Skip to Content
OpenStax Logo
Buy book
  1. Preface
  2. Unit 1. Thermodynamics
    1. 1 Temperature and Heat
      1. Introduction
      2. 1.1 Temperature and Thermal Equilibrium
      3. 1.2 Thermometers and Temperature Scales
      4. 1.3 Thermal Expansion
      5. 1.4 Heat Transfer, Specific Heat, and Calorimetry
      6. 1.5 Phase Changes
      7. 1.6 Mechanisms of Heat Transfer
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 The Kinetic Theory of Gases
      1. Introduction
      2. 2.1 Molecular Model of an Ideal Gas
      3. 2.2 Pressure, Temperature, and RMS Speed
      4. 2.3 Heat Capacity and Equipartition of Energy
      5. 2.4 Distribution of Molecular Speeds
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 3 The First Law of Thermodynamics
      1. Introduction
      2. 3.1 Thermodynamic Systems
      3. 3.2 Work, Heat, and Internal Energy
      4. 3.3 First Law of Thermodynamics
      5. 3.4 Thermodynamic Processes
      6. 3.5 Heat Capacities of an Ideal Gas
      7. 3.6 Adiabatic Processes for an Ideal Gas
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 The Second Law of Thermodynamics
      1. Introduction
      2. 4.1 Reversible and Irreversible Processes
      3. 4.2 Heat Engines
      4. 4.3 Refrigerators and Heat Pumps
      5. 4.4 Statements of the Second Law of Thermodynamics
      6. 4.5 The Carnot Cycle
      7. 4.6 Entropy
      8. 4.7 Entropy on a Microscopic Scale
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Unit 2. Electricity and Magnetism
    1. 5 Electric Charges and Fields
      1. Introduction
      2. 5.1 Electric Charge
      3. 5.2 Conductors, Insulators, and Charging by Induction
      4. 5.3 Coulomb's Law
      5. 5.4 Electric Field
      6. 5.5 Calculating Electric Fields of Charge Distributions
      7. 5.6 Electric Field Lines
      8. 5.7 Electric Dipoles
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    2. 6 Gauss's Law
      1. Introduction
      2. 6.1 Electric Flux
      3. 6.2 Explaining Gauss’s Law
      4. 6.3 Applying Gauss’s Law
      5. 6.4 Conductors in Electrostatic Equilibrium
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 7 Electric Potential
      1. Introduction
      2. 7.1 Electric Potential Energy
      3. 7.2 Electric Potential and Potential Difference
      4. 7.3 Calculations of Electric Potential
      5. 7.4 Determining Field from Potential
      6. 7.5 Equipotential Surfaces and Conductors
      7. 7.6 Applications of Electrostatics
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 8 Capacitance
      1. Introduction
      2. 8.1 Capacitors and Capacitance
      3. 8.2 Capacitors in Series and in Parallel
      4. 8.3 Energy Stored in a Capacitor
      5. 8.4 Capacitor with a Dielectric
      6. 8.5 Molecular Model of a Dielectric
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    5. 9 Current and Resistance
      1. Introduction
      2. 9.1 Electrical Current
      3. 9.2 Model of Conduction in Metals
      4. 9.3 Resistivity and Resistance
      5. 9.4 Ohm's Law
      6. 9.5 Electrical Energy and Power
      7. 9.6 Superconductors
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 10 Direct-Current Circuits
      1. Introduction
      2. 10.1 Electromotive Force
      3. 10.2 Resistors in Series and Parallel
      4. 10.3 Kirchhoff's Rules
      5. 10.4 Electrical Measuring Instruments
      6. 10.5 RC Circuits
      7. 10.6 Household Wiring and Electrical Safety
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 11 Magnetic Forces and Fields
      1. Introduction
      2. 11.1 Magnetism and Its Historical Discoveries
      3. 11.2 Magnetic Fields and Lines
      4. 11.3 Motion of a Charged Particle in a Magnetic Field
      5. 11.4 Magnetic Force on a Current-Carrying Conductor
      6. 11.5 Force and Torque on a Current Loop
      7. 11.6 The Hall Effect
      8. 11.7 Applications of Magnetic Forces and Fields
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    8. 12 Sources of Magnetic Fields
      1. Introduction
      2. 12.1 The Biot-Savart Law
      3. 12.2 Magnetic Field Due to a Thin Straight Wire
      4. 12.3 Magnetic Force between Two Parallel Currents
      5. 12.4 Magnetic Field of a Current Loop
      6. 12.5 Ampère’s Law
      7. 12.6 Solenoids and Toroids
      8. 12.7 Magnetism in Matter
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    9. 13 Electromagnetic Induction
      1. Introduction
      2. 13.1 Faraday’s Law
      3. 13.2 Lenz's Law
      4. 13.3 Motional Emf
      5. 13.4 Induced Electric Fields
      6. 13.5 Eddy Currents
      7. 13.6 Electric Generators and Back Emf
      8. 13.7 Applications of Electromagnetic Induction
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    10. 14 Inductance
      1. Introduction
      2. 14.1 Mutual Inductance
      3. 14.2 Self-Inductance and Inductors
      4. 14.3 Energy in a Magnetic Field
      5. 14.4 RL Circuits
      6. 14.5 Oscillations in an LC Circuit
      7. 14.6 RLC Series Circuits
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    11. 15 Alternating-Current Circuits
      1. Introduction
      2. 15.1 AC Sources
      3. 15.2 Simple AC Circuits
      4. 15.3 RLC Series Circuits with AC
      5. 15.4 Power in an AC Circuit
      6. 15.5 Resonance in an AC Circuit
      7. 15.6 Transformers
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    12. 16 Electromagnetic Waves
      1. Introduction
      2. 16.1 Maxwell’s Equations and Electromagnetic Waves
      3. 16.2 Plane Electromagnetic Waves
      4. 16.3 Energy Carried by Electromagnetic Waves
      5. 16.4 Momentum and Radiation Pressure
      6. 16.5 The Electromagnetic Spectrum
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
  12. Index

Problems

6.1 Electric Flux

20.

A uniform electric field of magnitude 1.1×104N/C1.1×104N/C is perpendicular to a square sheet with sides 2.0 m long. What is the electric flux through the sheet?

21.

Calculate the flux through the sheet of the previous problem if the plane of the sheet is at an angle of 60°60° to the field. Find the flux for both directions of the unit normal to the sheet.

22.

Find the electric flux through a rectangular area 3cm×2cm3cm×2cm between two parallel plates where there is a constant electric field of 30 N/C for the following orientations of the area: (a) parallel to the plates, (b) perpendicular to the plates, and (c) the normal to the area making a 30°30° angle with the direction of the electric field. Note that this angle can also be given as 180°+30°.180°+30°.

23.

The electric flux through a square-shaped area of side 5 cm near a large charged sheet is found to be 3×10−5N·m2/C3×10−5N·m2/C when the area is parallel to the plate. Find the charge density on the sheet.

24.

Two large rectangular aluminum plates of area 150cm2150cm2 face each other with a separation of 3 mm between them. The plates are charged with equal amount of opposite charges, ±20μC±20μC. The charges on the plates face each other. Find the flux through a circle of radius 3 cm between the plates when the normal to the circle makes an angle of 5°5° with a line perpendicular to the plates. Note that this angle can also be given as 180°+5°.180°+5°.

25.

A square surface of area 2cm22cm2 is in a space of uniform electric field of magnitude 103N/C103N/C. The amount of flux through it depends on how the square is oriented relative to the direction of the electric field. Find the electric flux through the square, when the normal to it makes the following angles with electric field: (a) 30°30°, (b) 90°90°, and (c) 0°0°. Note that these angles can also be given as 180°+θ180°+θ.

26.

A vector field is pointed along the z-axis, v=αx2+y2z^.v=αx2+y2z^. (a) Find the flux of the vector field through a rectangle in the xy-plane between a<x<ba<x<b and c<y<dc<y<d. (b) Do the same through a rectangle in the yz-plane between a<z<ba<z<b and c<y<dc<y<d. (Leave your answer as an integral.)

27.

Consider the uniform electric field E=(4.0j^+3.0k^)×103N/C.E=(4.0j^+3.0k^)×103N/C. What is its electric flux through a circular area of radius 2.0 m that lies in the xy-plane?

28.

Repeat the previous problem, given that the circular area is (a) in the yz-plane and (b) 45°45° above the xy-plane.

29.

An infinite charged wire with charge per unit length λλ lies along the central axis of a cylindrical surface of radius r and length l. What is the flux through the surface due to the electric field of the charged wire?

6.2 Explaining Gauss’s Law

30.

Determine the electric flux through each closed surface where the cross-section inside the surface is shown below.

Figure shows an irregular shape S1. Within it are four irregular shapes labeled S2, S3, S4 and S6 and a quadrilateral labeled S5. All these overlap with one or more of each other. A charge minus 2q is shown in the overlap region of S1, S2 and S4. A charge minus 2q is shown in the overlap region of S1, S4 and S5. A charge plus q is shown in the overlap region of S1 and S3. A charge plus 3q is shown in the overlap region of S1 and S6.
31.

Find the electric flux through the closed surface whose cross-sections are shown below.

Figure a shows an irregular shape with a positive charge inside it labeled 3 into 10 to the power minus 8 C. There is a negative charge outside it, labeled minus 2 into 10 to the power 8 C. Figure b shows an irregular shape with three charges outside it. These are plus 4 into 10 to the power minus 6 C, plus 5 into 10 to the power minus 6 C and minus three into 10 to the power minus 6 C. Figure c shows a square with the length of each side equal to a. There is a charge minus 2 into 10 to the power minus 6 C within it. Figure d shows a shaded strip with plus signs near the inside edges. It is labeled conductor. An arrow points outward from either end of the strip. These arrows are labeled infinity. A small rectangle is attached to one side of the strip, covering one plus sign. It is labeled end cap of area, 4 into 10 to the power minus 4 m squared. The strip is labeled sigma equal to 2 into 10 to the power minus 6 C by m squared.
32.

A point charge q is located at the center of a cube whose sides are of length a. If there are no other charges in this system, what is the electric flux through one face of the cube?

33.

A point charge of 10μC10μC is at an unspecified location inside a cube of side 2 cm. Find the net electric flux though the surfaces of the cube.

34.

A net flux of 1.0×104N·m2/C1.0×104N·m2/C passes inward through the surface of a sphere of radius 5 cm. (a) How much charge is inside the sphere? (b) How precisely can we determine the location of the charge from this information?

35.

A charge q is placed at one of the corners of a cube of side a, as shown below. Find the magnitude of the electric flux through the shaded face due to q. Assume q>0q>0.

Figure shows a cube with length of each side equal to a. The back surface of it is shaded. One front corner has a small circle on it labeled q.
36.

The electric flux through a cubical box 8.0 cm on a side is 1.2×103N·m2/C.1.2×103N·m2/C. What is the total charge enclosed by the box?

37.

The electric flux through a spherical surface is 4.0×104N·m2/C.4.0×104N·m2/C. What is the net charge enclosed by the surface?

38.

A cube whose sides are of length d is placed in a uniform electric field of magnitude E=4.0×103N/CE=4.0×103N/C so that the field is perpendicular to two opposite faces of the cube. What is the net flux through the cube?

39.

Repeat the previous problem, assuming that the electric field is directed along a body diagonal of the cube.

40.

A total charge 5.0×10−6C5.0×10−6C is distributed uniformly throughout a cubical volume whose edges are 8.0 cm long. (a) What is the charge density in the cube? (b) What is the electric flux through a cube with 12.0-cm edges that is concentric with the charge distribution? (c) Do the same calculation for cubes whose edges are 10.0 cm long and 5.0 cm long. (d) What is the electric flux through a spherical surface of radius 3.0 cm that is also concentric with the charge distribution?

6.3 Applying Gauss’s Law

41.

Recall that in the example of a uniform charged sphere, ρ0=Q/(43πR3).ρ0=Q/(43πR3). Rewrite the answers in terms of the total charge Q on the sphere.

42.

Suppose that the charge density of the spherical charge distribution shown in Figure 6.23 is ρ(r)=ρ0r/Rρ(r)=ρ0r/R for rRrR and zero for r>R.r>R. Obtain expressions for the electric field both inside and outside the distribution.

43.

A very long, thin wire has a uniform linear charge density of 50μC/m.50μC/m. What is the electric field at a distance 2.0 cm from the wire?

44.

A charge of −30μC−30μC is distributed uniformly throughout a spherical volume of radius 10.0 cm. Determine the electric field due to this charge at a distance of (a) 2.0 cm, (b) 5.0 cm, and (c) 20.0 cm from the center of the sphere.

45.

Repeat your calculations for the preceding problem, given that the charge is distributed uniformly over the surface of a spherical conductor of radius 10.0 cm.

46.

A total charge Q is distributed uniformly throughout a spherical shell of inner and outer radii r1andr2,r1andr2, respectively. Show that the electric field due to the charge is

E=0(rr1);E=Q4πε0r2(r3r13r23r13)r^(r1rr2);E=Q4πε0r2r^(rr2).E=0(rr1);E=Q4πε0r2(r3r13r23r13)r^(r1rr2);E=Q4πε0r2r^(rr2).

47.

When a charge is placed on a metal sphere, it ends up in equilibrium at the outer surface. Use this information to determine the electric field of +3.0μC+3.0μC charge put on a 5.0-cm aluminum spherical ball at the following two points in space: (a) a point 1.0 cm from the center of the ball (an inside point) and (b) a point 10 cm from the center of the ball (an outside point).

48.

A large sheet of charge has a uniform charge density of 10μC/m2.10μC/m2. What is the electric field due to this charge at a point just above the surface of the sheet?

49.

Determine if approximate cylindrical symmetry holds for the following situations. State why or why not. (a) A 300-cm long copper rod of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (b) A 10-cm long copper rod of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (c) A 150-cm wooden rod is glued to a 150-cm plastic rod to make a 300-cm long rod, which is then painted with a charged paint so that one obtains a uniform charge density. The radius of each rod is 1 cm, and we seek an electric field at a point that is 4 cm from the center of the rod. (d) Same rod as (c), but we seek electric field at a point that is 500 cm from the center of the rod.

50.

A long silver rod of radius 3 cm has a charge of 5μC/cm5μC/cm on its surface. (a) Find the electric field at a point 5 cm from the center of the rod (an outside point). (b) Find the electric field at a point 2 cm from the center of the rod (an inside point).

51.

The electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude 3 N/C and directed outward from the axis of the rod. (a) How much charge per unit length exists on the copper rod? (b) What would be the electric flux through a cube of side 5 cm situated such that the rod passes through opposite sides of the cube perpendicularly?

52.

A long copper cylindrical shell of inner radius 2 cm and outer radius 3 cm surrounds concentrically a charged long aluminum rod of radius 1 cm with a charge density of 4 pC/m. All charges on the aluminum rod reside at its surface. The inner surface of the copper shell has exactly opposite charge to that of the aluminum rod while the outer surface of the copper shell has the same charge as the aluminum rod. Find the magnitude and direction of the electric field at points that are at the following distances from the center of the aluminum rod: (a) 0.5 cm, (b) 1.5 cm, (c) 2.5 cm, (d) 3.5 cm, and (e) 7 cm.

53.

Charge is distributed uniformly with a density ρρ throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that

E=ρr2ε0(rR);E=ρR22ε0r(rR).E=ρr2ε0(rR);E=ρR22ε0r(rR).

54.

Charge is distributed throughout a very long cylindrical volume of radius R such that the charge density increases with the distance r from the central axis of the cylinder according to ρ=αr,ρ=αr, where αα is a constant. Show that the field of this charge distribution is directed radially with respect to the cylinder and that

E=αr23ε0(rR);E=αR33ε0r(rR).E=αr23ε0(rR);E=αR33ε0r(rR).

55.

The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball’s center and has magnitude 4.0×102N/C.4.0×102N/C. How much charge is on the surface of the ball?

56.

Charge is distributed throughout a spherical shell of inner radius r1r1 and outer radius r2r2 with a volume density given by ρ=ρ0r1/r,ρ=ρ0r1/r, where ρ0ρ0 is a constant. Determine the electric field due to this charge as a function of r, the distance from the center of the shell.

57.

Charge is distributed throughout a spherical volume of radius R with a density ρ=αr2,ρ=αr2, where αα is a constant. Determine the electric field due to the charge at points both inside and outside the sphere.

58.

Consider a uranium nucleus to be sphere of radius R=7.4×10−15mR=7.4×10−15m with a charge of 92e distributed uniformly throughout its volume. (a) What is the electric force exerted on an electron when it is 3.0×10−15m3.0×10−15m from the center of the nucleus? (b) What is the acceleration of the electron at this point?

59.

The volume charge density of a spherical charge distribution is given by ρ(r)=ρ0eαr,ρ(r)=ρ0eαr, where ρ0ρ0 and αα are constants. What is the electric field produced by this charge distribution?

6.4 Conductors in Electrostatic Equilibrium

60.

An uncharged conductor with an internal cavity is shown in the following figure. Use the closed surface S along with Gauss’ law to show that when a charge q is placed in the cavity a total charge –q is induced on the inner surface of the conductor. What is the charge on the outer surface of the conductor?

A metal sphere with a cavity is shown. It is labeled vector E equal to zero. There are plus signs surrounding it. There is a positive charge labeled plus q within the cavity. The cavity is surrounded by minus signs.
Figure 6.46 A charge inside a cavity of a metal. Charges at the outer surface do not depend on how the charges are distributed at the inner surface since E field inside the body of the metal is zero.
61.

An uncharged spherical conductor S of radius R has two spherical cavities A and B of radii a and b, respectively as shown below. Two point charges +qa+qa and +qb+qb are placed at the center of the two cavities by using non-conducting supports. In addition, a point charge +q0+q0 is placed outside at a distance r from the center of the sphere. (a) Draw approximate charge distributions in the metal although metal sphere has no net charge. (b) Draw electric field lines. Draw enough lines to represent all distinctly different places.

Figure shows a sphere with two cavities. A positive charge qa is in one cavity and a positive charge qb is in the other cavity. A positive charge q0 is outside the sphere at a distance r from its center.
62.

A positive point charge is placed at the angle bisector of two uncharged plane conductors that make an angle of 45°.45°. See below. Draw the electric field lines.

An acute angle is shown. Its bisector is a dotted line. A positive charge q is shown on the dotted line.
63.

A long cylinder of copper of radius 3 cm is charged so that it has a uniform charge per unit length on its surface of 3 C/m. (a) Find the electric field inside and outside the cylinder. (b) Draw electric field lines in a plane perpendicular to the rod.

64.

An aluminum spherical ball of radius 4 cm is charged with 5μC5μC of charge. A copper spherical shell of inner radius 6 cm and outer radius 8 cm surrounds it. A total charge of −8μC−8μC is put on the copper shell. (a) Find the electric field at all points in space, including points inside the aluminum and copper shell when copper shell and aluminum sphere are concentric. (b) Find the electric field at all points in space, including points inside the aluminum and copper shell when the centers of copper shell and aluminum sphere are 1 cm apart.

65.

A long cylinder of aluminum of radius R meters is charged so that it has a uniform charge per unit length on its surface of λλ. (a) Find the electric field inside and outside the cylinder. (b) Plot electric field as a function of distance from the center of the rod.

66.

At the surface of any conductor in electrostatic equilibrium, E=σ/ε0.E=σ/ε0. Show that this equation is consistent with the fact that E=kq/r2E=kq/r2 at the surface of a spherical conductor.

67.

Two parallel plates 10 cm on a side are given equal and opposite charges of magnitude 5.0×10−9C.5.0×10−9C. The plates are 1.5 mm apart. What is the electric field at the center of the region between the plates?

68.

Two parallel conducting plates, each of cross-sectional area 400cm2400cm2, are 2.0 cm apart and uncharged. If 1.0×10121.0×1012 electrons are transferred from one plate to the other, what are (a) the charge density on each plate? (b) The electric field between the plates?

69.

The surface charge density on a long straight metallic pipe is σσ. What is the electric field outside and inside the pipe? Assume the pipe has a diameter of 2a.

Figure shows a pipe, with a cylindrical section highlighted. An arrow pointing up and one pointing down along the pipe from the cylinder are labeled infinity. There are plus signs inside the walls of the cylinder.
70.

A point charge q=−5.0×10−12Cq=−5.0×10−12C is placed at the center of a spherical conducting shell of inner radius 3.5 cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is the charge density on the inner surface of the shell? (b) What is the charge density on the outer surface of the shell? (c) What is the net charge on the conductor?

71.

A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges +Q and –Q, respectively. Assuming that the length L of both conductors is much greater than a or b, determine the electric field as a function of r, the distance from the common central axis of the cylinders, for (a) r<a;r<a; (b) a<r<b;a<r<b; and (c)r>b.r>b.

Citation/Attribution

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4.0 and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/university-physics-volume-2/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/university-physics-volume-2/pages/1-introduction
Citation information

© Oct 6, 2016 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License 4.0 license. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.