College Physics 2013

Eugenia Etkina, Michael Gentle, Alan Van Heuvelen

Chapter 14

Electric Charge, Force, and Energy

Educators

Chapter Questions

Problem 1

BIO Ventricular defibrillation During ventricular fibrillation, the muscle fibers of the heart’s ventricles undergo uncoordinated rapid contractions, resulting in little or no blood circulation. To restore the heart’s normal rhythm, a defibrillator sends an abrupt jolt of about -0.20 C of electric charge through the chest into the heart. How many electrons pass through the body during this defibrillation?

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Problem 2

You rub two 4.0 -mg balloons with a wool sweater. The balloons hang from $0.50-\mathrm{m}$ -long very light strings. When you attach the strings together at the top, the balloons hang away from each other each string making an angle of $37^{\circ}$ with the vertical. (a) Represent the situation with the force diagram for each balloon and determine the magnitudes of the forces on the diagram. (b) What can you say about the magnitudes of the forces that the balloons exert on each other? Explain. (c) Will the relative magnitudes change if the charge on one balloon is two times larger than on the other? How do you know?

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Problem 3

Two balloons of different mass hang from strings near each other. You charge them about the same amount by rubbing each balloon with wool. Draw a force diagram for each of the balloons. Compare the angles of the threads with the vertical. How do your answers depend on whether the balloons have the same or different magnitude charge?

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Problem 4

Lightning A cloud has a large positive charge. Assume that this is the only cloud in the sky over Earth and that Earth is a good electrical conductor. Draw a sketch showing electric charge distribution on Earth due to the cloud’s electric charge. Explain why a person’s hair might stand on end before a lightning strike.

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Problem 5

EST (a) Earth has an excess of 60 electrons on each square centimeter of surface. Determine the electric charge in coulombs on each square centimeter of surface. (b) If, as you walk across a rug, about $10^{-22} \mathrm{kg}$ of electrons transfer to your body, estimate the number of electrons and the total charge in coulombs on your body.

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Problem 6

You have a small object with 0.0020 $\mathrm{C}$ of electric charge and another small object with 0.0060 $\mathrm{C}$ of charge. Compare the magnitude of the electric force that the $0.0020-\mathrm{C}$ object exerts on the $0.0060-\mathrm{C}$ object to the force that the $0.0060-\mathrm{C}$ object exerts on the $0.0020-\mathrm{C}$ object. Explain your answer.

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Problem 7

Determine the electrical force that two protons in the nucleus of a helium atom exert on each other when separated by $2.0 \times 10^{-15} \mathrm{m} .$

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Problem 8

Two charged objects exert a $4.0-\mathrm{N}$ force on each other when separated by 1.0 $\mathrm{m}$ . (a) What can you determine using this information? (b) You then perform four experiments: you double the separation; you reduce the separation by one-half; you reduce the magnitude of one charge by one-half; and you double both charges. What quantitative information about
the interaction of the objects can you determine for each of the experiments?

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Problem 9

Two identical small metal spheres are separated by $1.0 \times 10^{5} \mathrm{m}$ and exert an $18.9-\mathrm{N}$ repulsive force on each other. A wire is connected between the spheres and then removed. The spheres now repel each other, exerting a $22.5-\mathrm{N}$ force. (a) Explain why the force that these two objects exert on each other changed. (b) Determine everything you can about the situation before the wire was connected and after it was removed.

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Problem 10

Determine the number of electrons that must be transferred from Earth to the Moon so that the electrical attraction between them is equal in magnitude to their present gravitational attraction. What is the mass of this number of electrons?

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Problem 11

BIO lons on cell walls The membrane of a body cell has a positive ion of charge $+e$ on the outside wall and a negative ion of charge $-e$ on the inside wall. Determine the magnitude of the electrical force between these ions if the membrane thickness is $0.80 \times 10^{-9} \mathrm{m} .$ Ignore the effect of the material in which the ions are located.

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Problem 12

Sodium chloride (table salt) consists of sodium ions of charge $+e$ arranged in a crystal lattice with an equal number of chlorine ions of charge $-e .$ The mass of each sodium ion is $3.82 \times 10^{-26} \mathrm{kg}$ and that of each chlorine ion $5.89 \times 10^{-26} \mathrm{kg}$ . Suppose that the sodium ions could be separated into one pile and the chlorine ions into another. What mass of salt would be needed to get 1.00 $\mathrm{C}$ of charge into the sodium ion pile and $-1.00 \mathrm{C}$ into the chlorine ion pile?

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Problem 13

Electrical attraction Two friends each contain about $4 \times 10^{28}$ electrons and an equal number of protons. What will happen in terms of their interaction if 1$\%$ of one friend's electrons are transferred to the other, who is about 100 $\mathrm{m}$ away? What other physical quantities can you determine using this information?

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Problem 14

Hydrogen atom In a simplified model of a hydrogen atom, the electron moves around the proton nucleus in a circular orbit of radius $0.53 \times 10^{-10} \mathrm{m} .$ Use this information to determine at least four physical quantities related to this information.

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Problem 15

Three $1.0-\mathrm{C}$ charged objects are equally spaced on a straight line. The separation of each object from its neighbor is 100 $\mathrm{m} .$ Find the force exerted on the center object if (a) all charges are positive, (b) all charges are negative, and (c) the rightmost charge is negative and the other two are positive.

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Problem 16

Two objects with charges $q$ and 4$q$ are separated by 1.0 $\mathrm{m}$ . (a) Determine the sign, magnitude, and position of a third charged object that causes all three objects to remain in equilibrium. (b) Is the equilibrium stable or unstable? How do you know?

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Problem 17

Salt crystal Four ions $\left(\mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{Na}^{+}, \text { and } \mathrm{Cl}^{-}\right)$ in a row are each separated from their nearest neighbor by $3.0 \times 10^{-10} \mathrm{m} .$ The charge of a sodium ion is $+e$ and that of a chlorine ion is $-e$ . Determine the electric force exerted on the chlorine ion at the right end of the row due to the other three ions.

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Problem 18

$A+1.0-C$ charged object and $a+2.0-C$ charged object are separated by 100 m. Where should a $-1.0 \times 10^{-3}-\mathrm{C}$ charged object be located on a line between the positively charged objects so that the net electrical force exerted on the negatively charged object is zero?

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Problem 19

BIO Bee pollination Bees acquire an electric charge in flight from friction with the air, which causes pollen to cling to them. The pollen is then attracted to the stigma of the next flower (Figure P14.19). Suppose the bee’s body has a charge of $-10^{-9} \mathrm{C}$ and is about $3 \times 10^{-3} \mathrm{m}$ from the front edge of a spherical granule of pollen of diameter $5 \times 10^{-5} \mathrm{m} .$ Charged particles in the pollen become polarized with $+10^{-11} \mathrm{C}$ on the front edge and $-10^{-11} \mathrm{C}$ on the backside of the pollen $\left(3 \times 10^{-3}+5 \times 10^{-5}\right) \mathrm{m}$ from the bee. What useful physical quantities can you determine?

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Problem 20

A triangle with equal sides of length $1.0 \times 10^{3} \mathrm{m}$ has $-2.0-\mathrm{C}$ charged objects at each corner. Determine the electrical force (magnitude and direction) exerted on the object at the top corner due to the two objects at the base of the triangle.

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Problem 21

You have a small metal sphere hanging from a thread and another sphere attached to a plastic handle. You charge one of the spheres and then touch it with the second sphere. Draw a force-versus-time graph for the force that one sphere exerts on the other as you move the sphere on the handle slowly and steadily away from the hanging sphere. What information do you need in order to determine the magnitudes of the quantities on the graph?

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Problem 22

After the experiment in Problem 21, you touch the hanging sphere with your hand. Then you touch that hanging sphere with the sphere on the handle. Draw a force-versus-time graph for the force that one sphere exerts on the other as you move the sphere on the handle slowly and steadily away from the hanging sphere. How is this graph different from the graph in the previous problem?

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Problem 23

Coulomb's law is formulated for point-like charged objects. Imagine that you have two point-like charged objects $q_{1}$ and $q_{2}$ of unspecified sign separated by a distance $d$ and you also have two large spheres of radius $R$ with the same charges $q_{1}$ and $q_{2}$ The distance between the centers of the spheres is $d$. Compare the electric force that the point-like objects exert on each other to the force that the two spheres exert on each other. Consider all possibilities.

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Problem 24

(a) Determine the change in electric potential energy of a system of two charged objects when a $-1.5-$ - Charged object and a $-4.0-\mathrm{C}$ charged object move from an initial separation of 500 $\mathrm{km}$ to a final separation of 100 $\mathrm{km} .$ (b) What other quantities can you calculate using this information?

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Problem 25

You have a system of two positively charged objects separated by some arbitrary finite distance. (a) What is the sign of their potential energy? (Remember that charges that are infinitely far from each other have zero potential energy.) (b) What can you do to decrease this energy? (c) Draw an energy bar chart for this process of decreasing the energy.

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Problem 26

You have a system of two negatively charged objects separated by some arbitrary finite distance. (a) What is the sign of their potential energy? (Remember that charges that are infinitely far from each other have zero potential energy.) (b) What can you do to decrease this energy? (c) Draw an energy bar chart for this process of decreasing the energy.

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Problem 27

Repeat (a)—(c) of Problem 26 for a system with a negatively charged object and a positively charged object separated by some arbitrary finite distance.

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Problem 28

BIO Heart’s dipole charge At one instant of time, a person’s heart has a dipolar charge on it, with a positive charge on the bottom and a negative charge on the top of the heart. Will the electric potential energy of a sodium ion (charge $+e$) on the left side of the heart (as seen by another person) and at a level halfway between the heart’s charges increase, decrease, or remain the same if the sodium ion moves up? What will happen to the potential energy of a chlorine ion (charge $-e$) that starts at the same place and moves up? Justify each answer.

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Problem 29

The metal sphere on the top of a Van de Graaff generator has a relatively large positive charge. In which direction must a positively charged ion in the air move relative to the sphere in order for the electrical energy the ion-generator system to decrease? Justify your answer.

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Problem 30

EST An electron is 0.10 $\mathrm{cm}$ from an object with electric charge of $+3.0 \times 10^{-3} \mathrm{C}$ . (a) Determine the magnitude of the electrical force $F_{\mathrm{O} \text { on } e}$ that the object exerts on the electron. (b) The electron is pulled so that it moves to a distance of 0.11 $\mathrm{cm}$ from the charged object. Determine the magnitude of the electrical force $F_{\mathrm{O} \text { on } e}^{\prime}$ exerted by the charged object on the electron when at this distance. (c) Estimate the work done by the average force pulling the electron
$$\left(\frac{F_{\text { oone }}+F_{\mathrm{O} \text { on }} e^{\prime}}{2}\right) \Delta x$$
(d) Compare this number to the change in electric potential energy of the electron-charged-object system as the electron moves away from the object. Why should the numbers be approximately equal?

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Problem 31

(a) An object with charge $q_{4}=+3.0 \times 10^{-5} \mathrm{C}$ is moved to position C from infinity (Figure P14.31). $q_{1}=q_{2}=q_{3}=+10.0 \times 10^{-4} \mathrm{C} .$ Determine as many work-energy quantities as you can that characterize this process. Make sure you specify the system. (b) Repeat your calculations, but for $q_{1}=q_{3}=-0.01 \mathrm{C}$ and $q_{2}=+0.01 \mathrm{C}$

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Problem 32

An object with charge $+2.0 \times 10^{-5} \mathrm{C}$ is $\mathrm{moved}$ from position $\mathrm{C}$ to position $\mathrm{D}$ in Figure $\mathrm{P} 14.31$ $q_{1}=q_{3}=+10.0 \times 10^{-5} \mathrm{C}$ and $q_{2}=-20.0 \times 10^{-5} \mathrm{C}$ . All four charged objects are the system. What work-energy-related quantities can you determine for the process?

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Problem 33

A stationary block has a charge of $+6.0 \times 10^{-4} \mathrm{C}$ . A 0.80 -kg cart with a charge of $+4.0 \times 10^{-4} \mathrm{C}$ is initially at rest and separated by 4.0 $\mathrm{m}$ from the block. The cart is released and moves along a frictionless surface to a distance of 10.0 $\mathrm{m}$ from the block. Determine as many values of the physical quantities describing the motion of the cart as you can.

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Problem 34

An electric cannon, such as shown in Figure 14.15, consists of a 10 -kg metal ball with charge $+2.0 \times 10^{-4} \mathrm{C}$ compressed into a plastic barrel so that it is 0.10 $\mathrm{m}$ from an equally charged object at the closed end of the barrel. The barrel is oriented at $37^{\circ}$ with respect to the horizontal. When the ball is released, it shoots 3.0 m along the barrel from its starting position because of the repulsive force between the two charged objects. Determine three physical quantities that describe the motion of the ball after it leaves the barrel.

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Problem 35

Equation Jeopardy 1 The solution to a problem is represented by the following equation:
$$\begin{array}{l}{\left(9.0 \times 10^{9} \mathrm{N} \mathrm{m}^{2} / \mathrm{C}^{2}\right)(0.020 \mathrm{C})(0.050 \mathrm{C}) /(100 \mathrm{m})^{2}} \\ {+\left(9.0 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right)(0.010 \mathrm{C})(0.050 \mathrm{C}) /(50 \mathrm{m})^{2}=(10 \mathrm{kg}) a_{x}}\end{array}$$
Sketch a situation that the equation might represent and formulate a problem for which it is a solution (there are multiple possibilities).

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Problem 36

Equation Jeopardy 2 The solution to a problem is represented by the following equation:
$$\begin{array}{l}{\left(9.0 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right)(0.020 \mathrm{C})(0.050 \mathrm{C}) /(5 \mathrm{m})=} \\ {(1 / 2)(10 \mathrm{kg}) v_{x}^{2}+\left(9.0 \times 10^{9} \mathrm{N} \mathrm{m}^{2} / \mathrm{C}^{2}\right)(0.020 \mathrm{C})(0.050 \mathrm{C}) /(20 \mathrm{m})}\end{array}$$
Sketch a situation that the equation might represent and formulate a problem for which it is a solution (there are multiple possibilities).

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Problem 37

Equation Jeopardy 3 The solution to a problem is represented by the following equation:
$$\begin{array}{l}{\left(9.0 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right)(0.020 \mathrm{C})(0.050 \mathrm{C}) /(100 \mathrm{m})^{2}} \\ {-\left(9.0 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right)(0.010 \mathrm{C})(0.050 \mathrm{C}) /(50 \mathrm{m})^{2}=(10 \mathrm{kg}) a_{x}}\end{array}$$
Sketch a situation that the equation might represent and formulate a problem for which it is a solution (there are multiple possibilities).

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Problem 38

Equation Jeopardy 4 The solution to a problem is represented by the following equation:
$$\begin{array}{l}{\left(9.0 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right)(-0.020 \mathrm{C})(0.050 \mathrm{C}) /(20 \mathrm{m})} \\ {=(1 / 2)(10 \mathrm{kg}) v_{x}^{2}+\left(9.0 \times 10^{9} \mathrm{N} \mathrm{m}^{2} / \mathrm{C}^{2}\right)(-0.020 \mathrm{C})(0.050 \mathrm{C}) /(5 \mathrm{m})}\end{array}$$
Sketch a situation that the equation might represent and formulate a problem for which it is a solution (there are multiple possibilities).

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Problem 39

Evaluate the solution A student was given the following problem: A 0.20 -kg cannonball with a $+1.0 \times 10^{-4} \mathrm{C}$ charge starts at rest 0.40 $\mathrm{m}$ from a fixed $+2.0 \times 10^{-4} \mathrm{C}$ charge. When the cannonball is released, it flies vertically upward. How fast is it moving when 10 m above the fixed charge? The student gave this solution:
$$\left(9.0 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right)\left(+2.0 \times 10^{-4} \mathrm{C}\right)\left(+1.0 \times 10^{-4} \mathrm{C}\right) /(0.40 \mathrm{m})^{2}$
$=(1 / 2)(10 \mathrm{kg}) \mathrm{v}_{y}^{2}+(0.20 \mathrm{kg})\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right)(10 \mathrm{m})$$
or $v_{y}=15 \mathrm{m} / \mathrm{s}$ . Evaluate the solution to this problem and correct any errors you find.

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Problem 40

Construct separate force diagrams for each charged object shown in Figure P14.40. Use two-letter subscripts identifying each force.

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Problem 41

The six objects shown in Figure $P 14.41$ have equal-magnitude electric charge. Adjacent objects are separated by distance $a$ . Write an expression in terms of $q$ and $a$ for the force that the five objects on the right exert on the positive charge on the left.

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Problem 42

A small metal ball with positive charge $+q$ and mass $m$ is attached to a very light string, as shown in Figure $P 14.42$ . A larger metal ball with negative charge $-Q$ is securely held on a plastic rod to the ceiling. Write an expression for the magnitude of the force $T$ that the string exerts on the ball. Define any other quantities used in your expression.

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Problem 43

Four objects each with charge $+1.0 \times 10^{-4} \mathrm{C}$ are located at the corners of a square whose sides are 2.0 $\mathrm{m}$ long. Determine the values of two physical quantities describing the situation but not provided in the givens.

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Problem 44

Two 5.0 -g aluminum foil balls hang from $1.0-\mathrm{m}$ -long threads that are suspended from the same point at the top. The charge on each ball is $+5.0 \times 10^{-6} \mathrm{C}$ . Make a list of the physical quantities that you can determine using this information. Determine the values of two of those physical quantities.

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Problem 45

A 0.060 -kg ball with charge $+3.0 \times 10^{-6} \mathrm{C}$ hangs from a 0.50 -m-long string at an angle of $53^{\circ}$ below the horizontal. The string is attached at the top on the wall above a second Figure P14.45. (a) Determine the charge on the second object. (b) Make a list of other physical quantities that you can determine using the information in the problem. Describe how you can determine two of those quantities.

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Problem 46

A $0.40-\mathrm{kg}$ cart with charge $+4.0 \times 10^{-5} \mathrm{C}$ starts at rest on a horizontal frictionless surface 0.50 $\mathrm{m}$ a fixed object with charge $+2.0 \times 10^{-4} \mathrm{C}$ . When the cart is released, it moves away from the fixed object. (a) How fast is the cart moving when very far (infinity) from the fixed charge? (b) When 2.0 $\mathrm{m}$ from the fixed object?

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Problem 47

Electric cannon The cannonball shown in Figure P14.47 has charge $q=+8.0 \times 10^{-5} \mathrm{C}$ and mass 0.10 $\mathrm{kg}$ . The fixed object in the cannon has a charge of $Q=+9.0 \times 10^{-4} \mathrm{C}$ . The ball starts at $d=0.10 \mathrm{m}$ from the fixed charged object. (a) Determine the maximum height of the cannonball after its release. (b) Show how you can determine two other physical quantities relevant to the process.

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Problem 48

Electric shuttle train A shuttle train moves from one station to another. It is powered by equal-magnitude, oppositesign charges on top of each station (see Figure P14.48). If a $7000-\mathrm{N}$ friction force opposes the train's motion, how great must the dipole charge be to induce an initial acceleration of
1.0 $\mathrm{m} / \mathrm{s}^{2} ?$ The train's mass is $2.0 \times 10^{4} \mathrm{kg},$ and it has a positive charge of $+3.0 \times 10^{-2} \mathrm{C}$ on its roof.

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Problem 49

A small metal sphere with electric charge $+q$ is brought to a distance $d$ from a metal sphere with charge $Q$ sitting on the top of a nonconducting support. The mass of the small sphere is $m .$ What are the direction and magnitude of the electric force exerted by the large sphere on the small sphere? Make sure you analyze different possibilities.

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Problem 50

The dome of a Van de Graaff generator has a radius of 0.10 $\mathrm{m}$ . An electron in a hydrogen atom is located at a distance 0.20 $\mathrm{m}$ from the center of the dome. Determine the magnitude of the positive charge needed on the dome to exert a force on the electron that is equal to the force exerted by the atom’s nucleus on the electron. Is this a reasonable amount of charge on the dome? Explain.

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Problem 51

A Van de Graaff generator is placed in rarefied air at 0.4 times the density of air at atmospheric pressure. The average distance that free electrons move between collisions (mean free path) in that air is $(1 / 0.4) \times 10^{-6} \mathrm{m}$ . Determine the positive charge needed on the generator dome so that a free electron located 0.20 $\mathrm{m}$ from the center of the dome will gain at the end of the mean free path length the $2.0 \times 10^{-18} \mathrm{J}$ of kinetic energy needed to ionize a hydrogen atom during a collision.

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Problem 52

Two protons each of mass $1.67 \times 10^{-27} \mathrm{kg}$ and charge $+e$ are initially at rest and separated by $1.0 \times 10^{-14} \mathrm{m}$ (approximately the radius of a nucleus). When released, the protons fly apart. (a) Determine the change in their electric potential energy when they are $1.0 \times 10^{-10} \mathrm{m}$ apart (approximately the radius of an atom). (b) If the electric potential energy change is converted entirely into the kinetic energy of the protons (shared equally), what is the speed of one proton when $1.0 \times 10^{-10} \mathrm{m}$ from the other proton?

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Problem 53

Two protons, initially separated by a very large distance $\left(r_{1}\right.$ is infinity), move directly toward each other with the same initial speed $v_{\mathrm{i}}$ . (a) Determine their initial speeds if the distance of closest approach when their speeds are zero is $4.0 \times 10^{-14} \mathrm{m} .$ (b) Determine some other physical quantity relevant to the process.

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Problem 54

An alpha particle consists of two protons and two neutrons together in one nucleus with a mass of $6.64 \times 10^{-27} \mathrm{kg}$ and charge $+2 e .$ The alpha particle flies at $3.0 \times 10^{7} \mathrm{m} / \mathrm{s}$ from a large distance toward the nucleus of a stationary gold atom (charge $+79 e ) .(\text { a } \text { Make a list of physical quantities that you }$ can determine using this information and explain how you will calculate one of them. (b) Determine the distance of the alpha particle from the gold nucleus when it stops.

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Problem 55

Determine the speed that the proton shown in Figure P14.55 must be moving in order to get within $1.0 \times 10^{-15} \mathrm{m}$ of the helium- 3 nucleus that has two protons and one neutron. Assume that the helium nucleus is attached to a massive molecule and does not move.

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Problem 56

Suppose that Earth and the Moon initially have zero charge. Then 1000 kg of electrons are transferred from Earth to the Moon. Determine the radius of a stable moon orbit when both the electrical and gravitational forces of attraction are exerted on the Moon and it completes one rotation about Earth in 27.5 days.

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Problem 57

BIO Calcium ion synapse transfer Children have about $10^{16}$ synapses that can transfer signals between neurons in the brain and between neurons and muscle cells. Suppose that these synapses simultaneously transmit a signal, sending 1000 calcium ions $\left(\mathrm{Ca}^{2+}\right)$ across the membrane at each synaptic ending. Determine the total electric charge transfer in coulombs during that short time interval. By comparison, a lightning flash involves about 5 $\mathrm{C}$ of charge transfer. (Note: This is a fictional scenario. All human neurons do not simultaneously produce signals.)

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Problem 58

BIO DNA stretch The DNA molecule is spiral shaped, like a spring. A 10 -\mum-long DNA molecule has an effective spring constant of $10^{-8} \mathrm{N} / \mathrm{m}$ . Suppose a positive ion of charge $+e$ is attached on one end of the molecule and a positive ion of charge $+e$ is attached on the other end. What distance is the DNA stretched because of the electrical repulsion of these two ions?

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Problem 59

A small metal sphere of charge $-2.0 \times 10^{-4} \mathrm{C}$ sits on the roof of a $5.0-\mathrm{kg}$ cart, shown in Figure $\mathrm{P} 14.59 .$ The sphere moves toward another sphere of charge $+1.5 \times 10^{-3} \mathrm{C},$ located on the wall. As it moves, the cart pulls a cable that passes over a pulley and lifts an object with mass 10 $\mathrm{kg}$ . The cart starts at rest 5.0 $\mathrm{m}$ from the wall charge. (a) What is its speed when it is 2.0 $\mathrm{m}$ from the wall charge? (b) What assumptions did you make?

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Problem 60

Energy in the hydrogen atom (a) Write an expression for the total energy of the electron-proton system in a hydrogen atom. (b) Use circular motion dynamics and any other ideas you may need to show that the positive kinetic energy of the electron is half the magnitude of the negative electric potential energy of the proton-electron system. (c) Based on these results, do you need to do positive or negative work to remove the electron from the proton? Explain. Represent the removal process with a work-energy bar chart.

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Problem 61

You have been asked to analyze the feasibility of a transportation system that is operated using electric charges. A cart with a positively charged ball on the top is to move between two oppositely charged balls at opposite ends of a straight rail (see Figure P14.48). Suppose the charge on the stationary ball on the left is $+4.0 \times 10^{-4} \mathrm{C}$ and the charge on the right ball is $-4.0 \times 10^{-4} \mathrm{C} ;$ the charge on the cart is $+2.0 \times 10^{-4} \mathrm{C} .$ The cart's mass is 160 $\mathrm{kg}$ (including a passenger). A $60-\mathrm{N}$ effective friction force opposes the motion of the cart. Determine the cart’s acceleration when at the position shown in the figure. (Note that the acceleration changes as the cart’s position relative to the stationary charges changes.) Is this a feasible way to transport the cart along the rail?

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Problem 62

Electric nutcracker Suppose the electric nutcracker shown in Figure 14.16 has a stationary $+5.0 \times 10^{-5}-\mathrm{C}$ positive charge initially separated 0.40 $\mathrm{m}$ from a $-2.0 \times 10^{-5}-\mathrm{C}$ negatively charged $0.50-\mathrm{kg}$ block. When the block is released, it accelerates toward the positive charge and the nut. Determine its speed when it is 0.10 m from the negatively charged block—just before it hits the nut. Evaluate the feasibility of this nutcracker device.

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Problem 63

EST Shocking your friend (a) You shuffle across the rug and then place your finger near your friend’s nose, causing a small spark that transfers about $10^{-9} \mathrm{C}$ of charge from you to your friend. Determine the number of electrons transferred. (b) Estimate the fraction of electrons in your body that were transferred to the friend. Note that the electron mass is about 1/20,000 the mass of the atom—the nuclei are much more massive—and the mass of an average atom in the body is about $2 \times 10^{-26} \mathrm{kg}$. (Note: Don’t get hung up on minutia— this is a rough estimate.)

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Problem 64

You rub a balloon against your wool sweater and then place the balloon on the wall—it sticks. Why?
(a) The balloon and wall have opposite electric charges.
(b) The molecules on the wall redistribute their charge so that the charge opposite that on the balloon is nearest the balloon.
(c) Electric charge in Earth is pulled to the part of the wall nearest the balloon.
(d) a and c are correct.
(e) a, b, and c are correct.

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Problem 65

As you unload the clothes dryer, you find a sock clinging to a shirt. As you pull the sock off the shirt, you do positive work on the sock. What is the main form of energy increase?
(a) Gravitational $\quad$ (b) Elastic
(c) Electric potential $\quad$ (d) Thermal
(e) c and d

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Problem 66

Table salt, $\mathrm{Na}^{+} \mathrm{Cl}^{-},$ is made of ionized sodium and chlorine atoms. Which atom is most attractive for an excess electron?
(a) $\mathrm{Na} \quad$ (b) $\mathrm{Cl}$
(c) They are equally attractive.

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Problem 67

You add fabric softener to your next load of wash. Your clothes do not cling after they emerge from the dryer. What do the water softener molecules do?
(a) Carry away all the excess electrons.
(b) Cause sparks in the dryer that discharge the excess charge on the clothes.
(c) Form a protective coating that prevents the charge from joining the clothes.
(d) Make the cloth fluffy so the charge comes off naturally.
(e) Join the cloth molecules and make a conductive layer that prevents excess charge from accumulating on the clothes.

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Problem 68

You put many strips of aluminum foil in the dryer along with your clothes. Which answer below best represents the condition of the clothes after leaving the dryer?
(a) The clothes are uncharged because the excess charge is on the aluminum strips.
(b) The clothes are uncharged because they transfer excess charge to the strips, which transfer it to the metal dryer walls.
(c) The clothes are charged but the strips are not because they are conductive.
(d) The clothes are charged because the strips are not connected to anything.
(e) None of these answers is reasonable.

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Problem 69

You remove electric charge from your clean slacks by rubbing a metal clothes hanger down the inside of the slacks. Which answer below represents the best explanation for why this works?
(a) The charge travels from the cloth to the metal to your hand through your body to the ground.
(b) The metal hanger absorbs all the charge.
(c) The metal causes tiny sparks that send the charge into the air.
(d) The metal provides charge to the cloth that neutralizes its charge.
(e) None of these answers is reasonable.

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Problem 70

Which arrow in Figure P14.70 best represents the force exerted on a positive ion at position A?
(a) $\mathrm{I} \quad\quad$ (b) $\mathrm{II} \quad\quad$ (c) $\mathrm{III}$
(d) $\mathrm{IV} \quad\quad$ (e) $\mathrm{V} \quad\quad$ (f) $\mathrm{VI}$

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Problem 71

Which arrow in Figure P14.70 best represents the force exerted on a negative ion at position A?
(a) $\mathrm{I} \quad\quad$ (b) $\mathrm{II} \quad\quad$ (c) $\mathrm{III}$
(d) $\mathrm{IV} \quad\quad$ (e) $\mathrm{V} \quad\quad$ (f) $\mathrm{VI}$

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Problem 72

Which arrow in Figure P14.70 best represents the force exerted on a positive ion at position B?
(a) $\mathrm{I} \quad\quad$ (b) $\mathrm{II} \quad\quad$ (c) $\mathrm{III}$
(d) $\mathrm{IV} \quad\quad$ (e) $\mathrm{V} \quad\quad$ (f) $\mathrm{VI}$

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Problem 73

Which arrow in Figure P14.70 best represents the force exerted on a negative ion at position B?
(a) $\mathrm{I} \quad\quad$ (b) $\mathrm{II} \quad\quad$ (c) $\mathrm{III}$
(d) $\mathrm{IV} \quad\quad$ (e) $\mathrm{V} \quad\quad$ (f) $\mathrm{VI}$

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Problem 74

Based on the analysis in the first four questions, which charge detector in Figure P14.70 will be collecting negative electrons?
(a) $\mathrm{D}_{1} \quad\quad$ (b) $\mathrm{D}_{2}$
(c) Both $\mathrm{D}_{1}$ and $\mathrm{D}_{2} \quad\quad$ (d) Neither $\mathrm{D}_{1}$ nor $\mathrm{D}_{2}$

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Problem 75

The resistance to the motion of negative electrons through different types of materials is, in decreasing order, dry soil, moist soil, underground water, oil, and iron ore. How can this knowledge and the measurement of the charge reaching the detector per unit time help identify what type of material is under Earth’s surface?
(a) More electrons will reach the detector from iron than from dry soil.
(b) The electrons reaching the detector will carry water with them if water is under the surface.
(c) The electrons reaching the detector are affected very little by what’s under the surface.
(d) The detector will get more electric charge if the resistance to flow is less, and resistance is related to the type of material.
(e) a and d

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Problem 76

Electrode 1 has charge $q_{1}=+1.0 \times 10^{-5} \mathrm{C}$ and electrode 2 has charge $q_{2}=-1.0 \times 10^{-5} \mathrm{C}$ . The electrodes are separated by 800 $\mathrm{m}$ and a free electron is located 300 $\mathrm{m}$ under the ground halfway between electrode 1 and electrode $2 .$ What is the magnitude of the electric force that the electrodes exert on an electron at this position closest to?
(a) $1.1 \times 10^{-19} \mathrm{N} \quad$ (b) $1.4 \times 10^{-7} \mathrm{N} \quad(\mathrm{c}) 2.8 \times 10^{-7} \mathrm{N}$
(d) $9.2 \times 10^{-20} \mathrm{N} \quad$ (e) $2.8 \times 10^{-14} \mathrm{N}$

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