Simple Nature - Light and Matter

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8.6 ⋆ The Creation of the Elements . . . . . . . . . . . 502Creation of hydrogen and helium in the Big Bang, 502.—We arestardust, 503.Problems . . . . . . . . . . . . . . . . . . . . . . 504Exercises . . . . . . . . . . . . . . . . . . . . . . 5089 Circuits9.1 Current and Voltage . . . . . . . . . . . . . . . . 510Current, 510.—Circuits, 513.—Voltage, 514.—Resistance, 519.—Current-conducting properties of materials, 528.9.2 Parallel and Series Circuits . . . . . . . . . . . . . 532Schematics, 532.—Parallel resistances and the junction rule, 533.—Series resistances, 537.Problems . . . . . . . . . . . . . . . . . . . . . . 544Exercises . . . . . . . . . . . . . . . . . . . . . . 55210 Fields10.1 Fields of Force. . . . . . . . . . . . . . . . . . 557Why fields?, 558.—The gravitational field, 559.—The electric field,563.10.2 Voltage Related To Field . . . . . . . . . . . . . 567One dimension, 568.—Two or three dimensions, 571.10.3 Fields by Superposition . . . . . . . . . . . . . . 573Electric field of a continuous charge distribution, 573.—The fieldnear a charged surface, 579.10.4 Energy In Fields . . . . . . . . . . . . . . . . . 582Electric field energy, 582.—Gravitational field energy, 587.—Magneticfield energy, 587.10.5 LRC Circuits . . . . . . . . . . . . . . . . . . 589Capacitance and inductance, 589.—Oscillations, 593.—Voltage andcurrent, 595.—Decay, 600.—Review of complex numbers, 603.—Euler’s formula, 605.—Impedance, 607.—Power, 610.—Impedancematching, 613.—Impedances in series and parallel, 615.10.6 Fields by Gauss’ Law . . . . . . . . . . . . . . . 617Gauss’ law, 617.—Additivity of flux, 621.—Zero flux from outsidecharges, 621.—Proof of Gauss’ theorem, 625.—Gauss’ law as afundamental law of physics, 625.—Applications, 626.10.7 Gauss’ Law In Differential Form . . . . . . . . . . 629Problems . . . . . . . . . . . . . . . . . . . . . . 634Exercises . . . . . . . . . . . . . . . . . . . . . . 64411 Electromagnetism11.1 More About the Magnetic Field . . . . . . . . . . . 647Magnetic forces, 647.—The magnetic field, 651.—Some applications,655.—No magnetic monopoles, 656.—Symmetry and handedness,659.11.2 Magnetic Fields by Superposition . . . . . . . . . . 661Superposition of straight wires, 661.—Energy in the magnetic field,665.—Superposition of dipoles, 665.—The Biot-Savart law (optional),10 Contents
669.11.3 Magnetic Fields by Ampère’s Law. . . . . . . . . . 673Ampère’s law, 673.—A quick and dirty proof, 675.—Maxwell’sequations for static fields, 676.11.4 Ampère’s Law In Differential Form (Optional) . . . . . 678The curl operator, 678.—Properties of the curl operator, 679.11.5 Induced Electric Fields . . . . . . . . . . . . . . 684Faraday’s experiment, 684.—Why induction?, 688.—Faraday’s law,690.11.6 Maxwell’s Equations . . . . . . . . . . . . . . . 695Induced magnetic fields, 695.—Light waves, 697.11.7 Electromagnetic Properties of Materials . . . . . . . 707Conductors, 707.—Dielectrics, 708.—Magnetic materials, 710.—Maxwell’s equations in differential form, 716.Problems . . . . . . . . . . . . . . . . . . . . . . 717Exercises . . . . . . . . . . . . . . . . . . . . . . 73112 Optics12.1 The Ray Model of Light . . . . . . . . . . . . . . 733The nature of light, 734.—Interaction of light with matter, 737.—The ray model of light, 739.—Geometry of specular reflection,742.—⋆ The principle of least time for reflection, 746.12.2 Images by Reflection . . . . . . . . . . . . . . . 748A virtual image, 748.—Curved mirrors, 751.—A real image, 752.—Images of images, 753.12.3 Images, Quantitatively . . . . . . . . . . . . . . 758A real image formed by a converging mirror, 758.—Other caseswith curved mirrors, 762.—⋆ Aberrations, 766.12.4 Refraction. . . . . . . . . . . . . . . . . . . . 769Refraction, 770.—Lenses, 776.—⋆ The lensmaker’s equation, 778.—Dispersion, 779.—⋆ The principle of least time for refraction, 779.—⋆ Microscopic description of refraction, 780.12.5 Wave Optics. . . . . . . . . . . . . . . . . . . 782Diffraction, 782.—Scaling of diffraction, 784.—The correspondenceprinciple, 784.—Huygens’ principle, 785.—Double-slit diffraction,786.—Repetition, 790.—Single-slit diffraction, 791.—⋆ The principleof least time, 793.Problems . . . . . . . . . . . . . . . . . . . . . . 795Exercises . . . . . . . . . . . . . . . . . . . . . . 81113 Quantum Physics13.1 Rules of Randomness . . . . . . . . . . . . . . 821Randomness isn’t random., 822.—Calculating randomness, 823.—Probability distributions, 827.—Exponential decay and half-life,829.—Applications of calculus, 833.13.2 Light As a Particle . . . . . . . . . . . . . . . . 836Evidence for light as a particle, 837.—How much light is one photon?,839.—Wave-particle duality, 844.—Photons in three dimensions,849.Contents 11
Page 4 and 5: Fullerton, Californiawww.lightandma
Page 7 and 8: Contents0 Introduction and Review0.
Page 9: 5.5 More About Heat Engines . . . .
Page 13 and 14: The Mars Climate Orbiter is prepare
Page 15: temperatures and with many combinat
Page 19 and 20: idence that quarks have smaller par
Page 21 and 22: give clearer explanations.Finally,
Page 23 and 24: It can also be handy to have a rela
Page 25 and 26: The prefix centi-, meaning 10 −2
Page 27 and 28: goes like this:V = 1 3 Ah[1]A = πr
Page 29 and 30: the notation 10 0 to stand for one,
Page 32 and 33: calculation, 5.04 cm, was really no
Page 34 and 35: 0.2 Scaling and Order-of-Magnitude
Page 36 and 37: to many times your own height. The
Page 38 and 39: g / 1. This plank is as long as it
Page 40 and 41: the front panels of the three violi
Page 42 and 43: Correct solution #4: The area of a
Page 44 and 45: here?” The scientific Mr. Spock w
Page 46 and 47: 1. Don’t even attempt more than o
Page 48 and 49: Problem 10.mean, however, is define
Page 50 and 51: (d) Find the person’s acceleratio
Page 52 and 53: Albert Einstein, and his moustache,
Page 54 and 55: 54 Chapter 0 Introduction and Revie
Page 56 and 57: a / Portrait of Monsieur Lavoisiera
Page 58 and 59: 1.1.1 Problem-solving techniquesHow
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∆m = 0, where m is the total mass
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different substances will have diff
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c / Left: In a frame of referenceth
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f / Discussion question B.(discusse
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Self-check D.since the derivative o
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ProblemsThe symbols √ , , etc. ar
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difficult? ⊲ Solution, p. 932Key
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Heat energy can be convertedto ligh
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a new form of invisible “mystery
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f / A realistic drawing of Joule’
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numbers. With a purely numerical ap
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of gravity doesn’t change much if
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field. If the plane can start from
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m / Discussion question C.n / A hyd
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88 Chapter 2 Conservation of Energy
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A car drives over a cliff.new frame
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How long does it take to move 1 met
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a / Approximations to thebrachistoc
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a / An ellipse is circle that hasbe
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to deduce the general equation for
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to the mass of the object that inte
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The minimum velocity required for t
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and since sin θ dθ occurs in the
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that is deeper than r. Under the as
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2.3.6 ⋆ Evidence for repulsive gr
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a / A vivid demonstration thatheat
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ture. This is a very good question,
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Three functions with thesame curvat
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This looks like a cosine function,
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Problem 16.13 Anya and Ivan lean ov
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Problem 27.then we’d have U/m =
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37 Two springs with spring constant
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ExercisesExercise 2A: Reasoning wit
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128 Chapter 2 Conservation of Energ
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3.1 Momentum In One Dimensiona / Sy
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eing to the right. The initial mome
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3.1.3 Momentum compared to kinetic
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3.1.4 Collisions in one dimensiong
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could never do that again in a mill
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i / The highjumper’s body passeso
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where x 1 is the mass of the first
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3.1.6 The center of mass frame of r
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The airbag increases ∆tso as to r
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d / Two magnets exert forceson each
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x (m) t (s)10 1.8420 2.8630 3.8040
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3.2.4 Forces between solidsConserva
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Maximum acceleration of a car examp
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Discussion QuestionA Criticize the
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C A pool ball is rebounding from th
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forces, as if the hand were a pair
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This may not sound like an impressi
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stroke are both executed in straigh
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Accelerating a cart example 35If yo
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w / A wedge.x / Archimedes’ screw
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As in the preceding example, we hav
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that have the same frequency is a s
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around until I got this result, sin
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quality factor, Q, is defined as Q
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ight direction to add energy to the
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i / Example 45: a viola withouta mu
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Collapse of the Nimitz Freeway exam
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end up canceling out, however:Q =
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186 Chapter 3 Conservation of Momen
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c / Bullets are dropped and shot at
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the asteroid’s energy and boostin
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coordinate axes. Even though ∆x,
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of the three components,∆p x = 0
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A useless vector operation example
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Solving for the unknowns gives∆x
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o / Example 64.p / Adding vectors g
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How to generalize one-dimensional e
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needed to support the object in fig
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The easiest method is the one demon
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Incorrect solution #4:(same notatio
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The magnitude of the acceleration i
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dropped out like a trap door, showi
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af / Breaking trail, by WalterE. Bo
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know how to integrate with respect
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Problem 16.Problem 19.resistance.)1
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of gravity on Mars.(a) Find the tim
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partner force. (a) A swimmer speeds
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Problem 45the 0.4-gram masses would
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53 If you walk 35 km at an angle 25
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(b) Interpret this equation in the
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Problem 71.232 Chapter 3 Conservati
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77 A car accelerates from rest. At
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Problem 81.81 Complete example 71 o
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ExercisesExercise 3A: Force and Mot
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Exercise 3C: Worksheet on Resonance
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Exercise 3D: Vectors and MotionEach
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244 Chapter 3 Conservation of Momen
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An overhead view of apiece of putty
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inward toward the hinge will have n
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special case, we can choose to visu
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j / Two asteroids collide.k / Every
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Note that although the factors of 2
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Relationship between force and torq
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is straight down, which is perpendi
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⊲ All three objects in the figure
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aa / Example 10.to either side of e
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momentum tells us that L = mrv sin
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In the absence of any torque, a rig
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Radial acceleration at the surface
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The parallel axis theorem example 1
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differential. The result isarea ===
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of inertia as if the object was smo
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h / Moments of inertia of somegeome
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4.3 Angular Momentum In Three Dimen
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14 deg, and it points along an axis
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manner like this, then the definiti
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k / Example 27.torque to the left w
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We can also generalize the plane-ro
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Problem 1.Problem 6.Problem 8.Probl
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14 (a) The bar of mass m is attache
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Problem 22.22 The sun turns on its
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35 The nucleus 168 Er (erbium-168)
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ExercisesExercise 4A: TorqueEquipme
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pesky set of constraints on heat en
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mit more air into the cavity behind
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Pressure of lava underneath a volca
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h / A simplified version of anideal
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for us to construct a simple connec
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For the first time we have an inter
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a / 1. The temperature differencebe
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Carnot engines operating between a
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from A to B, he lets it by, but whe
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B When we run the Carnot engine in
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f / A phase space for a singleatom
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time, the energy sharing is very un
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will the the one that maximizes the
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If the gas is monoatomic, then we k
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5.4.4 The arrow of time, or “this
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5.4.6 Summary of the laws of thermo
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may be in the form of microscopic d
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significant amount of heat to flow
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while the smaller area under the bo
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7 (a) Determine the ratio between t
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338 Chapter 5 Thermodynamics
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end of this book, we’ll even see
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c / As the wave pattern passes the
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the wave move ahead faster and get
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k / Hitting a key on a pianocauses
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Our final result for the speed of t
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care, because the delay is the same
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An easy way to visualize this is in
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can be constructed as a superpositi
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⊲ Looking up the speed of light i
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scientists, to speak of the Big Ban
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6.2 Bounded WavesSpeech is what sep
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d / An uninverted reflection. There
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our intuitive expectation of strong
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valid solutions. In the following s
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j / In the mirror image, theareas o
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m / A pulse bounces backand forth.i
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q / Graphs of loudness versusfreque
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s / Standing waves on a rope. (PSSC
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“cavity” and “neck” parts o
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Problem 5.Problem 8.5 The figure sh
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Problem 16.16 A Fabry-Perot interfe
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c / Newton’s laws do not distingu
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f / The correspondence principlereq
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d / A Galilean version of therelati
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g / Three types of transformations
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system, velocities are always unitl
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p / Apparatus used for the testof r
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sumption, the assumption that it ma
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at rest relative to the water. But
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7.2.4 No action at a distanceThe Ne
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so that Alice can complete her moti
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time into different regions accordi
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position relative to the sun at exa
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7.2.7 ⋆ Four-vectors and the inne
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would depend on the relative veloci
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7.3 DynamicsSo far we have said not
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In this frame, as expected, the sma
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But this whole argument was based o
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meters per second, so converting to
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Expressing γ as ( 1 − v 2 /c 2)
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7.3.4 ⋆ ProofsThis optional secti
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these lines. For example, a car sit
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An Einstein’s ring. Thedistant ob
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two-dimensional universe as if it w
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h / 1. A ray of light is emittedupw
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object that that isn’t influenced
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it impossible for any observer to b
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a variant on the Penrose singularit
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in it. Instead, it is currently spe
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2 Astronauts in three different spa
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(d) Simplify your answer to part c
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Problem 25b. Redrawn fromVan Baak,
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ExercisesExercise 7A: The Michelson
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Exercise 7B: Sports in Slowlightlan
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448 Chapter 7 Relativity
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Exercise 7D: Misconceptions about R
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452 Chapter 7 Relativity
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sun, moon, stars, and planets were
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Two types of chargeWe can easily co
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the other acquires an equal amount
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to get the beam up to speed in the
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telling us that we know about matte
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the muddle. The row-and-column sche
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the force of air friction canceled
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ectly evaluate the implications of
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that they were indeed electrically
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C Thomson found that the m/q of an
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the object with a net positive char
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thickness of material the radioacti
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It was already known that although
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particle. It turned out that it was
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For example they could easily strip
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cording to Mosely, the atomic numbe
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that fly off to see what was inside
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solution was found by measuring the
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o / A nuclear power plant at Catten
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neutrons. In a nuclear fission bomb
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We can now list all four of the kno
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1. Our sun’s source of energy is
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a / The known nuclei, represented o
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killed, because the DNA becomes una
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e / Wild Przewalski’s horsesprosp
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Problem 1. Top: A realisticpicture
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12 The subatomic particles called m
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ExercisesExercise 8A: Nuclear decay
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saxophone, every technological tool
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Example 1Ions moving across a cell
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ut the original meaning was to trav
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Force depends only on position. Sin
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Here are a few questions and answer
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flow through it.For many substances
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superconductivity in metals that wo
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j / Example 9. In 1 and 2,charges t
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look like the usual resistor. The f
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9.1.5 Current-conducting properties
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attery acid becomes depleted of hyd
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9.2 Parallel and Series CircuitsIn
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to each resistance, resulting inI t
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where “...” means that the sum
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the two resistors in figure h/3.We
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Choice of high voltage for power li
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A complicated circuit example 20⊲
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Problem 2.ProblemsThe symbols √ ,
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Problem 16.only count that as one u
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knob turned all the way clockwise,
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A printed circuit board, likethe ki
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ExercisesExercise 9A: Voltage and C
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Exercise 9C: Reasoning About Circui
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556 Chapter 9 Circuits
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a / A bar magnet’s atoms are(part
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defined. The ship’s captain can m
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Reduction in gravity on Io due to J
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j / Example 3.self-check AFind an e
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a dipole moment — they are define
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10.2.1 One dimensionVoltage is elec
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The interpretation is that if you b
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Figure c shows some examples of way
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For large values of d, this express
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where Q is the total charge of the
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g / Example 12: variation of the fi
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corners to the disk and transform i
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10.4 Energy In Fieldsa / Two opposi
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self-check DWe can think of the qua
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of the inward field contributed by
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space, 2 while charge doesn’t, we
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a / The symbol for a capacitor.b /
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ounding each capacitor will be half
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in time:x ↔ qv ↔ Iself-check GH
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due to its own momentum. It perform
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or|V | =∣ LdIdt ∣ ,which in man
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the inductor resists such a sudden
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Example 26.Death by solenoid; spark
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ordering.( 1 √2+√ i ) 2 = √ 1
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x / The complex number e iφlies on
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Figure aa shows a useful way to vis
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Inductors tend to be big, heavy, ex
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The reason for using the trig ident
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a purely inductive or capacitive lo
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Resonance with damping example 33
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orE outward, on side 1 A + E outwar
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|E| = kq totalr 2 ,where r is the r
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y considering its point charges ind
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Discussion Questionsg / Discussion
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with charge, change the Coulomb con
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The symmetry between the two sides
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where dv is the volume of the cube.
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The three terms in the divergence a
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Problem 19.Problem 20.proton, for e
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the lightning strike.(b) Based on y
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units.(b) Verify that RC has units
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lating freely (without any driving
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ExercisesExercise 10A: Field Vector
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5. Now hook up the two solenoids in
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A large current is createdby shorti
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time I used it implicitly was in fi
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f / A standard dipole madefrom a sq
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and substituting q = λh and v = m/
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o / Magnetic forces cause abeam of
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electric field, a magnetic one, can
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u / In this scene from SwanLake, th
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so the total field in the z directi
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For the y component, we havee / A s
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We can pin down the result even mor
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i / The field of a dipole.where r i
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circulates around the y axis, so at
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to be, not where it is now. Coulomb
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We have found one specific example
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to a flagpole, we can cancel out a
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11.4 Ampère’s Law In Differentia
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y evaluating the field at the midpo
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i.e.,F = axˆx + byˆx + cˆx + dx
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k / A summary of the derivative, gr
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c / Detail from Ascending andDescen
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the magnet. Are these atomic curren
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field in her region of space has be
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A changing magnetic flux makes a cu
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nearly zero. By Faraday’s law, th
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c / An Ampèrian surface superimpos
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and Maxwell’s equations becomeΦ
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k / Red and blue light travelat the
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second, the zero-point is located a
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is the magnitude of the momentum ve
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Discussion question A.Discussion qu
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only penetrates to a very small dep
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elationship D = ɛE would actually
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esulting in cancellation.The opposi
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a low permeability, while the other
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n / A fluxgate compass.is externall
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6 Two parallel wires of length L ca
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an instant at the upper right, but
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Problem 25.20 Four long wires are a
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Problem 35.Problem 37.32 Verify Amp
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Problem 42.beam of light usually co
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(c) Discuss the relationship betwee
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(f) Use conservation of energy to r
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5. Now position yourself with your
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12.1.1 The nature of lightThe cause
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An image of Jupiter andits moon Io
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d / Two self-portraits of theauthor
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ultimate truth about light, but the
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• There is a tendency to conceptu
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self-check AEach of these diagrams
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m / Discussion question B.Discussio
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12.2 Images by ReflectionInfants ar
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Discussion QuestionA The figure sho
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down magnification is AB/DE. A repe
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i / A Newtonian telescopebeing used
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B Locate the images formed by two p
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12.3 Images, QuantitativelyIt sound
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⊲ The object and image angles are
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12.3.2 Other cases with curved mirr
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signs also have to be memorized for
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h / A diverging mirror in the shape
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j / Spherical mirrors are thecheape
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general type of eye that we share w
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shown on this graph and then attemp
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the mechanical model would predict
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that your calculator will flash an
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D Classify the examples shown in fi
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12.4.6 ⋆ Microscopic description
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12.5 Wave OpticsElectron microscope
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of a crystal? Sound waves are used
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j / Thomas Youngk / Double-slit dif
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object that diffracts it, so the tr
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Although the equation λ/d = sin θ
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things we’ve learned about diffra
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apidly changing distances; on reuni
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6 The figure on the next page shows
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14 Here’s a game my kids like to
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27 Suppose a converging lens is con
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same depth, but not quite. [Check:
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Problem 42.42 Panel 1 of the figure
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46 The figure below shows two diffr
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53 The beam of a laser passes throu
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Problem 59.the ancient problem of i
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3. Now imagine the following new si
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Exercise 12B: Object and Image Dist
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Exercise 12D: Double-Source Interfe
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Exercise 12E: Single-slit diffracti
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Exercise 12F: Diffraction of LightE
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energy, instead of being spread out
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correlated. If they have been playi
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small.The statement that the rule f
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But the y axis can no longer be a u
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for a long time once it gets there,
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j / Calibration of the 14 C dating
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given by(probability of a ≤ x ≤
Page 836 and 837:
k / In recent decades, a huge hole
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A wave is partially absorbed.c / A
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f / The hamster in her hamsterball
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How would you extract h from the gr
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F Does E = hf imply that a photon c
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of approaching this issue.)j / Bull
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We assume v is small enough so that
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the probability distribution will b
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trons that we have already used for
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equations of general validity are t
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wave carries high probability and w
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An infinite sine wave can only tell
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momentum implies a definite kinetic
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of snapshots would amount to a desc
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close are the electrons to the limi
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dimensional particle in a box, and
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Applying this to conservation of en
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the probability of making it throug
Page 872 and 873:
Three dimensionsFor simplicity, we
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1. Oscillations can go backand fort
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C The figure shows a skateboarder t
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a / Eight wavelengths fit aroundthi
Page 880 and 881:
As shown by these examples, the unc
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e / The three states of the hydroge
Page 884 and 885:
f / The energy levels of a particle
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∂r/∂x = x/r comes in handy. Com
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50% of its time in each atom. It’
Page 890 and 891:
tus to the z axis) and more memorab
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ut why does that have anything to d
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the data are only inaccurate due to
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14 The photoelectric effect can occ
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Problem 25.(b) Sketch a graph showi
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conservation of energy and momentum
Page 902 and 903:
Problem 43.43 On pp. 884-885 of sub
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ExercisesExercise 13A: Quantum Vers
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⊲ First we convert the equation i
Page 908 and 909:
Programming With PythonThe purpose
Page 910 and 911:
Appendix 2: MiscellanyUnphysical
Page 912 and 913:
18 bestt = t19 c1 = bestc120 c2 = b
Page 914 and 915:
p i + ∑ iThe spin theoremTheorem:
Page 916 and 917:
Appendix 3: Photo CreditsExcept as
Page 918 and 919:
Appendix 4: Hints and SolutionsHint
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Hints for Chapter 6Page 377, proble
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Answers to Self-Checks for Chapter
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Page 301: (1) Not valid. The equati
Page 926 and 927:
Page 584:N −1 m −2 C 2 V 2 m
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the dashed ray.Page 748: You should
Page 930 and 931:
direction it was initially going (i
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Page 52, problem 38: The cone of mi
Page 934 and 935:
Page 224, problem 37: (a) Spring co
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object, we have static friction, wh
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Page 549, problem 29:(a) Conservati
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Page 798, problem 19: (a) The objec
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.0.8 Notation and unitsquantity uni
Page 944 and 945:
surfaces. For comparison, a typical
Page 946 and 947:
elations:a = ∆v∆tx = 1 2 at2 +
Page 948 and 949:
we are moving along with the projec
Page 950 and 951:
the number of oscillations required
Page 952 and 953:
In general, the cross product of ve
Page 954 and 955:
Sound waves consist of increases an
Page 956 and 957:
signs for charge is that with this
Page 958 and 959:
know that there is a delay in time
Page 960 and 961:
is related byΦ = 4πkq into the ch
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to use sophisticated models such as
Page 964 and 965:
Chapter 13, Quantum Physics, page 8
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oth position and momentum, the Heis
Page 968 and 969:
Schrödinger’s, 864cathode rays,
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unstable, 87equipartition theorem,
Page 972 and 973:
Joule, James, 73paddlewheel experim
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Einstein’s early theory, 838energ
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Nikola, 178tesla (unit), 652thermal
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Simple Nature - Light and Matter

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