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  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

Check Your Understanding

6.1

Place it so that its unit normal is perpendicular to E.E.

6.2

mab2/2mab2/2

6.3

a. 3.4×105N·m2/C;3.4×105N·m2/C; b. −3.4×105N·m2/C;−3.4×105N·m2/C; c. 3.4×105N·m2/C;3.4×105N·m2/C; d. 0

6.4

In this case, there is only Eout.So,yes.Eout.So,yes.

6.5

E=λ02πε01dr^E=λ02πε01dr^; This agrees with the calculation of Example 5.5 where we found the electric field by integrating over the charged wire. Notice how much simpler the calculation of this electric field is with Gauss’s law.

6.6

If there are other charged objects around, then the charges on the surface of the sphere will not necessarily be spherically symmetrical; there will be more in certain direction than in other directions.

Conceptual Questions

1.

a. If the planar surface is perpendicular to the electric field vector, the maximum flux would be obtained. b. If the planar surface were parallel to the electric field vector, the minimum flux would be obtained.

3.

False. The net electric flux crossing a closed surface is always zero if and only if the net charge enclosed is zero.

5.

Since the electric field vector has a 1r21r2 dependence, the fluxes are the same since A=4πr2A=4πr2.

7.

a. no; b. zero

9.

Both fields vary as 1r21r2. Because the gravitational constant is so much smaller than 14πε014πε0, the gravitational field is orders of magnitude weaker than the electric field. Also, the gravitational flux through a closed surface is zero or positive; however, the electric flux is positive, negative, or zero, depending on the definition of flux for the given situation.

11.

No, it is produced by all charges both inside and outside the Gaussian surface.

13.

No, since the situation does not have symmetry, making Gauss’s law challenging to simplify.

15.

Any shape of the Gaussian surface can be used. The only restriction is that the Gaussian integral must be calculable; therefore, a box or a cylinder are the most convenient geometrical shapes for the Gaussian surface.

17.

No. If a metal was in a region of zero electric field, all the conduction electrons would be distributed uniformly throughout the metal.

19.

Since the electric field is zero inside a conductor, a charge of −2.0μC−2.0μC is induced on the inside surface of the cavity. This will put a charge of +2.0μC+2.0μC on the outside surface leaving a net charge of −3.0μC−3.0μC on the surface.

Problems

21.

Φ=E·AEAcosθ=2.2×104N·m2/CΦ=E·AEAcosθ=2.2×104N·m2/C electric field in direction of unit normal; Φ=E·AEAcosθ=−2.2×104N·m2/CΦ=E·AEAcosθ=−2.2×104N·m2/C electric field opposite to unit normal

23.

3×10−5N·m2/C(0.05m)2=Eσ=2.12×10−13C/m23×10−5N·m2/C(0.05m)2=Eσ=2.12×10−13C/m2

25.

a. Φ=0.17N·m2/C;Φ=0.17N·m2/C;
b. Φ=0Φ=0; c. Φ=EAcos0°=1.0×103N/C(2.0×10−4m)2cos0°=0.20N·m2/CΦ=EAcos0°=1.0×103N/C(2.0×10−4m)2cos0°=0.20N·m2/C

27.

Φ=3.8×104N·m2/CΦ=3.8×104N·m2/C

29.

E(z)=14πε02λzk^,E·n^dA=λε0lE(z)=14πε02λzk^,E·n^dA=λε0l

31.

a. Φ=3.39×103N·m2/CΦ=3.39×103N·m2/C; b. Φ=0Φ=0;
c. Φ=−2.25×105N·m2/CΦ=−2.25×105N·m2/C;
d. Φ=90.4N·m2/CΦ=90.4N·m2/C

33.

Φ=1.13×106N·m2/CΦ=1.13×106N·m2/C

35.

Make a cube with q at the center, using the cube of side a. This would take four cubes of side a to make one side of the large cube. The shaded side of the small cube would be 1/24th of the total area of the large cube; therefore, the flux through the shaded area would be
Φ=124qε0Φ=124qε0.

37.

q=3.54×10−7Cq=3.54×10−7C

39.

zero, also because flux in equals flux out

41.

r>R,E=Q4πε0r2;r<R,E=qr4πε0R3r>R,E=Q4πε0r2;r<R,E=qr4πε0R3

43.

EA=λlε0E=4.50×107N/CEA=λlε0E=4.50×107N/C

45.

a. 0; b. 0; c. E=6.74×106N/C(r^)E=6.74×106N/C(r^)

47.

a. 0; b. E=2.70×106N/CE=2.70×106N/C

49.

a. Yes, the length of the rod is much greater than the distance to the point in question. b. No, The length of the rod is of the same order of magnitude as the distance to the point in question. c. Yes, the length of the rod is much greater than the distance to the point in question. d. No. The length of the rod is of the same order of magnitude as the distance to the point in question.

51.

a. E=Rσ0ε01rr^σ0=5.31×10−11C/m2,E=Rσ0ε01rr^σ0=5.31×10−11C/m2,
λ=3.33×10−12C/mλ=3.33×10−12C/m;
b. Φ=qencε0=3.33×10−12C/m(0.05m)ε0=0.019N·m2/CΦ=qencε0=3.33×10−12C/m(0.05m)ε0=0.019N·m2/C

53.

E2πrl=ρπr2lε0E=ρr2ε0(rR)E2πrl=ρπr2lε0E=ρr2ε0(rR);
E2πrl=ρπR2lε0E=ρR22ε0r(rR)E2πrl=ρπR2lε0E=ρR22ε0r(rR)

55.

Φ=qencε0qenc=−1.0×10−9CΦ=qencε0qenc=−1.0×10−9C

57.

qenc=45παr5,qenc=45παr5,
E4πr2=4παr55ε0E=αr35ε0(rR),E4πr2=4παr55ε0E=αr35ε0(rR),
qenc=45παR5,E4πr2=4παR55ε0E=αR55ε0r2(rR)qenc=45παR5,E4πr2=4παR55ε0E=αR55ε0r2(rR)

59.

integrate by parts: qenc=4πρ0[eαr((r)2α+2rα2+2α3)+2α3]E=ρ0r2ε0[eαr((r)2α+2rα2+2α3)+2α3]qenc=4πρ0[eαr((r)2α+2rα2+2α3)+2α3]E=ρ0r2ε0[eαr((r)2α+2rα2+2α3)+2α3]

61.


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.
63.

a. Outside: E2πrl=λlε0E=3.0C/m2πε0rE2πrl=λlε0E=3.0C/m2πε0r; Inside Ein=0Ein=0; b.

A shaded circle is shown with plus signs around its edge. Arrows from the circle radiate outwards.
65.

a. E2πrl=λlε0E=λ2πε0rrRE2πrl=λlε0E=λ2πε0rrR E inside equals 0; b.

A graph of E versus r is shown.  The curve rises up in a vertical line from a point R on the x axis. It then drops gradually and evens out just above the x axis.
67.

E=5.65×104N/CE=5.65×104N/C

69.

λ=λlε0E=aσε0rraλ=λlε0E=aσε0rra, E=0E=0 inside since qenclosed=0qenclosed=0

71.

a. E=0E=0; b. E2πrL=Qε0E=Q2πε0rLE2πrL=Qε0E=Q2πε0rL; c. E=0E=0 since r would be either inside the second shell or if outside then q enclosed equals 0.

Additional Problems

73.

E·n^dA=a4E·n^dA=a4

75.

a. E·n^dA=E0r2πE·n^dA=E0r2π; b. zero, since the flux through the upper half cancels the flux through the lower half of the sphere

77.

Φ=qencε0Φ=qencε0; There are two contributions to the surface integral: one at the side of the rectangle at x=0x=0 and the other at the side at x=2.0mx=2.0m;
E(0)[1.5m2]+E(2.0m)[1.5m2]=qencε0=−100Nm2/CE(0)[1.5m2]+E(2.0m)[1.5m2]=qencε0=−100Nm2/C
where the minus sign indicates that at x=0x=0, the electric field is along positive x and the unit normal is along negative x. At x=2x=2, the unit normal and the electric field vector are in the same direction: qenc=ε0Φ=−8.85×10−10Cqenc=ε0Φ=−8.85×10−10C.

79.

didn’t keep consistent directions for the area vectors, or the electric fields

81.

a. σ=3.0×10−3C/m2σ=3.0×10−3C/m2, +3×10−3C/m2+3×10−3C/m2 on one and −3×10−3C/m2−3×10−3C/m2 on the other; b. E=3.39×108N/CE=3.39×108N/C

83.

Construct a Gaussian cylinder along the z-axis with cross-sectional area A.
|z|a2qenc=ρAa,Φ=ρAaε0E=ρa2ε0|z|a2qenc=ρAa,Φ=ρAaε0E=ρa2ε0,
|z|a2qenc=ρA2z,E(2A)=ρA2zε0E=ρzε0|z|a2qenc=ρA2z,E(2A)=ρA2zε0E=ρzε0

85.

a. r>b2E4πr2=43π[ρ1(b13a13)+ρ2(b23a23)ε0E=ρ1(b13a13)+ρ2(b23a23)3ε0r2r>b2E4πr2=43π[ρ1(b13a13)+ρ2(b23a23)ε0E=ρ1(b13a13)+ρ2(b23a23)3ε0r2;
b. a2<r<b2  E4πr2=43π[ρ1(b13a13)+ρ2(r3a23)]ε0E=ρ1(b13a13)+ρ2(r3a23)3ε0r2a2<r<b2  E4πr2=43π[ρ1(b13a13)+ρ2(r3a23)]ε0E=ρ1(b13a13)+ρ2(r3a23)3ε0r2;
c. b1<r<a2  E4πr2=43πρ1(b13a13)ε0E=ρ1(b13a13)3ε0r2b1<r<a2  E4πr2=43πρ1(b13a13)ε0E=ρ1(b13a13)3ε0r2;
d. a1<r<b1  E4πr2=43πρ1(r3a13)ε0E=ρ1(r3a13)3ε0r2a1<r<b1  E4πr2=43πρ1(r3a13)ε0E=ρ1(r3a13)3ε0r2; e. 0

87.

Electric field due to plate without hole: E=σ2ε0E=σ2ε0.
Electric field of just hole filled with σE=σ2ε0(1zR2+z2)σE=σ2ε0(1zR2+z2).
Thus, Enet=σ2ε0hR2+h2Enet=σ2ε0hR2+h2.

89.

a. E=0E=0; b. E=q14πε0r2E=q14πε0r2; c. E=q1+q24πε0r2E=q1+q24πε0r2; d. 0,q1,q1,q1+q20,q1,q1,q1+q2

Challenge Problems

91.

Given the referenced link, using a distance to Vega of 237×1015237×1015 m4 and a diameter of 2.4 m for the primary mirror,5 we find that at a wavelength of 555.6 nm, Vega is emitting 2.44×1024J/s2.44×1024J/s at that wavelength. Note that the flux through the mirror is essentially constant.

93.

The symmetry of the system forces EE to be perpendicular to the sheet and constant over any plane parallel to the sheet. To calculate the electric field, we choose the cylindrical Gaussian surface shown. The cross-section area and the height of the cylinder are A and 2x, respectively, and the cylinder is positioned so that it is bisected by the plane sheet. Since E is perpendicular to each end and parallel to the side of the cylinder, we have EA as the flux through each end and there is no flux through the side. The charge enclosed by the cylinder is σA,σA, so from Gauss’s law, 2EA=σAε0,2EA=σAε0, and the electric field of an infinite sheet of charge is
E=σ2ε0,E=σ2ε0, in agreement with the calculation of in the text.

95.

There is Q/2 on each side of the plate since the net charge is Q: σ=Q2Aσ=Q2A,
SE·n^dA=2σΔAε0EP=σε0=Qε02ASE·n^dA=2σΔAε0EP=σε0=Qε02A

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