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College Physics

Raymond A. Serway, Jerry S. Faughn, Chris Vuille

Chapter 15

Electric Forces and Electric Fields - all with Video Answers

Educators

Chapter Questions

03:16

Problem 1

A $7.5-n C$ charge is located $1.8 \mathrm{~m}$ from a $4.2-n \mathrm{C}$ charge. Find the magnitude of the electrostatic force that one charge exerts on the other. Is the force attractive or repulsive?

Vysakh M
Vysakh M
Numerade Educator
02:52

Problem 2

A charged particle $A$ exerts a force of $2.62 \mu \mathrm{N}$ to the right on charged particle $B$ when the particles are $13.7 \mathrm{~mm}$ apart. Particle $B$ moves straight away from $A$ to make the distance between them $17.7 \mathrm{~mm}$. What vector force does
particle $B$ then exert on $A$ ?

Ashly Sunny
Ashly Sunny
Numerade Educator
06:42

Problem 3

Two metal balls $A$ and $B$ of negligible radius are floating at rest on Space Station Freedom between two metal bulkheads, connected by a taut nonconducting thread of lengih $2.00 \mathrm{~m}$. Ball $A$ carries charge $q$, and ball $B$ carries charge $2 q$. Each ball is $1.00 \mathrm{~m}$ away from a bulkhead. (a) If the tension in the string is $2.50 \mathrm{~N}$, what is the magnitude of $q^{?}(\mathrm{~b})$ What happens to the system as time passes? Explain.

Linda Winkler
Linda Winkler
Numerade Educator
02:43

Problem 4

a) Find the electrostatic force between a $\mathrm{Na}^{+}$ ion and a $\mathrm{Cl}^{-}$ ion separated by $0.50 \mathrm{~nm} .$ (b) Would the answen change if the sodium ion were replaced by $\mathrm{Li}^{+}$ and the Chloride ion by Br $^{-}$ Explain.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:48

Problem 5

The nucleus of ${ }^{8} \mathrm{Be}$, which consists of 4 protons and 4 neutrons, is very unstable and spontaneously breaks into two alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons). (a) What is the force between the two alpha particles when they are $5.00 \times 10^{-15} \mathrm{~m}$ apart, and (b) what is the initial magnitude of the acceleration of the alpha particles due to this force? Note that the mass of an alpha particle is $4.0026 \mathrm{u}$.

Vysakh M
Vysakh M
Numerade Educator
05:12

Problem 6

A molecule of DNA (deoxyribonucleic acid) is $2.17 \mu \mathrm{m}$ long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses $1.00 \%$ upon becoming charged. Determine the effective spring constant of the molecule.

Meghan Miholics
Meghan Miholics
Numerade Educator
04:26

Problem 7

Suppose $1.00 \mathrm{~g}$ of hydrogen is separated into electrons and protons. Suppose also the protons are placed at the Earth's North Pole and the electrons are placed at the South Pole. What is the resulting compressional force on the Earth?

Mihajlo Grcic
Mihajlo Grcic
Numerade Educator
07:48

Problem 8

Four point charges are at the corners of a square of side $a$ as shown in Figure $\mathrm{P} 15.8$. Determine the magnitude and direction of the resultant electric force on $q$, with $k_{e}, q$, and $a$ left in symbolic form.

Vysakh M
Vysakh M
Numerade Educator
06:17

Problem 9

Two small identical conducting spheres are placed with their centers $0.30 \mathrm{~m}$ apart. One is given a charge of $12 \times 10^{-9} \mathrm{C}$, the other a charge of $-18 \times 10^{-9}$ C. (a) Find the electrostatic force exerted on one sphere by the other.
(b) The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached.

Vysakh M
Vysakh M
Numerade Educator
07:24

Problem 10

Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in Figure $\mathrm{P} 15.10 .$

Deepak Kohli
Deepak Kohli
Numerade Educator
04:43

Problem 11

Three charges are arranged as shown in Figure $\mathrm{P} 15.11$. Find the magnitude and direction of the electrostatic force on the charge at the origin.

Salamat Ali
Salamat Ali
Numerade Educator
09:55

Problem 12

Three charges are arranged as shown in Figure P15.12. Find the magnitude and direction of the electrostatic force on the $6.00-n C$ charge.

Linda Winkler
Linda Winkler
Numerade Educator
08:22

Problem 13

Three point charges are located at the corners of an equilateral triangle as in Figure $\mathrm{P} 15.13 .$ Find the magnitude and direction of the net electric force on the $2.00 \mu \mathrm{C}$ charge.

Vysakh M
Vysakh M
Numerade Educator
07:15

Problem 14

A charge of $-3.00 \mathrm{nC}$ and a charge of $-5.80 \mathrm{n} \mathrm{C}$ are separated by a distance of $50.0 \mathrm{~cm}$. Find the position at which a third charge of $+7.50 \mathrm{n} \mathrm{C}$ can be placed so that the net electrostatic force on it is zero.

Linda Winkler
Linda Winkler
Numerade Educator
07:48

Problem 15

Two small metallic spheres, each of mass $0.20 \mathrm{~g}$, are suspended as pendulums by light strings from a common point as shown in Figure P15.15. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of $5.0^{\circ}$ with the vertical. If each string is $30.0 \mathrm{~cm}$ long, what is the magnitude of the charge on each sphere?

Linda Winkler
Linda Winkler
Numerade Educator
10:56

Problem 16

Particle $A$ of charge $3.00 \times 10^{-4} \mathrm{C}$ is at the origin, particle $B$ of charge $-6.00 \times 10^{-4} \mathrm{C}$ is at $(4.00 \mathrm{~m}, 0)$ and particle $C$ of charge $1.00 \times 10^{-4} \mathrm{C}$ is at $(0,3.00 \mathrm{~m})$.
(a) What is the $x$ -component of the electric force exerted by $A$ on $C ?$ (b) What is the $y$ -component of the force exerted by $A$ on $C ?$ (c) Find the magnitude of the force exerted by $B$ on $C .$ (d) Calculate the $x$ -component of the force exerted by $B$ on C. (e) Calculate the $y$ -component of the force exerted by $B$ on $C$. (f) Sum the two $x$ -components to obtain the resultant $x$ -component of the electric force acting on $C .$ (g) Repeat part (f) for the $y$ -component.
(h) Find the magnitude and direction of the resultant electric force acting on $C$.

Linda Winkler
Linda Winkler
Numerade Educator
03:51

Problem 17

A small object of mass $3.80 \mathrm{~g}$ and charge $-18 \mu \mathrm{C}$ "floats" in a uniform electric field. What is the magnitude and direction of the electric field?

Vysakh M
Vysakh M
Numerade Educator
06:23

Problem 18

(a) Determine the electric field strength at a point $1.00 \mathrm{~cm}$ to the left of the middle charge shown in Figure P15.10. (b) If a charge of $-2.00 \mu \mathrm{C}$ is placed at this point, what are the magnitude and direction of the force on it?

Linda Winkler
Linda Winkler
Numerade Educator
05:20

Problem 19

An airplane is flying through a thundercloud at a height of $2000 \mathrm{~m}$. (Flying at this height is very dangerous because of updrafts, turbulence, and the possibility of electric discharge.) If there are charge concentrations of $+40.0 \mathrm{C}$ at a height of $3000 \mathrm{~m}$ within the cloud and $-40.0 \mathrm{C}$ at a height of $1000 \mathrm{~m}$, what is the elecuric field $\overrightarrow{\mathbf{E}}$ at the aircraft?

Linda Winkler
Linda Winkler
Numerade Educator
04:03

Problem 20

An electron is accelerated by a constant clectric ficld of magnitude $300 \mathrm{~N} / \mathrm{C}$. (a) Find the acceleration of the electron. (b) Use the equations of motion with constant acceleration to find the electron's speed after $1.00 \times 10^{-8} \mathrm{~s}$, assuming it starts from rest.

Vysakh M
Vysakh M
Numerade Educator
07:05

Problem 21

A charge of $-5.0 \mathrm{nC}$ is at the origin and a second charge of $7.0 \mathrm{nC}$ is at $x=4.00 \mathrm{~m}$. Find the magnitude and direction of the electric field halfway in between the two charges.

Vysakh M
Vysakh M
Numerade Educator
03:09

Problem 22

Each of the protons in a particle beam has a kinetic energy of $3.25 \times 10^{-15} \mathrm{~J} .$ What are the magnitude and direction of the electric field that will stop these protons in a distance of $1.25 \mathrm{~m}^{3}$

Vysakh M
Vysakh M
Numerade Educator
07:03

Problem 23

A proton accelerates from rest in a uniform electric field of $640 \mathrm{~N} / \mathrm{C}$. At some later time, its speed is $1.20 \times 10^{6} \mathrm{~m} / \mathrm{s}$.
(a) Find 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 that interval? (d) What is its kinetic energy at the later time?

Linda Winkler
Linda Winkler
Numerade Educator
08:34

Problem 24

(a) Find the magnitude and direction of the electric field at the position of the $2.00 \mu \mathrm{C}$ charge in Figure P15.13. (b) How would the electric field at that point be affected if the charge there were doubled? Would the magnitude of the electric force be affected?

Linda Winkler
Linda Winkler
Numerade Educator
06:44

Problem 25

An alpha particle (a helium nucleus) is traveling along the positive $x$ -axis at $1250 \mathrm{~m} / \mathrm{s}$ when it enters a cylindrical tube of radius $0.500 \mathrm{~m}$ centered on the $x$ -axis. Inside the tube is a uniform electric field of $4.50 \times 10^{-4} \mathrm{~N} / \mathrm{C}$ pointing in the negative $y$ -direction. How far does the particle travel before hitting the tube wall? Neglect any gravitational forces. Note: $m_{\alpha}=6.64 \times 10^{-27} \mathrm{~kg} ; q_{a}=2 e$

Linda Winkler
Linda Winkler
Numerade Educator
07:14

Problem 26

Two point charges lie along the $y$ -axis. A charge of $q_{1}=$ $-9.0 \mu \mathrm{C}$ is at $y=6.0 \mathrm{~m}$, and a charge of $q_{2}=-8.0 \mu \mathrm{C}$ is at $y=-4.0 \mathrm{~m}$. Locate the point (other than infinity) at which the total electric field is zero.

Linda Winkler
Linda Winkler
Numerade Educator
04:01

Problem 27

$\mathrm{P} 15.27$ determine the point (other than infinity) at which the total electric field is zero.

Vysakh M
Vysakh M
Numerade Educator
04:20

Problem 29

Three identical charges $(q=-5.0 \mu \mathrm{C})$ lie along a circle of radius $2.0 \mathrm{~m}$ at angles of $30^{\circ}, 150^{\circ}$, and $270^{\circ}$, as shown in Figure $P 15.29 .$ What is the resultant electric field at the
center of the circle?

Vysakh M
Vysakh M
Numerade Educator
02:02

Problem 30

Shows the electric field lines for two point charges separated by a small distance. (a) Determine the ratio $q_{1} / q_{2} .$ (b) What are the signs of $q_{1}$ and $q_{2}$ ?

Vysakh M
Vysakh M
Numerade Educator
02:36

Problem 31

(a) Sketch the clectric field lines around an isolated point charge $q>0 .$ (b) Sketch the electric field pattern around an isolated negative point charge of magnitude $-2 q$.

Vysakh M
Vysakh M
Numerade Educator
13:12

Problem 32

(a) Sketch the electric field pattern around two positive point charges of magnitude $1 \mu \mathrm{C}$ placed close together.
(b) Sketch the electric field pattern around two negative point charges of $-2 \mu \mathrm{C}$, placed close together. (c) Sketch the pattern around two point charges of $+1 \mu \mathrm{C}$ and $-2 \mu \mathrm{C}$, placed close together.

Narayan Hari
Narayan Hari
Numerade Educator
01:41

Problem 33

Two point charges are a small distance apart. (a) Sketch the electric field lines for the two if one has a charge four times that of the other and both charges are positive. (b) Repeat for the case in which both charges are negative.

Salamat Ali
Salamat Ali
Numerade Educator
06:05

Problem 34

(a) Sketch the electric field pattern set up by a positively charged hollow sphere. Include regions inside and regions outside the sphere. (b) A conducting cube is given a positive charge. Sketch the electric field pattern both inside and outside the cube.

Linda Winkler
Linda Winkler
Numerade Educator
05:16

Problem 35

Refer to The charge lowered into the center of the hollow conductor has a magnitude of $5 \mu \mathrm{C}$. Find the magnitude and sign of the charge on the inside and outside of the hollow conductor when the charge is as shown in (a) Figure $15.20 \mathrm{a}$, (b) Figure $15.20 \mathrm{~b}$, (c) Figure $15.20 \mathrm{c}$, and (d) Figure $15.20 \mathrm{~d}$.

Linda Winkler
Linda Winkler
Numerade Educator
04:15

Problem 36

The dome of a Van de Graaff generator receives a charge of $2.0 \times 10^{-4} \mathrm{C}$. Find the strength of the electric field
(a) inside the dome, (b) at the surface of the dome, assuming it has a radius of $1.0 \mathrm{~m}$, and $(\mathrm{c}) 4.0 \mathrm{~m}$ from the center of the dome. (Iint: See Section $15.6$ to review properties of conductors in electrostatic equilibrium. Also, use that the points on the surface are outside a spherically symmetric charge distribution; the total charge may be considered to be located at the center of the sphere.)

Vysakh M
Vysakh M
Numerade Educator
03:02

Problem 37

If the electric field strength in air exceeds $3.0 \times 10^{6} \mathrm{~N} / \mathrm{C}$, the air becomes a conductor. Using this fact, determine the maximum amount of charge that can be carried by a metal sphere $2.0 \mathrm{~m}$ in radius.

Vysakh M
Vysakh M
Numerade Educator
04:25

Problem 38

In the Millikan oil-drop experiment, an atomizer (a sprayer with a fine nozzle) is used to introduce many tiny droplets of oil between two oppositely charged parallel metal plates. Some of the droplets pick up one or more excess electrons. The charge on the plates is adjusted so that the electric force on the excess electrons exactly balances the weight of the droplet. The idea is to look for a droplet that has the smallest electric force and assume it has only one excess clectron. This strategy lets the observer measure the charge on the electron. Suppose we are using an electric field of $3 \times 10^{4} \mathrm{~N} / \mathrm{C}$. The charge on one electron is about $1.6 \times 10^{-19} \mathrm{C}$. Estimate the radius of an oil drop of density $858 \mathrm{~kg} / \mathrm{m}^{3}$ for which its weight could be balanced by the electric force of this field on one electron. (Problem 38 is courtesy of E. F. Redish. For more problems of this type, visit www.physics.umd.edu/perg/.)

Vysakh M
Vysakh M
Numerade Educator
02:53

Problem 39

A Van de Graaff generator is charged so that a proton at its surface accelerates radially outward at $1.52 \times 10^{12} \mathrm{~m} / \mathrm{s}^{2} .$ Find (a) the magnitude of the electric force on the proton at that instant and (b) the magnitude and direction of the electric field at the surface of the generator:

Vysakh M
Vysakh M
Numerade Educator
02:58

Problem 40

A flat surface having an area of $3.2 \mathrm{~m}^{2}$ is rotated in a uniform electric field of magnitude $E=6.2 \times 10^{3} \mathrm{~N} / \mathrm{C} .$ Determine the electric flux through this area (a) when the electric field is perpendicular to the surface and (b) when the electric field is parallel to the surface.

Vysakh M
Vysakh M
Numerade Educator
04:26

Problem 41

]An electric field of intensity $3.50 \mathrm{kN} / \mathrm{C}$ is applied along the $x$ -axis. Calculate the electric flux through a rectangular plane $0.350 \mathrm{~m}$ wide and $0.700 \mathrm{~m}$ long if (a) the plane is parallel to the $y z$ -plane, (b) the plane is parallel to the xy-plane, and (c) the plane contains the $y$ -axis and its normal makes an angle of $40.0^{\circ}$ with the $x$ -axis.

Vysakh M
Vysakh M
Numerade Educator
05:15

Problem 42

The electric field everywhere on the surface of a charged sphere of radius $0.230 \mathrm{~m}$ has a magnitude of $575 \mathrm{~N} / \mathrm{C}$ and points radially outward from the center of the sphere. (a) What is the net charge on the sphere?
(b) What can you conclude about the nature and distribution of charge inside the sphere?

Narayan Hari
Narayan Hari
Numerade Educator
04:19

Problem 43

Four closed surfaces, $\mathrm{S}_{1}$ through $\mathrm{S}_{4}$, together with the charges $-2 Q, Q$, and $-Q$, are sketched in Figure $\mathrm{P} 15.43 .$ (The colored lines are the intersections of the surfaces with the page.) Find the electric flux through each surface.

Narayan Hari
Narayan Hari
Numerade Educator
02:38

Problem 44

A vertical electric field of magnitude $1.80 \times 10^{4} \mathrm{~N} / \mathrm{C}$ exists above Earth's surface on a stormy day. A car with a rectangular size of $5.50 \mathrm{~m}$ by $2.00 \mathrm{~m}$ is traveling along a horizontal roadway. Find the magnitude of the electric flux through the bottom of the car.

Vysakh M
Vysakh M
Numerade Educator
04:41

Problem 45

A point charge $q$ is located at the center of a spherical shell of radius $a$ that has a charge $-q$ uniformly distributed on its surface. Find the electric field (a) for all points outside the spherical shell and (b) for a point inside the shell a distance $r$ from the center.

Vysakh M
Vysakh M
Numerade Educator
04:43

Problem 46

A charge of $1.70 \times 10^{2} \mu \mathrm{C}$ is at the center of a cube of edge $80.0 \mathrm{~cm}$. No other charges are nearby. (a) Find the flux through the whole surface of the cube. (b) Find the flux through each face of the cube. (c) Would your answers to parts (a) or (b) change if the charge were not at the center? Explain.

Vysakh M
Vysakh M
Numerade Educator
02:00

Problem 47

Suppose the conducting spherical shell of Figure $15.29$ carries a charge of $3.00 \mathrm{nC}$ and that a charge of $-2.00 \mathrm{nC}$ is at the center of the sphere. If $a=2.00 \mathrm{~m}$ and $b=2.40 \mathrm{~m}$, find the electric field at (a) $r=1.50 \mathrm{~m}$, (b) $r=2.20 \mathrm{~m}$, and
(c) $r=2.50 \mathrm{~m}$.
(d) What is the charge distribution on the sphere?

Salamat Ali
Salamat Ali
Numerade Educator
05:15

Problem 48

A very large nonconducting plate lying in the $x y$ plane carries a charge per unit area of $\sigma, A$ second such plate located at $z=2.00 \mathrm{~cm}$ and oriented parallel to the $x y$ -plane carries a charge per unit area of $-2 \sigma .$ Find the electric field (a) for $z<0$, (b) $0<z<2.00 \mathrm{~cm}$, and $(\mathrm{c}) z>$ $2.00 \mathrm{~cm} .$

Linda Winkler
Linda Winkler
Numerade Educator
03:22

Problem 49

In deep space two spheres each of radius $5.00 \mathrm{~m}$ are connected by a $3.00 \times 10^{2} \mathrm{~m}$ nonconducting cord. If a uniformly distributed charge of $35.0 \mathrm{mC}$ resides on the surface of each sphere, calculate the tension in the cord.

Vysakh M
Vysakh M
Numerade Educator
03:54

Problem 50

Iecp A nonconducting, thin plane sheet of charge carries a uniform charge per unit area of $5.20 \mu \mathrm{C} / \mathrm{m}^{2} \mathrm{as}$ in Figure $15.30 .$ (a) Find the electric field at a distance of $8.70 \mathrm{~cm}$ from the plate.
(b) Explain whether your result changes as the distance from the sheet is varied.

Vysakh M
Vysakh M
Numerade Educator
03:33

Problem 51

Three point charges are aligned along the $x$ -axis as shown in Figure $\mathrm{P} 15.5 \mathrm{l}$. Find the electric field at the position $x=$ $+2.0 \mathrm{~m}, y=0 .$

Vysakh M
Vysakh M
Numerade Educator
00:30

Problem 52

A small, $2.00-\mathrm{g}$ plastic ball is suspended by a $20.0-\mathrm{cm}$ long string in a uniform electric field, as shown in Figure $\mathrm{P} 15.52$. If the ball is in equilibrium when the string makes a $15.0^{\circ}$ angle with the vertical as indicated, what is the net charge on the ball?

Jennifer Stoner
Jennifer Stoner
Numerade Educator
07:17

Problem 53

(a) Two identical point charges $+q$ are located on the $y$ -axis at $y=+a$ and $y=-a .$ What is the electric field along the $x$ -axis at $x=b ?$ (b) A circular ring of charge of radius $a$ has a total positive charge $Q$ distributed uniformly around it. The ring is in the $x=0$ plane with its center at the origin. What is the electric field along the $x$ -axis at $x=b$ due to the ring of charge? (Hint: Consider the charge $Q$ to consist of many pairs of identical point charges positioned at the ends of diameters of the ring.

Linda Winkler
Linda Winkler
Numerade Educator
02:08

Problem 54

The electrons in a particle beam each have a kinetic energy $K$. Find the magnitude of the electric field that will stop these electrons in a distance $d$, expressing the answer symbolically in terms of $K, e$, and $d .$ Should the clectric ficld point in the direction of the motion of the electron, or should it point in the opposite direction?

Vysakh M
Vysakh M
Numerade Educator
06:42

Problem 55

A vertical spring with constant $845 \mathrm{~N} / \mathrm{m}$ has a ball of mass $4.00 \mathrm{~kg}$ attached to the bottom of it, which is held with the spring unstretched. (a) How far must the ball be
lowered to reach its equilibrium position? (b) The ball is given a charge of $0.0500$ C. If an electric field directed upward is applied, increasing slowly to a maximum value of $355.0 \mathrm{~N} / \mathrm{C}$, how far below the unstretched position is the new equilibrium position of the ball?

Linda Winkler
Linda Winkler
Numerade Educator
05:02

Problem 56

A $2.00-\mathrm{m}$ C charged $1.00-\mathrm{g}$ cork ball is suspended verlically on a $0.500-$ m-long light string in the presence of a uniform downward-directed electric field of magnitude $E=1.00 \times 10^{5} \mathrm{~N} / \mathrm{C}$. If the ball is displaced slightly from the vertical, it oscillates like a simple pendulum. (a) Determine the period of the ball's oscillation. (b) Should gravity be included in the calculation for part (a)? Explain.

Vysakh M
Vysakh M
Numerade Educator
09:09

Problem 57

Two 2.0-g spheres are suspended by $10.0-\mathrm{cm}$ -long light strings (Fig. P15.57). A uniform electric field is applied in the $x$ -direction. If the spheres have charges of $-5.0 \times$ $10^{-8}$ Cand $+5.0 \times 10^{-8} \mathrm{C}$, determine the electric field intensity that enables the spheres to be in equilibrium at $\theta=10^{\circ}$.

Linda Winkler
Linda Winkler
Numerade Educator
10:36

Problem 58

A point charge of magnitude $5.00 \mu \mathrm{C}$ is at the origin of a coordinate system, and a charge of $-4.00 \mu \mathrm{C}$ is at the point $x=1.00 \mathrm{~m}$. There is a point on the $x$ -axis, at $x$ less than infinity, where the electric field goes to zero. (a) Show by conceptual arguments that this point cannot be located between the charges. (b) Show by conceptual arguments that the point cannot be at any location between $x=0$ and negative infinity. (c) Show by conceptual arguments that the point must be between $x=1.00 \mathrm{~m}$ and $x=$ positive infinity. (d) Use the values given to find the point and show that it is consistent with your conceptual argument.

Vysakh M
Vysakh M
Numerade Educator
07:17

Problem 59

Two hard rubber spheres of mass $15 \mathrm{~g}$ are rubbed vigorously with fur on a dry day and are then suspended from a rod with two insulating strings of length $5.0 \mathrm{~cm}$. They are observed to hang at equilibrium as shown in Figure P15. 59 , each at an angle of $10^{\circ}$ with the vertical. Estimate the amount of charge that is found on each sphere. (Problem 59 is courtesy of $\mathrm{E}$. F. Redish. For more problems of this type, visit www.physics.umd.edu/perg/.)

Linda Winkler
Linda Winkler
Numerade Educator
06:40

Problem 60

Two small silver spheres, each with a mass of $100 \mathrm{~g}$, are separated by $1.00 \mathrm{~m} .$ Calculate the fraction of the electrons in one sphere that must be transferred to the other Lo produce an attractive force of $1.00 \times 10^{4} \mathrm{~N}$ (about 1 ton) between the spheres. (The number of electrons per atom of silver is 47, and the number of atoms per gram is Avogadro's number divided by the molar mass of silver, $107.87 \mathrm{~g} / \mathrm{mol} .)$

Linda Winkler
Linda Winkler
Numerade Educator
04:19

Problem 61

A solid conducting sphere of radius $2.00 \mathrm{~cm}$ has a charge of $8.00 \mu \mathrm{C}$. A conducting spherical shell of inner radius $4.00 \mathrm{~cm}$ and outer radius $5.00 \mathrm{~cm}$ is concentric with the solid sphere and has a charge of $-4.00 \mu \mathrm{C}$. Find the electric field at (a) $r=1.00 \mathrm{~cm}$, (b) $r=3.00 \mathrm{~cm}$,
(c) $r=4.50 \mathrm{~cm}$, and
(d) $r=7.00 \mathrm{~cm}$ from the center of this charge configuration.

Aja S
Aja S
Numerade Educator
03:43

Problem 62

Three identical point charges, each of mass $m=0.100 \mathrm{~kg}$, hang from three strings, as shown in Figure $\mathrm{P} 15.62 .$ If the lengths of the left and right strings are each $L=30.0 \mathrm{~cm}$ and if the angle $\theta$ is $45.0^{\circ}$, determine the value of $q$.

Dading Chen
Dading Chen
Numerade Educator
09:30

Problem 63

Each of the electrons in a particle beam has a kinetic energy of $1.60 \times 10^{-17} \mathrm{~J}$. (a) What is the magnitude of the uniform electric field (pointing in the direction of the electrons' movement) that will stop these electrons in a distance of $10.0 \mathrm{~cm}$ ? (b) How long will it take to stop the electrons? (c) After the electrons stop, what will they do? Explain.

Linda Winkler
Linda Winkler
Numerade Educator
14:41

Problem 64

Protons are projected with an initial speed $v_{0}=9550 \mathrm{~m} / \mathrm{s}$ into a region where a uniform electric field $E=720 \mathrm{~N} / \mathrm{C}$ is present (Fig. P15.64). The protons are to hit a target that lies a horizontal distance of $1.27 \mathrm{~mm}$ from the point where the protons are launched. Find (a) the two projection angles $\theta$ that will result in a hit and (b) the total duration of flight for each of the two trajectories.

Linda Winkler
Linda Winkler
Numerade Educator