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University Physics Volume 2

Chapter 11

University Physics Volume 2Chapter 11
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Table of contents
  1. Preface
  2. 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. 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

11.1

a. 0 N; b. 2.4×10−14k^N;2.4×10−14k^N; c. 2.4×10−14j^N;2.4×10−14j^N; d. (7.2j^+2.2k^)×10−15N(7.2j^+2.2k^)×10−15N

11.2

a. 9.6×10−12N9.6×10−12N toward the south; b. wFm=1.7×10−15wFm=1.7×10−15

11.3

a. bends upward; b. bends downward

11.4

a. aligned or anti-aligned; b. perpendicular

11.5

a. 1.1 T; b. 1.6 T

11.6

0.32 m

Conceptual Questions

1.

Both are field dependent. Electrical force is dependent on charge, whereas magnetic force is dependent on current or rate of charge flow.

3.

The magnitude of the proton and electron magnetic forces are the same since they have the same amount of charge. The direction of these forces however are opposite of each other. The accelerations are opposite in direction and the electron has a larger acceleration than the proton due to its smaller mass.

5.

The magnetic field must point parallel or anti-parallel to the velocity.

7.

A compass points toward the north pole of an electromagnet.

9.

Velocity and magnetic field can be set together in any direction. If there is a force, the velocity is perpendicular to it. The magnetic field is also perpendicular to the force if it exists.

11.

A force on a wire is exerted by an external magnetic field created by a wire or another magnet.

13.

Poor conductors have a lower charge carrier density, n, which, based on the Hall effect formula, relates to a higher Hall potential. Good conductors have a higher charge carrier density, thereby a lower Hall potential.

Problems

15.

a. left; b. into the page; c. up the page; d. no force; e. right; f. down

17.

a. right; b. into the page; c. down

19.

a. into the page; b. left; c. out of the page

21.

a. 2.64×10−8N;2.64×10−8N; north b. The force is very small, so this implies that the effect of static charges on airplanes is negligible.

23.

10.1 ° ; 169.9 ° 10.1 ° ; 169.9 °

25.

4.27 m

27.

a. 4.80×10−19C;4.80×10−19C; b. 3; c. This ratio must be an integer because charges must be integer numbers of the basic charge of an electron. There are no free charges with values less than this basic charge, and all charges are integer multiples of this basic charge.

29.

(a) 3.27 x 103 m/s (b) 1252.5 m (c) 29.2 m (d) 0.683 m.

31.

a. 1.8×107m/s;1.8×107m/s; b. 6.8×106eV;6.8×106eV; c. 3.4×106V3.4×106V

33.

a. left; b. into the page; c. up; d. no force; e. right; f. down

35.

a. into the page; b. left; c. out of the page

37.

a. 2.50 N; b. This means that the light-rail power lines must be attached in order not to be moved by the force caused by Earth’s magnetic field.

39.

a. τ=NIAB,τ=NIAB, so ττ decreases by 5.00% if B decreases by 5.00%; b. 5.26% increase

41.

10.0 A

43.

A · m 2 · T = A · m 2 . N A · m = N · m A · m 2 · T = A · m 2 . N A · m = N · m

45.

3.48 × 10 −26 N · m 3.48 × 10 −26 N · m

47.

0.666 N · m 0.666 N · m

49.

5.8 × 10 −6 V 5.8 × 10 −6 V

51.

4.8 × 10 7 C/kg 4.8 × 10 7 C/kg

53.

a. 4.4×10−8s;4.4×10−8s; b. 0.21 m

55.

a. 1.92×10−12J;1.92×10−12J; b. 12 MeV; c. 12 MV; d. 5.2×10−8s;5.2×10−8s; e. 1.92×10−12J,1.92×10−12J, 12 MeV, 12 V, 10.4×10−8s10.4×10−8s

57.

a. 2.50×10−2m;2.50×10−2m; b. Yes, this distance between their paths is clearly big enough to separate the U-235 from the U-238, since it is a distance of 2.5 cm.

Additional Problems

59.

−7.2 × 10 −15 N j ^ −7.2 × 10 −15 N j ^

61.

9.8×10−5j^T;9.8×10−5j^T; the magnetic and gravitational forces must balance to maintain dynamic equilibrium

63.

1.13 × 10 −3 T 1.13 × 10 −3 T

65.

( 1.6 i ^ − 1.4 j ^ − 1.1 k ^ ) × 10 5 V/m ( 1.6 i ^ − 1.4 j ^ − 1.1 k ^ ) × 10 5 V/m

67.

a. circular motion in a north, down plane; b. (1.61j^−0.58k^)×10−14N(1.61j^−0.58k^)×10−14N

69.

The proton has more mass than the electron; therefore, its radius and period will be larger.

71.

1.3 × 10 −25 kg 1.3 × 10 −25 kg

73.

1:0.707:1

75.

1/4

77.

a. 2.3×10−4m;2.3×10−4m; b. 1.37×10−4m1.37×10−4m

79.

a. 30.0°;30.0°; b. 4.80 N

81.

a. 0.283 N; b. 0.4 N; c. 0 N; d. 0 N

83.

0 N and 0.012 Nm

85.

a. 0.31Am2;0.31Am2; b. 0.16 Nm

87.

0.024 Am 2 0.024 Am 2

89.

a. 0.16Am2;0.16Am2; b. 0.016 Nm; c. 0.028 J

91.

(Proof)

93.

4.65 × 10 −7 V 4.65 × 10 −7 V

95.

Since E=Blv,E=Blv, where the width is twice the radius, I=2r,I=2r, I=nqAvd,I=nqAvd,
 vd=InqA=Inqπr2vd=InqA=Inqπr2 so E=B×2r×Inqπr2=2IBnqπ r∝1r∝1d.E=B×2r×Inqπr2=2IBnqπ r∝1r∝1d.
 The Hall voltage is inversely proportional to the diameter of the wire.

97.

6.92×107m/s;6.92×107m/s; 0.602 m

99.

a. 2.4×10−19C;2.4×10−19C; b. not an integer multiple of e; c. need to assume all charges have multiples of e, could be other forces not accounted for

101.

a. B = 5 T; b. very large magnet; c. applying such a large voltage

Challenge Problems

103.

R = ( m v sin θ ) / q B ; R = ( m v sin θ ) / q B ; p = ( 2 π m e B ) v cos θ p = ( 2 π m e B ) v cos θ

105.

I a L 2 / 2 I a L 2 / 2

107.

m = q B 0 2 8 V acc x 2 m = q B 0 2 8 V acc x 2

109.

0.23 N

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