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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

72.

A vector field EE (not necessarily an electric field; note units) is given by E=3x2k^.E=3x2k^. Calculate SE·n^da,SE·n^da, where S is the area shown below. Assume that n^=k^.n^=k^.

A square S with length of each side equal to a is shown in the xy plane.
73.

Repeat the preceding problem, with E=2xi^+3x2k^.E=2xi^+3x2k^.

74.

A circular area S is concentric with the origin, has radius a, and lies in the yz-plane. Calculate SE·n^dASE·n^dA for E=3z2i^.E=3z2i^.

75.

(a) Calculate the electric flux through the open hemispherical surface due to the electric field E=E0k^E=E0k^ (see below). (b) If the hemisphere is rotated by 90°90° around the x-axis, what is the flux through it?

A hemisphere with radius R is shown with its base in the xy plane and center of base at the origin. An arrow is shown beside it, labeled vector E equal to E0 k hat.
76.

Suppose that the electric field of an isolated point charge were proportional to 1/r2+σ1/r2+σ rather than 1/r2.1/r2. Determine the flux that passes through the surface of a sphere of radius R centered at the charge. Would Gauss’s law remain valid?

77.

The electric field in a region is given by E=a/(b+cx)i^,E=a/(b+cx)i^, where a=200N·m/C,a=200N·m/C,b=2.0m,b=2.0m, and c=2.0.c=2.0. What is the net charge enclosed by the shaded volume shown below?

Figure shows a cuboid with one corner on the origin of the coordinate axes. Its length along the x axis is 2 m, along y axis is 1.5 m and along z axis is 1 m. An arrow outside the cuboid points along the x axis. It is labeled vector E.
78.

Two equal and opposite charges of magnitude Q are located on the x-axis at the points +a and –a, as shown below. What is the net flux due to these charges through a square surface of side 2a that lies in the yz-plane and is centered at the origin? (Hint: Determine the flux due to each charge separately, then use the principle of superposition. You may be able to make a symmetry argument.)

A shaded square is shown in the yz plane with its center at the origin. Its side parallel to z axis is labeled to be of length 2a. A charge labeled plus Q is shown on the positive x axis at a distance a from the origin. A charge labeled minus Q is shown on the negative x axis at a distance a from the origin.
79.

A fellow student calculated the flux through the square for the system in the preceding problem and got 0. What went wrong?

80.

A 10cm×10cm10cm×10cm piece of aluminum foil of 0.1 mm thickness has a charge of 20μC20μC that spreads on both wide side surfaces evenly. You may ignore the charges on the thin sides of the edges. (a) Find the charge density. (b) Find the electric field 1 cm from the center, assuming approximate planar symmetry.

81.

Two 10cm×10cm10cm×10cm pieces of aluminum foil of thickness 0.1 mm face each other with a separation of 5 mm. One of the foils has a charge of +30μC+30μC and the other has 30μC30μC. (a) Find the charge density at all surfaces, i.e., on those facing each other and those facing away. (b) Find the electric field between the plates near the center assuming planar symmetry.

82.

Two large copper plates facing each other have charge densities ±4.0C/m2±4.0C/m2 on the surface facing the other plate, and zero in between the plates. Find the electric flux through a 3cm×4cm3cm×4cm rectangular area between the plates, as shown below, for the following orientations of the area. (a) If the area is parallel to the plates, and (b) if the area is tilted θ=30°θ=30° from the parallel direction. Note, this angle can also be θ=180°+30°.θ=180°+30°.

Figure shows two parallel plates and a dotted line exactly between the two, parallel to them. A third plate forms an angle theta with the dotted line.
83.

The infinite slab between the planes defined by z=a/2z=a/2 and z=a/2z=a/2 contains a uniform volume charge density ρρ (see below). What is the electric field produced by this charge distribution, both inside and outside the distribution?

Figure shows a cuboid with its center at the origin of the coordinate axes. Arrows perpendicular to the surfaces of the cuboid point outward. The arrows along positive x and y axes are labeled infinity and the arrows along the negative x and y axes are labeled minus infinity. The cuboid is labeled rho. Its top surface is labeled z equal to plus a by 2 and its bottom surface is labeled z equal to minus a by 2.
84.

A total charge Q is distributed uniformly throughout a spherical volume that is centered at O1O1 and has a radius R. Without disturbing the charge remaining, charge is removed from the spherical volume that is centered at O2O2 (see below). Show that the electric field everywhere in the empty region is given by

E=Qr4πε0R3,E=Qr4πε0R3,

where rr is the displacement vector directed from O1toO2.O1toO2.

Figure shows a circle with center O1 and radius R. Another smaller circle with center O2 is shown within it. An arrow from O1 to O2 is labeled vector r.
85.

A non-conducting spherical shell of inner radius a1a1 and outer radius b1b1 is uniformly charged with charged density ρ1ρ1 inside another non-conducting spherical shell of inner radius a2a2 and outer radius b2b2 that is also uniformly charged with charge density ρ2ρ2. See below. Find the electric field at space point P at a distance r from the common center such that (a) r>b2,r>b2, (b) a2<r<b2,a2<r<b2, (c) b1<r<a2,b1<r<a2, (d) a1<r<b1,a1<r<b1, and (e) r<a1r<a1.

Figure shows two concentric circular shells. The inner and outer radii of the inner shell are a1 and a2 respectively. The inner and outer radii of the outer shell are a2 and b2 respectively. The distance from the center to a point P between the two shells is labeled r.
86.

Two non-conducting spheres of radii R1R1 and R2R2 are uniformly charged with charge densities ρ1ρ1 and ρ2,ρ2, respectively. They are separated at center-to-center distance a (see below). Find the electric field at point P located at a distance r from the center of sphere 1 and is in the direction θθ from the line joining the two spheres assuming their charge densities are not affected by the presence of the other sphere. (Hint: Work one sphere at a time and use the superposition principle.)

Two circles are shown side by side with the distance between their centers being a. The bigger circle has radius R1 and the smaller one has radius R2. An arrow r is shown from the center of the bigger circle to a point P outside the circles. r forms an angle theta with a.
87.

A disk of radius R is cut in a non-conducting large plate that is uniformly charged with charge density σσ (coulomb per square meter). See below. Find the electric field at a height h above the center of the disk. (h>>R,h<<lorw).(h>>R,h<<lorw). (Hint: Fill the hole with ±σ.)±σ.)

A plate with length l and width w has a hole in the center. A point P above the plate is at a distance h from its center.
88.

Concentric conducting spherical shells carry charges Q and –Q, respectively (see below). The inner shell has negligible thickness. Determine the electric field for (a) r<a;r<a; (b) a<r<b;a<r<b; (c) b<r<c;b<r<c; and (d) r>c.r>c.

Section of two concentric spherical shells is shown. The inner shell has a radius a. It is labeled Q and has plus signs around it. The outer shell has an inner radius b and an outer radius c. It is labeled minus Q and has minus signs around it.
89.

Shown below are two concentric conducting spherical shells of radii R1R1 and R2R2, each of finite thickness much less than either radius. The inner and outer shell carry net charges q1q1 and q2,q2, respectively, where both q1q1 and q2q2 are positive. What is the electric field for (a) r<R1;r<R1; (b) R1<r<R2;R1<r<R2; and (c) r>R2?r>R2? (d) What is the net charge on the inner surface of the inner shell, the outer surface of the inner shell, the inner surface of the outer shell, and the outer surface of the outer shell?

Figure shows section of two concentric spherical shells. The inner one has radius R1 and the outer one has radius R2.
90.

A point charge of q=5.0×10−8Cq=5.0×10−8C is placed at the center of an uncharged spherical conducting shell of inner radius 6.0 cm and outer radius 9.0 cm. Find the electric field at (a) r=4.0cmr=4.0cm, (b) r=8.0cmr=8.0cm, and (c) r=12.0cmr=12.0cm. (d) What are the charges induced on the inner and outer surfaces of the shell?

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