Understanding Physics

Karen Cummings, Priscilla W. Laws, Edward F. Redish

Chapter 22

Electric Charge - all with Video Answers

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Chapter Questions

Problem 1

A Large Charge What is the total charge in coulombs of $75.0 \mathrm{~kg}$ of electrons?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 2

How Many? How many megacoulombs of positive (or negative) charge are in $1.00 \mathrm{~mol}$ of neutral molecular-hydrogen gas $\left(\mathrm{H}_{2}\right)$ ?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 3

How Many Electrons How many electrons would have to be removed from a coin to leave it with a charge of $+1.0 \times 10^{-7} \mathrm{C}$ ?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 4

Glass of Water Calculate the number of coulombs of positive charge in $250 \mathrm{~cm}^{3}$ of (neutral) water (about a glassful).

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 5

Cosmic Ray Protons Earth's atmosphere is constantly bombarded by cosmic ray protons that originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth's surface would intercept protons at the average rate of 1500 protons per second. What would be the corresponding rate of charge flow intercepted by the total surface area of the planet?

Alfjad Alfjad

Numerade Educator

Problem 6

Fibrillation A charge flow of $0.300 \mathrm{C} / \mathrm{s}$ through your chest can send your heart into fibrillation, disrupting the flow of blood (and thus oxygen) to your brain. If that current persists for $2.00 \mathrm{~min}$, how many conduction electrons pass through your chest?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 7

Beta Decay In beta decay a massive fundamental particle changes to another massive particle, and either an electron of charge $-e$ or a positron of charge $+e$ (positive particle with the same amount of charge and mass as an electron) is emitted. (a) If a proton undergoes beta decay to become a neutron, which particle is emitted? (b) If a neutron undergoes beta decay to become a proton, which particle is emitted?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 8

Identify $\mathbf{X}$ Identify $\mathrm{X}$ in the following nuclear reactions (in the first, $n$ represents a neutron): (a) ${ }^{1} \mathrm{H}+{ }^{9} \mathrm{Be} \rightarrow \mathrm{X}+\mathrm{n} ;$ (b) ${ }^{12} \mathrm{C}+$
${ }^{1} \mathrm{H} \rightarrow \mathrm{X} ;$ (c) ${ }^{15} \mathrm{~N}+{ }^{1} \mathrm{H} \rightarrow{ }^{4} \mathrm{He}+\mathrm{X}$. Appendix $\mathrm{F}$ will help.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 9

What Distance At what distance between point charge $q_{A}=$ $26.0 \mu \mathrm{C}$ and point charge $q_{B}=-47.0 \mu \mathrm{C}$ will the electrostatic force between them have a magnitude of $5.70 \mathrm{~N}$ ?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 10

Force on Each A point charge of $+3.00 \times 10^{-6} \mathrm{C}$ is $12.0 \mathrm{~cm}$ from a second point charge of $-1.50 \times 10^{-6} \mathrm{C}$. Calculate the magnitude of the force on each charge.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 11

Two Equally Charged Two equally charged particles, held $3.2 \times 10^{-3} \mathrm{~m}$ apart, are released from rest. The initial acceleration of the first particle is observed to be $7.0 \mathrm{~m} / \mathrm{s}^{2}$ and that of the second to be $9.0 \mathrm{~m} / \mathrm{s}^{2}$. If the mass of the first particle is $6.3 \times 10^{-7} \mathrm{~kg}$, what are (a) the mass of the second particle and (b) the amount of charge on each particle?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 12

Isolated Conducting Spheres Identical isolated conducting spheres $A$ and $B$ have the same excess charges and are separated by a distance that is large compared with their diameters (Fig. $22-20 a)$. The electrostatic force acting on sphere $B$ due to sphere $A$ is $\vec{F}_{A \rightarrow B}$. Suppose now that a third identical sphere $C$, having an insulating handle and initially neutral, is touched first to sphere $A$ (Fig. $22-20 b$ ), then to sphere $B$ (Fig. $22-20 c$ ), and finally removed (Fig. $22-20 d$ ). In terms of the force magnitude $F_{A \rightarrow B}$, what is the magnitude of the electrostatic force $\vec{F}_{A \rightarrow B}^{\prime}$ that now acts on sphere $B ?$

Kian Maleki

Numerade Educator

Problem 13

The Square , what are the (a) horizontal and (b) vertical components of the net electrostatic force on the charged particle in the lower left corner of the square if $q=1.0 \times 10^{-7} \mathrm{C}$ and $a=5.0 \mathrm{~cm}$ ?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 14

Where Along the Line Point charges $q_{A}$ and $q_{B}$ lie on the $x$ axis at points $x=-d$ and $x=+d$, respectively.
(a) How must $q_{A}$ and $q_{B}$ be related for the net electrostatic force on point charge $+Q$, placed at $x=+d / 2$, to be zero? (b) Repeat (a) but with point charge $+Q$ now placed at $x=+3 d / 2$.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 15

Two Identical Spheres Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of $0.108 \mathrm{~N}$ when separated by $50.0 \mathrm{~cm}$, center to center. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of $0.0360 \mathrm{~N}$. What were the initial charges on the spheres?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 16

Three Charges three charged particles lie on a straight line and are separated by distances $d$. Charges $q_{A}$ and $q_{B}$ are held fixed. Charge $q_{C}$ is free to move but happens to be in equilibrium (no net electrostatic force acts on it). Find $q_{A}$ in terms of $q_{B}$.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 17

Two Free Particles Two free particles (that is, free to move) with charges $+q$ and $+4 q$ are a distance $L$ apart. A third charge is placed so that the entire system is in equilibrium. (a) Find the location, amount and sign of the third charge. (b) Show that the equilibrium is unstable.

Urvashi Arora

Numerade Educator

Problem 18

Two Fixed Particles Two fixed particles, of charges $q_{A}=+1.0 \mu \mathrm{C}$ and $q_{B}=-3.0 \mu \mathrm{C}$, are $10 \mathrm{~cm}$ apart. How far from each should a third charge be located so that no net electrostatic force acts on it?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 19

A Certain Charge $Q$ A certain charge $Q$ is divided into two parts $q$ and $Q-q$, which are then separated by a certain distance. What must $q$ be in terms of $Q$ to maximize the electrostatic repulsion between the two charges?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 20

Charges and Coordinates The charges and coordinates of two charged particles held fixed in the $x y$ plane are $q_{A}=+3.0 \mu \mathrm{C}, x_{A}=$ $3.5 \mathrm{~cm}, y_{A}=0.50 \mathrm{~cm}$, and $q_{B}=-4.0 \mu \mathrm{C}, x_{B}=-2.0 \mathrm{~cm}, y_{B}=$
$1.5 \mathrm{~cm} .$ (a) Find the magnitude and direction of the electrostatic force on $q_{B} .$ (b) Where could you locate a third charge $q_{C}=$ $+4.0 \mu \mathrm{C}$ such that the net electrostatic force on $q_{B}$ is zero?

Neelesh Sharma

Numerade Educator

Problem 21

Identical Ions The magnitude of the electrostatic force between two identical ions that are separated by a distance of $5.0 \times$ $10^{-10} \mathrm{~m}$ is $3.7 \times 10^{-9} \mathrm{~N}$. (a) What is the charge of each ion? (b) How many electrons are "missing" from each ion (thus giving the ion its charge imbalance)?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 22

Salt Crystal What is the magnitude of the electrostatic force between a singly charged sodium ion $\left(\mathrm{Na}^{+}\right.$, of charge $\left.+e\right)$ and an adjacent singly charged chlorine ion $\left(\mathrm{Cl}^{-}\right.$, of charge $\left.-e\right)$ in a salt crystal if their separation is $2.82 \times 10^{-10} \mathrm{~m}$ ?

Salamat Ali

Numerade Educator

Problem 23

Cesium Chloride In the basic $\mathrm{CsCl}$ (cesium chloride) crystal structure, $\mathrm{Cs}^{+}$ ions form the corners of a cube and a $\mathrm{Cl}^{-}$ ion is at the cube's center . The edge length of the cube is $0.40 \mathrm{~nm}$. The $\mathrm{Cs}^{+}$ ions are each deficient by one electron (and thus each has a charge of $+e$ ), and the $\mathrm{Cl}^{-}$ ion has one excess electron (and thus has a charge of
$-e$ ). (a) What is the magnitude of the net electrostatic force exerted on the $\mathrm{Cl}^{-}$ ion by the eight $\mathrm{Cs}^{+}$ ions at the corners of the cube? (b) If one of the $\mathrm{Cs}^{+}$ ions is missing, the crystal is said to have a defect; what is the magnitude of the net electrostatic force exerted on the $\mathrm{Cl}^{-}$ ion by the seven remaining $\mathrm{Cs}^{+}$ ions?

Christina Vaughan

Christina Vaughan

Numerade Educator

Problem 24

Water Drops Two tiny, spherical water drops, with identical charges of $-1.00 \times 10^{-16} \mathrm{C}$, have a center-to-center separation of $1.00 \mathrm{~cm} .$ (a) What is the magnitude of the electrostatic force acting between them? (b) How many excess electrons are on each drop, giving it its charge imbalance?

Salamat Ali

Numerade Educator

Problem 25

25. Beads shows four tiny charged beads that can be slid or fixed in place on wires that stretch along $x$ and $y$ axes. A central bead at the crossing point of the wires (the origin) has a charge of $+e$. The other beads each have a charge of $-e$. Initially beads $A, B$, and $C$ are at distance $d=10.0 \mathrm{~cm}$ from the central bead, and bead $D$ is at a distance of $d / 2 .$
(a) How far from the central bead must you position bead $A$ so that the direction of the net electrostatic force $\vec{F}^{\text {net }}$ on the central bead rotates counterclockwise by $30^{\circ} ?$ (b) With bead $A$ still in its new position, where must you slide bead $C$ so that the direction of $\vec{F}$ net rotates back by $30^{\circ}$ ?

Raj Bala

Numerade Educator

Problem 26

Two Copper Coins We know that the negative charge on the electron and the positive charge on the proton are equal in amount. Suppose, however, that these amounts differ from each other by $0.00010 \%$. With what force would two copper coins, placed $1.0 \mathrm{~m}$ apart, repel each other? Assume that each coin contains $3 \times 10^{22}$ copper atoms. (Hint: A neutral copper atom contains 29 protons and 29 electrons.) What do you conclude?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 27

Particles $A$ and $ a$ shows charged particles $A$ and $B$ that are fixed in place on an $x$ axis. Particle $A$ has an amount of charge of $\left|q_{A}\right|=8.00 e$. Particle $C$, with a charge of $q_{C}=+8.00 e$, is initially on the $x$ axis near particle $B$. Then particle $C$ is gradually moved in the positive direction of the $x$ axis. As a result, the magnitude of the net electrostatic force $\vec{F}_{B}^{\text {net }}$ on particle $B$ due to particles $A$ and $C$ changes. Figure $22-25 b$ gives the $x$ -component of that net force as a function of the position $x$ of particle $C$. The plot has an asymptote of $\vec{F}_{B}^{\text {net }}=1.5 \times 10^{-25} \mathrm{~N}$ as $x \rightarrow \infty .$ As a multiple of $e$, what is the charge $q_{B}$ of particle $B$ ?

Sheh Lit Chang

University of Washington

Problem 28

Above the Floor , a particle of charge $+4 e$ is above a floor by distance $d_{1}=2.0 \mathrm{~mm}$ and a particle of charge $+6 e$ is on the floor at horizontal distance $d_{2}=$ $6.0 \mathrm{~mm}$ from the first particle. What is the $x$ -component of the electrostatic force on the second
narticle due to the first particle?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 29

Fixed on the $x$ Axis a, particle $A$ (with charge $q_{A}$ ) and particle $B$ (with charge $q_{B}$ ) are fixed in place on an $x$ axis, $8.00 \mathrm{~cm}$ apart. Particle $C$ with a charge $q_{C}=+5 e$ is to be placed on the line between particles $A$ and $B$, so that they produce a net electrostatic force $\vec{F}_{C}^{\text {net }}$ on it. Figure $22-27 b$ gives the $x$ component of that force versus the coordinate $x$ at which particle $C$ is placed. What are (a) the sign of charge $q_{A}$ and (b) the ratio $q_{B} / q_{A} ?$

Neelesh Sharma

Numerade Educator

Problem 30

Four Charged Particles shows four charged particles that are fixed along an axis, separated by distance $d=2.00 \mathrm{~cm} .$ The charges are indicated. Find the magnitude and direction of the net electrostatic force on (a) the particle with charge $+2 e$ and (b) the particle with charge $-e$, due to the other particles.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 31

Split in Two A charge of $6.0 \mu \mathrm{C}$ is to be split into two parts that are then separated by $3.0 \mathrm{~mm}$. What is the maximum possible magnitude of the electrostatic force between those two parts?

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 32

Two on the Axis shows two particles, each of charge $+2 e$, that are fixed on a $y$ axis, each at a distance $d=17 \mathrm{~cm}$ from the $x$ axis. A third particle, of charge $+4 e$, is moved slowly along the $x$ axis, from $x=0$ to $x=+5.0 \mathrm{~m}$. At what values of $x$ will the magnitude of the electrostatic force on the third particle from the other two particles be (a) minimum and (b) maximum? What are (c) the minimum magnitude and (d) the maximum magnitude?

Neelesh Sharma

Numerade Educator

Problem 33

How Far how far from the charged particle on the right and in what direction is there a point where a third charged particle will be in balance?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 34

Three Positive Charges In Fig $22-31 a$, three positively charged particles are fixed on an $x$ axis. Particles $B$ and $C$ are so close to each other that they can be considered to be at the same dis-
tance from particle $A .$ The net force on particle $A$ due to parti- cles $B$ and $C$ is $2.014 \times 10^{-23} \mathrm{~N}$ in the negative direction of the $x$ axis. In Fig. $22-31 b$, particle $B$ has been moved to the opposite side of $A$ but is still at the same distance from it. The net force on $A$ is now $2.877 \times 10^{-24} \mathrm{~N}$ in the negative direction of the $x$ axis. What is the ratio of the charge of particle $C$ to that of particle $B$ ?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 35

Fixed at the Origin A particle of charge $Q$ is fixed at the origin of an $x y$ coordinate system. At $t=0$ a particle $(m=0.800 \mathrm{~g}, q=$ $4.00 \mu \mathrm{C})$ is located on the $x$ axis at $x=20.0 \mathrm{~cm}$, moving with a speed of $50.0 \mathrm{~m} / \mathrm{s}$ in the positive $y$ direction. For what value of $Q$ will the moving particle execute circular motion? (Assume that the gravitational force on the particle may be neglected.)

Sheh Lit Chang

University of Washington

Problem 36

Seven Charges shows an arrangement of seven positively charged particles that are separated from the central particle by distances of either $d(=1.0 \mathrm{~cm})$ or $2 d$, as drawn. The charges are indicated. What are the magnitude and direction of the net electrostatic force on the central particle due to the other six particles?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 37

What is $\boldsymbol{q}$ , what is $q$ in terms of $Q$ if the net electrostatic force on the charged particle at the upper left corner of the square array is to be zero?

Saman Zulfiqar

Numerade Educator

Problem 38

Charges shows an arrangement of three charged particles separated by distance $d$. Particles $A$ and $C$ are fixed on the $x$ axis, but particle $B$ \text { can be moved along a circle centered on particle } A . \text { During the }

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 39

Two Electrons-Two Ions shows two electrons $($ charge $-e)$ on an $x$ axis and two negative ions of identical charges $-q$ and at identical angles $\theta$. The central electron is free to move; the other particles are fixed in place at horizontal distances $R$ and are intended to hold the free electron in place. (a) Plot the required amount of $q$ versus angle $\theta$ if this is to happen. (b) From the plot, determine which values of $\theta$ will be needed for physically possible values of $q \leq 5 e$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 40

Diamond shows an arrangement of four charged particles, with angle $\theta=30^{\circ}$ and distance $d=2.00 \mathrm{~cm}$. The two negatively charged particles on the $y$ axis are electrons that are fixed in place. The particle at the right has a charge $q_{B}=+5 e$. (a) Find distance $D$ such that the net force on $q_{A}$, the particle at the left, due to the three other particles, is zero. (b) If the two electrons were moved closer to the $x$ axis, would the required value of $D$ be greater than, less than, or the same as in part (a)?

Mukesh Devi

Numerade Educator

Problem 41

Each Positive Two particles, each of positive charge $q$, are fixed in place on an $x$ axis, one at $x=0$ and the other at $x=+d$. A particle of positive charge $Q$ is to be placed along that axis at locations given by $x=\alpha d$. (a) Write expressions, in terms of $\alpha$, that give the net electrostatic force $\vec{F}^{\text {elec }}$ acting on the third particle when it is in the three regions $x<0,0<x<d$, and $d<x$. The expressions should give a positive result when $\vec{F}^{\text {elec }}$ acts in the positive direction of the $x$ axis and a negative result when $\vec{F}^{\text {elec }}$ acts in the negative direction. (b) Graph the magnitude of $\vec{F}^{\text {elec }}$ versus $\alpha$ for the range $-2<\alpha<3$.

Neelesh Sharma

Numerade Educator

Problem 42

Particles $A$ and $B$, particles $A$ and $B$ are fixed in place on an $x$ axis, at a separation of $L=8.00$ $\mathrm{cm} .$ Their charges are $q_{A}=+e$ and $q_{B}=-27 e$. Particle $C$ with charge $q_{C}$ $=+4 e$ is to be placed on the line between particles $A$ and $B$, so that they produce a net electrostatic force $\vec{F}_{C}^{\mathrm{net}}$ on it. (a) At what coordinate should particle $C$ be placed to minimize the magnitude of that force? (b) What is that minimum magnitude?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 43

Earth and Moon (a) What equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction? Do you need to know the lunar distance to solve this problem? Why or why not? (b) How many kilograms of hydrogen would be needed to provide the positive charge calculated in (a)?

Alfjad Alfjad

Numerade Educator

Problem 44

A Particle with Charge $Q$ A particle with charge $Q$ is fixed at each of two opposite corners of a square, and a particle with charge $q$ is placed at each of the other two corners. (a) If the net electrostatic force on each particle with charge $Q$ is zero, what is $Q$ in terms of $q$ ?
(b) Is there any value of $q$ that makes the net electrostatic force on each of the four particles zero? Explain.

Brandy Heflin

Numerade Educator

Problem 45

Hang from Thread , two tiny conducting balls of identical mass $m$ and identical charge $q$ hang from nonconducting threads of length $L$. Assume that $\theta$ is so small that $\tan \theta$ can be replaced by its approximate equal, $\sin \theta$. (a) Show that, for equilibrium,
$$
x=\left(\frac{2 k q^{2} L}{m g}\right)^{1 / 3}
$$

where $x$ is the separation between the balls. (b) If $L=120 \mathrm{~cm}, m=10 \mathrm{~g}$, and $x=5.0 \mathrm{~cm}$, what is $q$ ?

Alfjad Alfjad

Numerade Educator

Problem 46

What Happens? Explain what happens to the balls of Problem $45 \mathrm{~b}$ if one of them is discharged (loses its charge $q$ to, say, the ground), and find the new equilibrium separation $x$, using the given values of $L$ and $m$ and the computed value of $q$.

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 47

Pivot shows a long, nonconducting, massless rod of length $L$, pivoted at its center and balanced with a block of weight $W$ at a distance $x$ from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges $q$ and $2 q$, respectively. At distance $h$ directly beneath each of these spheres is a fixed sphere with positive charge $Q \cdot(\mathrm{a})$ Find the distance $x$ when the rod is horizontal and balanced. (b) What value should $h$ have so that the rod exerts no vertical force on the bearing when the rod is horizontal and balanced?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 48

An Electron in a Vacuum An electron is in a vacuum near the surface of Earth. Where should a second electron be placed so that the electrostatic force it exerts on the first electron balances the gravitational force on the first electron due to Earth?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 49

Opposites Attract It is said that unlike charges attract. You can observe that after the sticky side of a piece of scotch tape is pulled quickly off the smooth side of another piece of tape the tapes attract each other. Perhaps each tape has a like charge and the rule has been stated backwards. Why do you believe the charges on the two tapes are different? Note: It is not acceptable to answer "because unlike charges attract and I observed the attraction."

Kayla Gephart

Numerade Educator

Problem 50

Hanging Ball of Foil (a) Explain how a metal conductor such as a hanging ball of aluminum foil can be attracted to a charged insulator even though the ball of foil has no net charge so that it is electrically neutral. (b) Can two metal balls with no net charge attract each other? Explain. (c) Can the process of induction cause a neutral conductor to be repelled from a charged insulator? Explain.

Ajay Singhal

Numerade Educator

Problem 51

Four Balls Consider four lightweight metal-coated balls suspended on nonconducting threads pended on nonconducting threads as shown. Suppose ball $A$ is stroked with a plastic rod that has been rubbed with fur. When you observe interactions between pairs of balls one at a time you find that:
1. $B, C$, and $D$ are each at$\operatorname{tracted}$ to $A$. 2. $B$ and $C$ seem to have no effect on each other.
3. $B$ and $C$ are both attracted to $D$.
Use the concept of electric induction to figure out what type of net charge is on each of the balls: Negative charge? Positive charge? No charge at all? Explain your reasoning. [Based on question 5.9, Arons, Homework and Test Questions for Introductory Physics Teaching (Wiley, New York, 1994).]

Vishal Gupta

Numerade Educator

Problem 52

Plastic Rubbed with Fur Suppose you rub a plastic rod with fur that gives it a negative charge. You then bring it close to an uncharged metal coated Styrofoam ball that is suspended from a string. (a) When the rod gets close to the ball, the ball starts moving toward it. Use the concept of induction to explain what happens to the atomic electrons and protons in the ball. Include a sketch of the ball and the rod that shows the excess negative charges on the rod. Also show how the charges are distributed on the ball just before it touches the rod. (b) After the ball touches the rod, it moves away from the rod quickly. Explain why.

Kayla Gephart

Numerade Educator

Problem 53

Small Charged Sphere A small, charged sphere of mass $5.0 \mathrm{~g}$ is released $32 \mathrm{~cm}$ away from a fixed point charge of $+5.0 \times 10^{-9} \mathrm{C}$. Immediately after release, the sphere is observed to accelerate toward the charge at $2.5 \mathrm{~m} / \mathrm{s}^{2}$. What is the charge on the sphere? Hint:
The force of gravity can be ignored in your calculation.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 54

Lightning Bolt In a lightning bolt electrons travel from a thundercloud to the ground. If there are $1.0 \times 10^{20}$ electrons in a lightning bolt, how many coulombs of charge are dumped onto the ground?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 55

Estimating Charge Two hard rubber spheres of mass $\sim 10 \mathrm{~g}$ are rubbed vigorously with fur on a dry day. They are then suspended from a rod with two insulating strings. They are observed to hang at equilibrium as shown in Fig. 22-41, which is drawn approximately to scale. Estimate the amount of charge that is found on each sphere.

Linda Winkler

Numerade Educator

Problem 56

Various Arrangements Various arrangements of two fixed charges are shown along with a point labeled $P$. The amount of each charge is the same but the charges are positive or negative as indicated. All the distances between charges and between point $P$ and the charge nearest to it are the same. Rank these arrangements in order of the strength of the force (that is, its magnitude) on a tiny positive test charge located at point $P$ in each case. Go from greatest to least and indicate when force magnitudes are the same using an equal to sign. For example, if the force magnitudes at $(d)$ and $(c)$ were the same as each other and were the greatest and $(b)$ was less than $(d)$ and $(c)$ with $(a)$ being the least, your answer would be $(d)=(b)>(c)>(a)$. Include a diagram and sketch the individual force vectors in each case. [Based on Ranking Task 128 O'Kuma, et. al., Ranking Task Exercises in Physics (Prentice Hall, Upper Saddle River NJ,2000).]

Vishal Gupta

Numerade Educator