numerade Educator

Problem 60

A small 2.0 g plastic ball is suspended by a $20.0 \mathrm{cm}$ string in a uniform electric field of $1.0 \times 10^{4} \mathrm{N} / \mathrm{C}$, as shown in Figure $17-32$
a. Is the ball's charge positive or negative?
b. If the ball is in equilibrium when the string makes $a 15^{\circ}$ angle with the vertical as indicated, what is the net charge on the ball?

Timothy Vitale

Numerade Educator

Problem 61

In a laboratory experiment, five equal negative point charges are placed symmetrically around the circumference of a circle of radius $r$. Calculate the electric field at the center of the circle.

Rodger Claar

Numerade Educator

Problem 62

If the electric field strength is increased to about $3.0 \times 10^{6} \mathrm{N} / \mathrm{C}$ air "breaks down" and loses its insulating quality. Under these conditions, sparking results.
a. What acceleration does an electron experience when the electron is placed in such an electric field?
b. If the electron starts from rest when it is placed in an electric field under these conditions, in what distance does it acquire a speed equal to 10,0 percent of the speed of light?
c. What acceleration does a proton experience when the proton is placed in such an electric field?

Surjit Tewari

Numerade Educator