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

Check Your Understanding

13.1

1.1 T/s

13.2

To the observer shown, the current flows clockwise as the magnet approaches, decreases to zero when the magnet is centered in the plane of the coil, and then flows counterclockwise as the magnet leaves the coil.

Figure shows a magnet that is moving into and through the loop with the South pole facing the loop. Position (a) corresponds to magnet approaching the loop; position (b) corresponds to the magnet directly into the loop. Position (c) corresponds to the magnet moving away from the loop.
13.4

ε=Bl2ω/2,ε=Bl2ω/2, with O at a higher potential than S

13.5

1.5 V

13.6

a. yes; b. Yes; however there is a lack of symmetry between the electric field and coil, making E·dlE·dl a more complicated relationship that can’t be simplified as shown in the example.

13.7

3.4×10−3V/m3.4×10−3V/m

13.8

P1,P2,P4P1,P2,P4

13.9

a. 3.1×106V;3.1×106V; b. 2.0×107V/m2.0×107V/m

Conceptual Questions

1.

The emf depends on the rate of change of the magnetic field.

3.

Both have the same induced electric fields; however, the copper ring has a much higher induced emf because it conducts electricity better than the wooden ring.

5.

a. no; b. yes

7.

As long as the magnetic flux is changing from positive to negative or negative to positive, there could be an induced emf.

9.

Position the loop so that the field lines run perpendicular to the area vector or parallel to the surface.

11.

a. CW as viewed from the circuit; b. CCW as viewed from the circuit

13.

As the loop enters, the induced emf creates a CCW current while as the loop leaves the induced emf creates a CW current. While the loop is fully inside the magnetic field, there is no flux change and therefore no induced current.

15.

a. CCW viewed from the magnet; b. CW viewed from the magnet; c. CW viewed from the magnet; d. CCW viewed from the magnet; e. CW viewed from the magnet; f. no current

17.

Positive charges on the wings would be to the west, or to the left of the pilot while negative charges would be pulled east or to the right of the pilot. Thus, the left hand tips of the wings would be positive and the right hand tips would be negative.

19.

The work is greater than the kinetic energy because it takes energy to counteract the induced emf.

21.

The conducting sheet is shielded from the changing magnetic fields by creating an induced emf. This induced emf creates an induced magnetic field that opposes any changes in magnetic fields from the field underneath. Therefore, there is no net magnetic field in the region above this sheet. If the field were due to a static magnetic field, no induced emf will be created since you need a changing magnetic flux to induce an emf. Therefore, this static magnetic field will not be shielded.

23.

a. zero induced current, zero force; b. clockwise induced current, force is to the left; c. zero induced current, zero force; d. counterclockwise induced current, force is to the left; e. zero induced current, zero force.

Problems

25.

a. 3.8 V; b. 2.2 V; c. 0 V

27.

B=1.5t,0t<2.0ms,B=3.0mT,2.0mst5.0ms,B=−3.0t+18mT,5.0ms<t6.0ms,ε=dΦmdt=d(BA)dt=AdBdt,ε=π(0.100m)2(1.5T/s)=−47mV(0t<2.0ms),ε=π(0.100m)2(0)=0(2.0mst5.0ms),ε=π(0.100m)2(−3.0T/s)=94mV(5.0ms<t<6.0ms).B=1.5t,0t<2.0ms,B=3.0mT,2.0mst5.0ms,B=−3.0t+18mT,5.0ms<t6.0ms,ε=dΦmdt=d(BA)dt=AdBdt,ε=π(0.100m)2(1.5T/s)=−47mV(0t<2.0ms),ε=π(0.100m)2(0)=0(2.0mst5.0ms),ε=π(0.100m)2(−3.0T/s)=94mV(5.0ms<t<6.0ms).

Figure shows the Emf in mV plotted as a function of time in ms. Emf is equal to -47 mV when the time is equal to zero. It increases in a step fashion to 0 when the time reaches 2 ms. Emf remains the same till 5 ms and then increases in a step fashion to 94 mV. It stays constant till time reaches 6 ms.
29.

Each answer is 20 times the previously given answers.

31.

n^=k^,dΦm=Cysin(ωt)dxdy,Φm=Cab2sin(ωt)2,ε=Cab2ωcos(ωt)2.n^=k^,dΦm=Cysin(ωt)dxdy,Φm=Cab2sin(ωt)2,ε=Cab2ωcos(ωt)2.

33.

a. 7.8×10−3V7.8×10−3V; b. CCW from the same view as the magnetic field

35.

a. 150 A downward through the resistor; b. 46 A upward through the resistor; c. 0.019 A downward through the resistor

37.

0.0015 V

39.

ε=B0ldωcos(Ωt)ld+B0sin(Ωt)lv ε=B0ldωcos(Ωt)ld+B0sin(Ωt)lv

41.

ε=Blvcosθε=Blvcosθ

43.

a. 2×10−19T2×10−19T; b. 1.25 V/m; c. 0.3125 V; d. 16 m/s

45.

0.018 A, CW as seen in the diagram

47.

9.375 V/m

49.

Inside, B=μ0nI,E·dl=(πr2)μ0ndIdt,B=μ0nI,E·dl=(πr2)μ0ndIdt, so, E=μ0nr2·dIdtE=μ0nr2·dIdt (inside). Outside, E(2πr)=πR2μ0ndIdt,E(2πr)=πR2μ0ndIdt, so, E=μ0nR22r·dIdtE=μ0nR22r·dIdt (outside)

51.

a. Einside=r2dBdtEinside=r2dBdt, Eoutside=r22RdBdtEoutside=r22RdBdt; b. W=4.19×10−23JW=4.19×10−23J; c. 0 J; d. Fmag=4×10−13N,Fmag=4×10−13N, Felec=2.7×10−22NFelec=2.7×10−22N

53.

7.1μA7.1μA

55.

three turns with an area of 1 m2

57.

a. ω=120πrad/s,ε=850sin120πt V;ω=120πrad/s,ε=850sin120πt V;
b. P=720sin2120πtW;P=720sin2120πtW;
c. P=360sin2120πtWP=360sin2120πtW

59.

a. B is proportional to Q; b. If the coin turns easily, the magnetic field is perpendicular. If the coin is at an equilibrium position, it is parallel.

61.

a. 1.33 A; b. 0.50 A; c. 60 W; d. 37.5 W; e. 22.5W

Additional Problems

63.

4.8 × 106 A/s

65.

2.83×10−4A2.83×10−4A, the direction as follows for increasing magnetic field:

Figure shows a circular loop placed between two poles of a horseshoe electromagnet.
67.

0.375 V

69.

a. 0.94 V; b. 0.70 N; c. 3.52 J/s; d. 3.52 W

71.

(dBdt)A2πr(dBdt)A2πr

73.

a. Rf+Ra=120V2.0A=60Ω,soRf=50ΩRf+Ra=120V2.0A=60Ω,soRf=50Ω;
b. I=εsεiRf+Ra,εi=90VI=εsεiRf+Ra,εi=90V;
c. εi=60Vεi=60V

Challenge Problems

75.

N is a maximum number of turns allowed.

77.

0.848 V

79.

Φ=μ0I0a2πln(1+bx),ε=μ0I0abv2πx(x+b),soI=μ0I0abv2πRx(x+b)Φ=μ0I0a2πln(1+bx),ε=μ0I0abv2πx(x+b),soI=μ0I0abv2πRx(x+b)

81.

a. 1.01×10−6V1.01×10−6V; b. 1.37×10−7V1.37×10−7V; c. 0 V

83.

a. v=mgRsinθB2l2cos2θ;v=mgRsinθB2l2cos2θ; b. mgvsinθmgvsinθ; c. mcΔTmcΔT; d. current would reverse direction but bar would still slide at the same speed

85.

a.
B=μ0nI,Φm=BA=μ0nIA,ε=9.9×10−4V;B=μ0nI,Φm=BA=μ0nIA,ε=9.9×10−4V;
b. 9.9×10−4V9.9×10−4V;
c. E·dl=ε,E=1.6×10−3V/mE·dl=ε,E=1.6×10−3V/m; d. 9.9×10−4V9.9×10−4V;
e. no, because there is no cylindrical symmetry

87.

a. 1.92×106rad/s=1.83×107rpm1.92×106rad/s=1.83×107rpm; b. This angular velocity is unreasonably high, higher than can be obtained for any mechanical system. c. The assumption that a voltage as great as 12.0 kV could be obtained is unreasonable.

89.

2μ0πa2I0nωR2μ0πa2I0nωR

91.

mRvoB2D2mRvoB2D2

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.