# Physics for Scientists & Engineers, 5th edition

Published by Pearson (June 11, 2021) © 2022

**Douglas C. Giancoli**

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**Physics for Scientists and Engineers** combines outstanding pedagogy and a clear direct narrative with applications to draw you into the physics at hand. You'll gain an understanding of the basic concepts of physics from mechanics to modern physics. Each topic begins with concrete observations and experiences that you can relate to your everyday life and to future professions, and then you'll move to generalizations and aspects of physics that show why we believe what we believe.

The **5th Edition** presents new applications and includes the physics of digital and added problem-solving techniques.

**Physics for Scientists & Engineers is available in the following versions:**

**Complete version**contains 44 Chapters including 9 Chapters of modern physics**Classic version**contains 37 Chapters, 35 on classical physics, plus one each on relativity and quantum theory

**3 Volume version: Available separately or packaged together.**

**Volume 1: Chapters 1-20**on mechanics, including fluids, oscillations, waves, plus heat and thermodynamics.**Volume 2: Chapters 21-35**on electricity and magnetism, plus light and optics.**Volume 3: Chapters 36-44**on modern physics: relativity, quantum theory, atomic physics, condensed matter, nuclear physics, elementary particles, cosmology and astrophysics.

*NOTE: Sections marked with a star * may be considered optional.*

**Introduction, Measurement, Estimating**- 1.1 How Science Works
- 1.2 Models, Theories, and Laws
- 1.3 Measurement and Uncertainty; Significant Figures
- 1.4 Units, Standards, and the SI System
- 1.5 Converting Units
- 1.6 Order of Magnitude: Rapid Estimating
- *1.7 Dimensions and Dimensional Analysi s

**Describing Motion: Kinematics in One Dimension**- 2.1 Reference Frames and Displacement
- 2.2 Average Velocity
- 2.3 Instantaneous Velocity
- 2.4 Acceleration
- 2.5 Motion at Constant Acceleration
- 2.6 Solving Problems
- 2.7 Freely Falling Objects
- *2.8 Variable Acceleration; Integral Calculus

**Kinematics in Two or Three Dimensions; Vectors**- 3.1 Vectors and Scalars
- 3.2 Addition of Vectors--Graphical Methods
- 3.3 Subtraction of Vectors, and Multiplication of a Vector by a Scalar
- 3.4 Adding Vectors by Components
- 3.5 Unit Vectors
- 3.6 Vector Kinematics
- 3.7 Projectile Motion
- 3.8 Solving Problems Involving Projectile Motion
- 3.9 Relative Velocity

**Dynamics: Newton's Laws of Motion**- 4.1 Force
- 4.2 Newton's First Law of Motion
- 4.3 Mass
- 4.4 Newton's Second Law of Motion
- 4.5 Newton's Third Law of Motion
- 4.6 Weight--the Force of Gravity; and the Normal Force
- 4.7 Solving Problems with Newton's Laws: Free-Body Diagrams
- 4.8 Problem Solving--A General Approach

**Using Newton's Laws: Friction, Circular Motion, Drag Forces**- 5.1 Using Newton's Laws with Friction
- 5.2 Uniform Circular Motion--Kinematics
- 5.3 Dynamics of Uniform Circular Motion
- 5.4 Highway Curves: Banked and Unbanked
- 5.5 Nonuniform Circular Motion
- *5.6 Velocity-Dependent Forces: Drag and Terminal Velocity

**Gravitation and Newton's Synthesis**- 6.1 Newton's Law of Universal Gravitation
- 6.2 Vector Form of Newton's Law of Universal Gravitation
- 6.3 Gravity Near the Earth's Surface
- 6.4 Satellites and "Weightlessness"
- 6.5 Planets, Kepler's Laws, and Newton's Synthesis
- 6.6 Moon Rises an Hour Later Each Day
- 6.7 Types of Forces in Nature
- *6.8 Gravitational Field
- *6.9 Principle of Equivalence; Curvature of Space; Black Holes

**Work and Energy**- 7.1 Work Done by a Constant Force
- 7.2 Scalar Product of Two Vectors
- 7.3 Work Done by a Varying Force
- 7.4 Kinetic Energy and the Work-Energy Principle

**Conservation of Energy**- 8.1 Conservative and Nonconservative Forces
- 8.2 Potential Energy
- 8.3 Mechanical Energy and Its Conservation
- 8.4 Problem Solving Using Conservation of Mechanical Energy
- 8.5 The Law of Conservation of Energy
- 8.6 Energy Conservation with Dissipative Forces: Solving Problems
- 8.7 Gravitational Potential Energy and Escape Velocity
- 8.8 Power
- 8.9 Potential Energy Diagrams; Stable and Unstable Equilibrium
- *8.10 Gravitational Assist (Slingshot)

**Linear Momentum**- 9.1 Momentum and Its Relation to Force
- 9.2 Conservation of Momentum
- 9.3 Collisions and Impulse
- 9.4 Conservation of Energy and Momentum in Collisions
- 9.5 Elastic Collisions in One Dimension
- 9.6 Inelastic Collisions
- 9.7 Collisions in 2 or 3 Dimensions
- 9.8 Center of Mass (cm)
- 9.9 Center of Mass and Translational Motion
- *9.10 Systems of Variable Mass; Rocket Propulsion

**Rotational Motion**- 10.1 Angular Quantities
- 10.2 Vector Nature of Angular Quantities
- 10.3 Constant Angular Acceleration
- 10.4 Torque
- 10.5 Rotational Dynamics; Torque and Rotational Inertia
- 10.6 Solving Problems in Rotational Dynamics
- 10.7 Determining Moments of Inertia
- 10.8 Rotational Kinetic Energy
- 10.9 Rotational plus Translational Motion; Rolling
- *10.10 Why Does a Rolling Sphere Slow Down?

**Angular Momentum; General Rotation**- 11.1 Angular Momentumâ€Š--â€ŠObjects Rotating About a Fixed Axis
- 11.2 Vector Cross Product; Torque as a Vector
- 11.3 Angular Momentum of a Particle
- 11.4 Angular Momentum and Torque for a System of Particles; General Motion
- 11.5 Angular Momentum and Torque for a Rigid Object
- 11.6 Conservation of Angular Momentum
- *11.7 The Spinning Top and Gyroscope
- 11.8 Rotating Frames of Reference; Inertial Forces
- *11.9 The Coriolis Effect

**Static Equilibrium; Elasticity and Fracture**- 12.1 The Conditions for Equilibrium
- 12.2 Solving Statics Problems
- *12.3 Applications to Muscles and Joints
- 12.4 Stability and Balance
- 12.5 Elasticity; Stress and Strain
- 12.6 Fracture
- *12.7 Trusses and Bridges
- *12.8 Arches and Domes

**Fluids**- 13.1 Phases of Matter
- 13.2 Density and Specific Gravity
- 13.3 Pressure in Fluids
- 13.4 Atmospheric Pressure and Gauge Pressure
- 13.5 Pascal's Principle
- 13.6 Measurement of Pressure; Gauges and the Barometer
- 13.7 Buoyancy and Archimedes' Principle
- 13.8 Fluids in Motion; Flow Rate and the Equation of Continuity
- 13.9 Bernoulli's Equation
- 13.10 Applications of Bernoulli's Principle: Torricelli, Airplanes, Baseballs, Blood Flow
- 13.11 Viscosity
- *13.12 Flow in Tubes: Poiseuille's Equation, Blood Flow
- *13.13 Surface Tension and Capillarity
- *13.14 Pumps, and the Heart

**Oscillations**- 14.1 Oscillations of a Spring
- 14.2 Simple Harmonic Motion
- 14.3 Energy in the Simple Harmonic Oscillator
- 14.4 Simple Harmonic Motion Related to Uniform Circular Motion
- 14.5 The Simple Pendulum
- *14.6 The Physical Pendulum and the Torsion Pendulum
- 14.7 Damped Harmonic Motion
- 14.8 Forced Oscillations; Resonance

**Wave Motion**- 15.1 Characteristics of Wave Motion
- 15.2 Types of Waves: Transverse and Longitudinal
- 15.3 Energy Transported by Waves
- 15.4 Mathematical Representation of a Traveling Wave
- *15.5 The Wave Equation
- 15.6 The Principle of Superposition
- 15.7 Reflection and Transmission
- 15.8 Interference
- 15.9 Standing Waves; Resonance
- 15.10 Refraction
- 15.11 Diffraction

**Sound**- 16.1 Characteristics of Sound
- 16.2 Mathematical Representation of Longitudinal Waves
- 16.3 Intensity of Sound: Decibels
- 16.4 Sources of Sound: Vibrating Strings and Air Columns
- *16.5 Quality of Sound, and Noise; Superposition
- 16.6 Interference of Sound Waves; Beats
- 16.7 Doppler Effect
- *16.8 Shock Waves and the Sonic Boom
- *16.9 Applications: Sonar, Ultrasound, and Medical Imaging

**Temperature, Thermal Expansion, and the Ideal Gas Law**- 17.1 Atomic Theory of Matter
- 17.2 Temperature and Thermometers
- 17.3 Thermal Equilibrium and the Zeroth Law of Thermodynamics
- 17.4 Thermal Expansion
- *17.5 Thermal Stresses
- 17.6 The Gas Laws and Absolute Temperature
- 17.7 The Ideal Gas Law
- 17.8 Problem Solving with the Ideal Gas Law
- 17.9 Ideal Gas Law in Terms of Molecules: Avogadro's Number
- *17.10 Ideal Gas Temperature Scale--â€Ša Standard

**Kinetic Theory of Gases**- 18.1 The Ideal Gas Law and the Molecular Interpretation of Temperature
- 18.2 Distribution of Molecular Speeds
- 18.3 Real Gases and Changes of Phase
- 18.4 Vapor Pressure and Humidity
- 18.5 Temperature of Water Decrease with Altitude
- 18.6 Van der Waals Equation of State
- 18.7 Mean Free Path
- 18.8 Diffusion

**Heat and the First Law of Thermodynamics**- 19.1 Heat as Energy Transfer
- 19.2 Internal Energy
- 19.3 Specific Heat
- 19.4 Calorimetry--â€ŠSolving Problems
- 19.5 Latent Heat
- 19.6 The First Law of Thermodynamics
- 19.7 Thermodynamic Processes and the First Law
- 19.8 Molar Specific Heats for Gases, and the Equipartition of Energy
- 19.9 Adiabatic Expansion of a Gas
- 19.10 Heat Transfer: Conduction, Convection, Radiation

**Second Law of Thermodynamics**- 20.1 The Second Law of Thermodynamics--â€Šâ€ŠIntroduction
- 20.2 Heat Engines
- 20.3 The Carnot Engine; Reversible and Irreversible Processes
- 20.4 Refrigerators, Air Conditioners, and Heat Pumps
- 20.5 Entropy
- 20.6 Entropy and the Second Law of Thermodynamics
- 20.7 Order to Disorder
- 20.8 Unavailability of Energy; Heat Death
- 20.9 Statistical Interpretation of Entropy and the Second Law
- *20.10 Thermodynamic Temperature; Third Law of Thermodynamics
- 20.11 Thermal Pollution, Global Warming, and Energy Resources

**Electric Charge and Electric Field**- 21.1 Static Electricity; Electric Charge and Its Conservation
- 21.2 Electric Charge in the Atom
- 21.3 Insulators and Conductors
- 21.4 Induced Charge; the Electroscope
- 21.5 Coulomb's Law
- 21.6 The Electric Field
- 21.7 Electric Field Calculations for Continuous Charge Distributions
- 21.8 Field Lines
- 21.9 Electric Fields and Conductors
- 21.10 Motion of a Charged Particle in an Electric Field
- 21.11 Electric Dipoles
- *21.12 Electric Forces in Molecular Biology: DNA Structure and Replication

**Gauss's Law**- 22.1 Electric Flux
- 22.2 Gauss's Law
- 22.3 Applications of Gauss's Law
- *22.4 Experimental Basis of Gauss's and Coulomb's Laws

**Electric Potential**- 23.1 Electric Potential Energy and Potential Difference
- 23.2 Relation between Electric Potential and Electric Field
- 23.3 Electric Potential Due to Point Charges
- 23.4 Potential Due to Any Charge Distribution
- 23.5 Equipotential Lines and Surfaces
- 23.6 Potential Due to Electric Dipole; Dipole Moment
- 23.7 Eâ†'Determined from
*V* - 23.8 Electrostatic Potential Energy; the Electron Volt
- 23.9 Digital; Binary Numbers; Signal Voltage
- *23.10 TV and Computer Monitors
- *23.11 Electrocardiogram (ECG or EKG)

**Capacitance, Dielectrics, Electric Energy Storage**- 24.1 Capacitors
- 24.2 Determination of Capacitance
- 24.3 Capacitors in Series and Parallel
- 24.4 Storage of Electric Energy
- 24.5 Dielectrics
- *24.6 Molecular Description of Dielectrics

**Electric Current and Resistance**- 25.1 The Electric Battery
- 25.2 Electric Current
- 25.3 Ohm's Law: Resistance and Resistors
- 25.4 Resistivity
- 25.5 Electric Power
- 25.6 Power in Household Circuits
- 25.7 Alternating Current
- 25.8 Microscopic View of Electric Current
- *25.9 Superconductivity
- *25.10 Electrical Conduction in the Human Nervous System

**DC Circuits**- 26.1 EMF and Terminal Voltage
- 26.2 Resistors in Series and in Parallel
- 26.3 Kirchhoff's Rules
- 26.4 EMFs in Series and in Parallel; Charging a Battery
- 26.5 RC Circuitsâ€Š--â€ŠResistor and Capacitor in Series
- 26.6 Electric Hazards and Safety
- 26.7 Ammeters and Voltmeters--â€ŠMeasurement Affects Quantity Measured

**Magnetism**- 27.1 Magnets and Magnetic Fields
- 27.2 Electric Currents Produce Magnetic Fields
- 27.3 Force on an Electric Current in a Magnetic Field; Definition of Bâ†'
- 27.4 Force on an Electric Charge Moving in a Magnetic Field
- 27.5 Torque on a Current Loop; Magnetic Dipole Moment
- 27.6 Applications: Motors, Loudspeakers, Galvanometers
- 27.7 Discovery and Properties of the Electron
- 27.8 The Hall Effect
- 27.9 Mass Spectrometer

**Sources of Magnetic Field**- 28.1 Magnetic Field Due to a Straight Wire
- 28.2 Force between Two Parallel Wires
- 28.3 Definitions of the Ampere and the Coulomb
- 28.4 AmpÃ¨re's Law
- 28.5 Magnetic Field of a Solenoid and a Toroid
- 28.6 Biot-Savart Law
- 28.7 Magnetic Field Due to a Single Moving Charge
- 28.8 Magnetic Materials--â€ŠFerromagnetism
- 28.9 Electromagnets and Solenoids--â€ŠApplications
- 28.10 Magnetic Fields in Magnetic Materials; Hysteresis
- *28.11 Paramagnetism and Diamagnetism

**Electromagnetic Induction and Faraday's Law**- 29.1 Induced EMF
- 29.2 Faraday's Law of Induction; Lenz's Law
- 29.3 EMF Induced in a Moving Conductor
- 29.4 Electric Generators
- 29.5 Back EMF and Counter Torque; Eddy Currents
- 29.6 Transformers and Transmission of Power
- 29.7A Changing Magnetic Flux Produces an Electric Field
- *29.8 Information Storage: Magnetic and Semiconductor
- *29.9 Applications of Induction: Microphone, Seismograph, GFCI

**Inductance, Electromagnetic Oscillations, and AC Circuits**- 30.1 Mutual Inductance
- 30.2 Self-Inductance; Inductors
- 30.3 Energy Stored in a Magnetic Field
- 30.4 LR Circuits
- 30.5 LC Circuits and Electromagnetic Oscillations
- 30.6 LC Oscillations with Resistance (LRC Circuit)
- 30.7 AC Circuits and Reactance
- 30.8 LRC Series AC Circuit; Phasor Diagrams
- 30.9 Resonance in AC Circuits
- 30.10 Impedance Matching
- *30.11 Three-Phase AC

**Maxwell's Equations and Electromagnetic Waves**- 31.1 Changing Electric Fields Produce Magnetic Fields; Displacement Current
- 31.2 Gauss's Law for Magnetism
- 31.3 Maxwell's Equations
- 31.4 Production of Electromagnetic Waves
- 31.5 Electromagnetic Waves, and Their Speed, Derived from Maxwell's Equations
- 31.6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum
- 31.7 Measuring the Speed of Light
- 31.8 Energy in EM Waves; the Poynting Vector
- 31.9 Radiation Pressure
- 31.10 Radio and Television; Wireless Communication

**Light: Reflection and Refraction**- 32.1 The Ray Model of Light
- 32.2 Reflection; Image Formation by a Plane Mirror
- 32.3 Formation of Images by Spherical Mirrors
- 32.4 Seeing Yourself in a Magnifying Mirror (Concave)
- 32.5 Convex (Rearview) Mirrors
- 32.6 Index of Refraction
- 32.7 Refraction: Snell's Law
- 32.8 The Visible Spectrum and Dispersion
- 32.9 Total Internal Reflection; Fiber Optics
- *32.10 Refraction at a Spherical Surface

**Lenses and Optical Instruments**- 33.1 Thin Lenses; Ray Tracing and Focal Length
- 33.2 The Thin Lens Equation
- 33.3 Combinations of Lenses
- 33.4 Lensmaker's Equation
- 33.5 Cameras: Film and Digital
- 33.6 The Human Eye; Corrective Lenses
- 33.7 Magnifying Glass
- 33.8 Telescopes
- 33.9 Compound Microscope
- 33.10 Aberrations of Lenses and Mirrors

**The Wave Nature of Light: Interference and Polarization**- 34.1 Waves vs. Particles; Huygens' Principle and Diffraction
- 34.2 Huygens' Principle and the Law of Refraction
- 34.3 Interference--â€ŠYoung's Double-Slit Experiment
- 34.4 Intensity in the Double-Slit Interference Pattern
- 34.5 Interference in Thin Films
- 34.6 Michelson Interferometer
- 34.7 Polarization
- *34.8 Liquid Crystal Displays (LCD)
- *34.9 Scattering of Light by the Atmosphere
- 34.10 Lumens, Luminous Flux, and Luminous Intensity
- *34.11 Efficiency of Lightbulbs

**Diffraction**- 35.1 Diffraction by a Single Slit or Disk
- 35.2 Intensity in Single-Slit Diffraction Pattern
- 35.3 Diffraction in the Double-Slit Experiment
- 35.4 Interference vs. Diffraction
- 35.5 Limits of Resolution; Circular Apertures
- 35.6 Resolution of Telescopes and Microscopes; the Î» Limit
- 35.7 Resolution of the Human Eye and Useful Magnification
- 35.8 Diffraction Grating
- 35.9 The Spectrometer and Spectroscopy
- *35.10 Peak Widths and Resolving Power for a Diffraction Grating
- 35.11 X-Rays and X-Ray Diffraction
- *35.12 X-Ray Imaging and Computed Tomography (CT Scan)
- *35.13 Specialty Microscopes and Contrast

**The Special Theory of Relativity**- 36.1 Galilean.Newtonian Relativity
- 36.2 The Michelson.Morley Experiment
- 36.3 Postulates of the Special Theory of Relativity
- 36.4 Simultaneity
- 36.5 Time Dilation and the Twin Paradox
- 36.6 Length Contraction
- 36.7 Four-Dimensional Space.Time
- 36.8 Galilean and Lorentz Transformations
- 36.9 Relativistic Momentum
- 36.10 The Ultimate Speed
- 36.11 E = mc2; Mass and Energy
- 36.12 Doppler Shift for Light
- 36.13 The Impact of Special Relativity

**Early Quantum Theory and Models of the Atom**- 37.1 Blackbody Radiation; Planck's Quantum Hypothesis
- 37.2 Photon Theory of Light and the Photoelectric Effect
- 37.3 Energy, Mass, and Momentum of a Photon
- 37.4 Compton Effect
- 37.5 Photon Interactions; Pair Production
- 37.6 Wave.Particle Duality; the Principle of Complementarity
- 37.7 Wave Nature of Matter
- 37.8 Electron Microscopes
- 37.9 Early Models of the Atom
- 37.10 Atomic Spectra: Key to the Structure of the Atom
- 37.11 The Bohr Model
- 37.12 de Broglie's Hypothesis Applied to Atoms

**Quantum Mechanics**- 38.1 Quantum Mechanics--A New Theory
- 38.2 The Wave Function and Its Interpretation; the Double-Slit Experiment
- 38.3 The Heisenberg Uncertainty Principle
- 38.4 Philosophic Implications; Probability Versus Determinism
- 38.5 The SchrÃ¶dinger Equation in One Dimension-- Time-Independent Form
- *38.6 Time-Dependent SchrÃ¶dinger Equation
- 38.7 Free Particles; Plane Waves and Wave Packets
- 38.8 Particle in an Infinitely Deep Square Well Potential (a Rigid Box)
- 38.9 Finite Potential Well
- 38.10 Tunneling through a Barrier

**Quantum Mechanics of Atoms**- 39.1 Quantum-Mechanical View of Atoms
- 39.2 Hydrogen Atom: SchrÃ¶dinger Equation and Quantum Numbers
- 39.3 Hydrogen Atom Wave Functions
- 39.4 Multielectron Atoms; the Exclusion Principle
- 39.5 Periodic Table of Elements
- 39.6 X-Ray Spectra and Atomic Number
- *39.7 Magnetic Dipole Moment; Total Angular Momentum
- 39.8 Fluorescence and Phosphorescence
- 39.9 Lasers
- *39.10 Holography

**Molecules and Solids**- 40.1 Bonding in Molecules
- 40.2 Potential-Energy Diagrams for Molecules
- 40.3 Weak (van der Waals) Bonds
- 40.4 Molecular Spectra
- 40.5 Bonding in Solids
- 40.6 Free-Electron Theory of Metals; Fermi Energy
- 40.7 Band Theory of Solids
- 40.8 Semiconductors and Doping
- 40.9 Semiconductor Diodes, LEDs, OLEDs
- 40.10 Transistors: Bipolar and MOSFETs
- 40.11 Integrated Circuits, 14-nm Technology

**Nuclear Physics and Radioactivity**- 41.1 Structure and Properties of the Nucleus
- 41.2 Binding Energy and Nuclear Forces
- 41.3 Radioactivity
- 41.4 Alpha Decay
- 41.5 Beta Decay
- 41.6 Gamma Decay
- 41.7 Conservation of Nucleon Number and Other Conservation Laws
- 41.8 Half-Life and Rate of Decay
- 41.9 Decay Series
- 41.10 Radioactive Dating
- 41.11 Detection of Particles

**Nuclear Energy; Effects and Uses of Radiation**- 42.1 Nuclear Reactions and the Transmutation of Elements
- 42.2 Cross Section
- 42.3 Nuclear Fission; Nuclear Reactors
- 42.4 Nuclear Fusion
- 42.5 Passage of Radiation Through Matter; Biological Damage
- 42.6 Measurement of Radiation--Dosimetry
- *42.7 Radiation Therapy
- *42.8 Tracers in Research and Medicine
- *42.9 Emission Tomography: PET and SPECT
- *42.10 Nuclear Magnetic Resonance (NMR); Magnetic Resonance Imaging (MRI)

**Elementary Particles**- 43.1 High-Energy Particles and Accelerators
- 43.2 Beginnings of Elementary Particle Physics--Particle Exchange
- 43.3 Particles and Antiparticles
- 43.4 Particle Interactions and Conservation Laws
- 43.5 Neutrinos
- 43.6 Particle Classification
- 43.7 Particle Stability and Resonances
- 43.8 Strangeness? Charm? Towards a New Model
- 43.9 Quarks
- 43.10 The Standard Model: QCD and Electroweak Theory
- 43.11 Grand Unified Theories
- 43.12 Strings and Supersymmetry

**Astrophysics and Cosmology**- 44.1 Stars and Galaxies
- 44.2 Stellar Evolution: Birth and Death of Stars, Nucleosynthesis
- 44.3 Distance Measurements
- 44.4 General Relativity: Gravity and the Curvature of Space
- 44.5 The Expanding Universe: Redshift and Hubble's Law
- 44.6 The Big Bang and the Cosmic Microwave Background
- 44.7 The Standard Cosmological Model: Early History of the Universe
- 44.8I nflation: Explaining Flatness, Uniformity, and Structure
- 44.9 Dark Matter and Dark Energy
- 44.10 Large-Scale Structure of the Universe
- 44.11 Gravitational Waves--LIGO
- 44.12 Finally . . .

### APPENDICES

- A. Mathematical Formulas
- B. Derivatives and Integrals
- C. Numerical Integration
- D. More on Dimensional Analysis
- E. Gravitational Force Due to a Spherical Mass Distribution
- F. Differential Form of Maxwell's Equations
- G. Selected Isotopes

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