Simple Nature - Light and Matter

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Discussion question A.Discussion question B.Discussion questions C andD.a single thing traveling in a single direction, whereas no such assumptionwas made in arguing for the E × B form. For instance, iftwo light beams of equal strength are traveling through one another,going in opposite directions, their total momentum is zero, which isconsistent with the E × B form, but not with U/c.Some examples were given in chapter 3 of situations where itactually matters that light has momentum. Figure q shows the firstconfirmation of this fact in the laboratory.Angular momentum of light wavesFor completeness, we note that since light carries momentum, itmust also be possible for it to have angular momentum. If you’vestudied chemistry, here’s an example of why this can be important.You know that electrons in atoms can exist in states labeled s, p,d, f, and so on. What you might not have realized is that theseare angular momentum labels. The s state, for example, has zeroangular momentum. If light didn’t have angular momentum, then,for example, it wouldn’t be possible for a hydrogen atom in a p stateto change to the lower-energy s state by emitting light. Conservationof angular momentum requires that the light wave carry away allthe angular momentum originally possessed by the electron in thep state, since in the s state it has none.Discussion QuestionsA Positive charges 1 and 2 are moving as shown. What electric andmagnetic forces do they exert on each other? What does this imply forconservation of momentum?B 1. The figure shows a line of charges moving to the right, creatinga current I. An Ampèrian surface in the form of a disk has been superimposed.Use Maxwell’s equations to find the field B at point P.2. A tiny gap is chopped out of the line of charge. What happens whenthis gap is directly underneath the point P?C The diagram shows an electric field pattern frozen at one moment intime. Let’s imagine that it’s the electric part of an electromagnetic wave.Consider four possible directions in which it could be propagating: left,right, up, and down. Determine whether each of these is consistent withMaxwell’s equations. If so, infer the direction of the magnetic field.D Discuss what happens to the wave pattern shown in the diagram ifwe switch to a frame of reference moving along with the wave.706 Chapter 11 Electromagnetism
11.7 Electromagnetic Properties of MaterialsDifferent types of matter have a variety of useful electrical and magneticproperties. Some are conductors, and some are insulators.Some, like iron and nickel, can be magnetized, while others haveuseful electrical properties, e.g., dielectrics, discussed qualitativelyin the discussion question on page 592, which allow us to makecapacitors with much higher values of capacitance than would otherwisebe possible. We need to organize our knowledge about theproperties that materials can possess, and see whether this knowledgeallows us to calculate anything useful with Maxwell’s equations.11.7.1 ConductorsA perfect conductor, such as a superconductor, has no DC electricalresistance. It is not possible to have a static electric fieldinside it, because then charges would move in response to that field,and the motion of the charges would tend to reduce the field, contraryto the assumption that the field was static. Things are a littledifferent at the surface of a perfect conductor than on the interior.We expect that any net charges that exist on the conductor willspread out under the influence of their mutual repulsion, and settleon the surface. As we saw in chapter 10, Gauss’s law requires thatthe fields on the two sides of a sheet of charge have |E ⊥,1 − E ⊥,2 |proportional to the surface charge density, and since the field insidethe conductor is zero, we infer that there can be a field on or immediatelyoutside the conductor, with a nonvanishing componentperpendicular to the surface. The component of the field parallelto the surface must vanish, however, since otherwise it would causethe charges to move along the surface.On a hot summer day, the reason the sun feels warm on yourskin is that the oscillating fields of the light waves excite currentsin your skin, and these currents dissipate energy by ohmic heating.In a perfect conductor, however, this could never happen, becausethere is no such thing as ohmic heating. Since electric fields can’tpenetrate a perfect conductor, we also know that an electromagneticwave can never pass into one. By conservation of energy, weknow that the wave can’t just vanish, and if the energy can’t bedissipated as heat, then the only remaining possibility is that all ofthe wave’s energy is reflected. This is why metals, which are goodelectrical conductors, are also highly reflective. They are not perfectelectrical conductors, however, so they are not perfectly reflective.The wave enters the conductor, but immediately excites oscillatingcurrents, and these oscillating currents dissipate the energy both byohmic heating and by reradiating the reflected wave. Since the partsof Maxwell’s equations describing radiation have time derivatives inthem, the efficiency of this reradiation process depends strongly onfrequency. When the frequency is high and the material is a goodconductor, reflection predominates, and is so efficient that the waveSection 11.7 Electromagnetic Properties of Materials 707
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Fullerton, Californiawww.lightandma
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Contents0 Introduction and Review0.
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5.5 More About Heat Engines . . . .
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669.11.3 Magnetic Fields by Ampère
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The Mars Climate Orbiter is prepare
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temperatures and with many combinat
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idence that quarks have smaller par
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give clearer explanations.Finally,
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It can also be handy to have a rela
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The prefix centi-, meaning 10 −2
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goes like this:V = 1 3 Ah[1]A = πr
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the notation 10 0 to stand for one,
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calculation, 5.04 cm, was really no
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0.2 Scaling and Order-of-Magnitude
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to many times your own height. The
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g / 1. This plank is as long as it
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the front panels of the three violi
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Correct solution #4: The area of a
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here?” The scientific Mr. Spock w
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1. Don’t even attempt more than o
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Problem 10.mean, however, is define
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(d) Find the person’s acceleratio
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Albert Einstein, and his moustache,
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54 Chapter 0 Introduction and Revie
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a / Portrait of Monsieur Lavoisiera
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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/
Page 656 and 657: o / Magnetic forces cause abeam of
Page 658 and 659: electric field, a magnetic one, can
Page 660 and 661: u / In this scene from SwanLake, th
Page 662 and 663: so the total field in the z directi
Page 664 and 665: For the y component, we havee / A s
Page 666 and 667: We can pin down the result even mor
Page 668 and 669: i / The field of a dipole.where r i
Page 670 and 671: circulates around the y axis, so at
Page 672 and 673: to be, not where it is now. Coulomb
Page 674 and 675: We have found one specific example
Page 676 and 677: to a flagpole, we can cancel out a
Page 678 and 679: 11.4 Ampère’s Law In Differentia
Page 680 and 681: y evaluating the field at the midpo
Page 682 and 683: i.e.,F = axˆx + byˆx + cˆx + dx
Page 684 and 685: k / A summary of the derivative, gr
Page 686 and 687: c / Detail from Ascending andDescen
Page 688 and 689: the magnet. Are these atomic curren
Page 690 and 691: field in her region of space has be
Page 692 and 693: A changing magnetic flux makes a cu
Page 694 and 695: nearly zero. By Faraday’s law, th
Page 696 and 697: c / An Ampèrian surface superimpos
Page 698 and 699: and Maxwell’s equations becomeΦ
Page 700 and 701: k / Red and blue light travelat the
Page 702 and 703: second, the zero-point is located a
Page 704 and 705: is the magnitude of the momentum ve
Page 708 and 709: only penetrates to a very small dep
Page 710 and 711: elationship D = ɛE would actually
Page 712 and 713: esulting in cancellation.The opposi
Page 714 and 715: a low permeability, while the other
Page 716 and 717: n / A fluxgate compass.is externall
Page 718 and 719: 6 Two parallel wires of length L ca
Page 720 and 721: an instant at the upper right, but
Page 722 and 723: Problem 25.20 Four long wires are a
Page 724 and 725: Problem 35.Problem 37.32 Verify Amp
Page 726 and 727: Problem 42.beam of light usually co
Page 728 and 729: (c) Discuss the relationship betwee
Page 730 and 731: (f) Use conservation of energy to r
Page 732 and 733: 5. Now position yourself with your
Page 734 and 735: 12.1.1 The nature of lightThe cause
Page 736 and 737: An image of Jupiter andits moon Io
Page 738 and 739: d / Two self-portraits of theauthor
Page 740 and 741: ultimate truth about light, but the
Page 742 and 743: • There is a tendency to conceptu
Page 744 and 745: self-check AEach of these diagrams
Page 746 and 747: m / Discussion question B.Discussio
Page 748 and 749: 12.2 Images by ReflectionInfants ar
Page 750 and 751: Discussion QuestionA The figure sho
Page 752 and 753: down magnification is AB/DE. A repe
Page 754 and 755: 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
Page 794 and 795:
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
Page 814 and 815:
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
Page 824 and 825:
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
Page 854 and 855:
equations of general validity are t
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wave carries high probability and w
Page 858 and 859:
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
Page 866 and 867:
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
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As shown by these examples, the unc
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e / The three states of the hydroge
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f / The energy levels of a particle
Page 886 and 887:
∂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
Page 898 and 899:
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
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Appendix 4: Hints and SolutionsHint
Page 920 and 921:
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
Page 928 and 929:
the dashed ray.Page 748: You should
Page 930 and 931:
direction it was initially going (i
Page 932 and 933:
Page 52, problem 38: The cone of mi
Page 934 and 935:
Page 224, problem 37: (a) Spring co
Page 936 and 937:
object, we have static friction, wh
Page 938 and 939:
Page 549, problem 29:(a) Conservati
Page 940 and 941:
Page 798, problem 19: (a) The objec
Page 942 and 943:
.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
Page 962 and 963:
to use sophisticated models such as
Page 964 and 965:
Chapter 13, Quantum Physics, page 8
Page 966 and 967:
oth position and momentum, the Heis
Page 968 and 969:
Schrödinger’s, 864cathode rays,
Page 970 and 971:
unstable, 87equipartition theorem,
Page 972 and 973:
Joule, James, 73paddlewheel experim
Page 974 and 975:
Einstein’s early theory, 838energ
Page 976 and 977:
Nikola, 178tesla (unit), 652thermal
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Simple Nature - Light and Matter

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