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University Physics Volume 2

Additional Problems

University Physics Volume 2Additional Problems
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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

Additional Problems

58.

Calculate the magnetic force on a hypothetical particle of charge 1.0×10−19C1.0×10−19C moving with a velocity of 6.0×104i^m/s6.0×104i^m/s in a magnetic field of 1.2k^T.1.2k^T.

59.

Repeat the previous problem with a new magnetic field of (0.4i^+1.2k^)T.(0.4i^+1.2k^)T.

60.

An electron is projected into a uniform magnetic field (0.5i^+0.8k^)T(0.5i^+0.8k^)T with a velocity of (3.0i^+4.0j^)×106m/s.(3.0i^+4.0j^)×106m/s. What is the magnetic force on the electron?

61.

The mass and charge of a water droplet are 1.0×10−4g1.0×10−4g and 2.0×10−8C,2.0×10−8C, respectively. If the droplet is given an initial horizontal velocity of 5.0×105i^m/s,5.0×105i^m/s, what magnetic field will keep it moving in this direction? Why must gravity be considered here?

62.

Four different proton velocities are given. For each case, determine the magnetic force on the proton in terms of e, v0,v0, and B0.B0.

B = B naught k hat. v 1 = v naught k hat. v 2 = v naught I hat. v 3 = v naught j hat. v 4 = v naught times (one half I hat plus one half root 3 j hat)
63.

An electron of kinetic energy 2000 eV passes between parallel plates that are 1.0 cm apart and kept at a potential difference of 300 V. What is the strength of the uniform magnetic field B that will allow the electron to travel undeflected through the plates? Assume E and B are perpendicular.

64.

An alpha-particle (m=6.64×10−27kg,(m=6.64×10−27kg, q=3.2×10−19C)q=3.2×10−19C) moving with a velocity v=(2.0i^4.0k^)×106m/sv=(2.0i^4.0k^)×106m/s enters a region where E=(5.0i^2.0j^)×104V/mE=(5.0i^2.0j^)×104V/m and B=(1.0i^+4.0k^)×10−2T.B=(1.0i^+4.0k^)×10−2T. What is the initial force on it?

65.

An electron moving with a velocity v=(4.0i^+3.0j^+2.0k^)×106m/sv=(4.0i^+3.0j^+2.0k^)×106m/s enters a region where there is a uniform electric field and a uniform magnetic field. The magnetic field is given by B=(1.0i^2.0j^+4.0k^)×10−2T.B=(1.0i^2.0j^+4.0k^)×10−2T. If the electron travels through a region without being deflected, what is the electric field?

66.

At a particular instant, an electron is traveling west to east with a kinetic energy of 10 keV. Earth’s magnetic field has a horizontal component of 1.8×10−5T1.8×10−5T north and a vertical component of 5.0×10−5T5.0×10−5T down. (a) What is the path of the electron? (b) What is the radius of curvature of the path?

67.

What is the (a) path of a proton and (b) the magnetic force on the proton that is traveling west to east with a kinetic energy of 10 keV in Earth’s magnetic field that has a horizontal component of 1.8 x 10–5 T north and a vertical component of 5.0 x 10–5 T down?

68.

What magnetic field is required in order to confine a proton moving with a speed of 4.0×106m/s4.0×106m/s to a circular orbit of radius 10 cm?

69.

An electron and a proton move with the same speed in a plane perpendicular to a uniform magnetic field. Compare the radii and periods of their orbits.

70.

A proton and an alpha-particle have the same kinetic energy and both move in a plane perpendicular to a uniform magnetic field. Compare the periods of their orbits.

71.

A singly charged ion takes 2.0×10−3s2.0×10−3s to complete eight revolutions in a uniform magnetic field of magnitude 2.0×10−2T.2.0×10−2T. What is the mass of the ion?

72.

A particle moving downward at a speed of 6.0×106m/s6.0×106m/s enters a uniform magnetic field that is horizontal and directed from east to west. (a) If the particle is deflected initially to the north in a circular arc, is its charge positive or negative? (b) If B = 0.25 T and the charge-to-mass ratio (q/m) of the particle is 4.0×107C/kg,4.0×107C/kg, what is the radius of the path? (c) What is the speed of the particle after it has moved in the field for 1.0×10−5s?1.0×10−5s? for 2.0 s?

73.

A proton, deuteron, and an alpha-particle are all accelerated from rest through the same potential difference. They then enter the same magnetic field, moving perpendicular to it. Compute the ratios of the radii of their circular paths. Assume that md=2mpmd=2mp and mα=4mp.mα=4mp.

74.

A singly charged ion is moving in a uniform magnetic field of 7.5×10−2T7.5×10−2T completes 10 revolutions in 3.47×10−4s.3.47×10−4s. Identify the ion.

75.

Two particles have the same linear momentum, but particle A has four times the charge of particle B. If both particles move in a plane perpendicular to a uniform magnetic field, what is the ratio RA/RBRA/RB of the radii of their circular orbits?

76.

A uniform magnetic field of magnitude BB is directed parallel to the z-axis. A proton enters the field with a velocity v=(4j^+3k^)×106m/sv=(4j^+3k^)×106m/s and travels in a helical path with a radius of 5.0 cm. (a) What is the value of BB? (b) What is the time required for one trip around the helix? (c) Where is the proton 5.0×10−7s5.0×10−7s after entering the field?

77.

An electron moving along the +x -axis at 5.0×106m/s5.0×106m/s enters a magnetic field that makes a 75o75o angle with the x-axis of magnitude 0.20 T. Calculate the (a) pitch and (b) radius of the trajectory.

78.

(a) A 0.750-m-long section of cable carrying current to a car starter motor makes an angle of 60º with Earth’s 5.5×10−5T5.5×10−5T field. What is the current when the wire experiences a force of 7.0×10−3N?7.0×10−3N? (b) If you run the wire between the poles of a strong horseshoe magnet, subjecting 5.00 cm of it to a 1.75-T field, what force is exerted on this segment of wire?

79.

(a) What is the angle between a wire carrying an 8.00-A current and the 1.20-T field it is in if 50.0 cm of the wire experiences a magnetic force of 2.40 N? (b) What is the force on the wire if it is rotated to make an angle of 90º with the field?

80.

A 1.0-m-long segment of wire lies along the x-axis and carries a current of 2.0 A in the positive x-direction. Around the wire is the magnetic field of (3.0i^×4.0k^)×10−3T.(3.0i^×4.0k^)×10−3T. Find the magnetic force on this segment.

81.

A 5.0-m section of a long, straight wire carries a current of 10 A while in a uniform magnetic field of magnitude 8.0×10−3T.8.0×10−3T. Calculate the magnitude of the force on the section if the angle between the field and the direction of the current is (a) 45°; (b) 90°; (c) 0°; or (d) 180°.

82.

An electromagnet produces a magnetic field of magnitude 1.5 T throughout a cylindrical region of radius 6.0 cm. A straight wire carrying a current of 25 A passes through the field as shown in the accompanying figure. What is the magnetic force on the wire?

The field in the vertical gap of an electromagnet points down. The gap is 12.0 cm wide. A horizontal wire passes through the gap and carries a current of 25 A, flowing to the right.
83.

The current loop shown in the accompanying figure lies in the plane of the page, as does the magnetic field. Determine the net force and the net torque on the loop if I = 10 A and B = 1.5 T.

The current loop forms a parallelogram: the top and bottom are horizontal and 10 cm long, the sides are tilted at an angle of 60 degrees up from the +x direction and are 8.0 cm long. A current of 20 A flows counterclockwise. The magnetic field is up.
84.

A circular coil of radius 5.0 cm is wound with five turns and carries a current of 5.0 A. If the coil is placed in a uniform magnetic field of strength 5.0 T, what is the maximum torque on it?

85.

A circular coil of wire of radius 5.0 cm has 20 turns and carries a current of 2.0 A. The coil lies in a magnetic field of magnitude 0.50 T that is directed parallel to the plane of the coil. (a) What is the magnetic dipole moment of the coil? (b) What is the torque on the coil?

86.

A current-carrying coil in a magnetic field experiences a torque that is 75% of the maximum possible torque. What is the angle between the magnetic field and the normal to the plane of the coil?

87.

A 4.0-cm by 6.0-cm rectangular current loop carries a current of 10 A. What is the magnetic dipole moment of the loop?

88.

A circular coil with 200 turns has a radius of 2.0 cm. (a) What current through the coil results in a magnetic dipole moment of 3.0 Am2? (b) What is the maximum torque that the coil will experience in a uniform field of strength 5.0×10−2T?5.0×10−2T? (c) If the angle between μ and B is 45°, what is the magnitude of the torque on the coil? (d) What is the magnetic potential energy of coil for this orientation?

89.

The current through a circular wire loop of radius 10 cm is 5.0 A. (a) Calculate the magnetic dipole moment of the loop. (b) What is the torque on the loop if it is in a uniform 0.20-T magnetic field such that μμ and B are directed at 30°30° to each other? (c) For this position, what is the potential energy of the dipole?

90.

A wire of length 1.0 m is wound into a single-turn planar loop. The loop carries a current of 5.0 A, and it is placed in a uniform magnetic field of strength 0.25 T. (a) What is the maximum torque that the loop will experience if it is square? (b) If it is circular? (c) At what angle relative to B would the normal to the circular coil have to be oriented so that the torque on it would be the same as the maximum torque on the square coil?

91.

Consider an electron rotating in a circular orbit of radius r. Show that the magnitudes of the magnetic dipole moment μ and the angular momentum L of the electron are related by:

μL=e2m.μL=e2m.
92.

The Hall effect is to be used to find the sign of charge carriers in a semiconductor sample. The probe is placed between the poles of a magnet so that magnetic field is pointed up. A current is passed through a rectangular sample placed horizontally. As current is passed through the sample in the east direction, the north side of the sample is found to be at a higher potential than the south side. Decide if the number density of charge carriers is positively or negatively charged.

93.

The density of charge carriers for copper is 8.47×10288.47×1028 electrons per cubic meter. What will be the Hall voltage reading from a probe made up of 3cm×2 cm×1 cm(L×W×T)3cm×2 cm×1 cm(L×W×T) copper plate when a current of 1.5 A is passed through it in a magnetic field of 2.5 T perpendicular to the 3cm×2 cm.3cm×2 cm.

94.

The Hall effect is to be used to find the density of charge carriers in an unknown material. A Hall voltage 40 μVμV for 3-A current is observed in a 3-T magnetic field for a rectangular sample with length 2 cm, width 1.5 cm, and height 0.4 cm. Determine the density of the charge carriers.

95.

Show that the Hall voltage across wires made of the same material, carrying identical currents, and subjected to the same magnetic field is inversely proportional to their diameters. (Hint: Consider how drift velocity depends on wire diameter.)

96.

A velocity selector in a mass spectrometer uses a 0.100-T magnetic field. (a) What electric field strength is needed to select a speed of 4.0×106m/s?4.0×106m/s? (b) What is the voltage between the plates if they are separated by 1.00 cm?

97.

Find the radius of curvature of the path of a 25.0-MeV proton moving perpendicularly to the 1.20-T field of a cyclotron.

98.

Unreasonable results To construct a non-mechanical water meter, a 0.500-T magnetic field is placed across the supply water pipe to a home and the Hall voltage is recorded. (a) Find the flow rate through a 3.00-cm-diameter pipe if the Hall voltage is 60.0 mV. (b) What would the Hall voltage be for the same flow rate through a 10.0-cm-diameter pipe with the same field applied?

99.

Unreasonable results A charged particle having mass 6.64×10−27kg6.64×10−27kg (that of a helium atom) moving at 8.70×105m/s8.70×105m/s perpendicular to a 1.50-T magnetic field travels in a circular path of radius 16.0 mm. (a) What is the charge of the particle? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

100.

Unreasonable results An inventor wants to generate 120-V power by moving a 1.00-m-long wire perpendicular to Earth’s 5.00×10−5T5.00×10−5T field. (a) Find the speed with which the wire must move. (b) What is unreasonable about this result? (c) Which assumption is responsible?

101.

Unreasonable results Frustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a 0.500-V output for blood moving at 30.0 cm/s in a 1.50-cm-diameter vessel. (a) What magnetic field strength is needed? (b) What is unreasonable about this result? (c) Which premise is responsible?

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