MOTION MOUNTAIN

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346 challenge hints and solutions Poynting vector field cable, forward current Resistance-free cable cable, backward Loss-free transformer Poynting vector field F I G U R E 172 The Poynting vector field for a cable without electrical resistance and the situation a long transformer without losses. Challenge 77, page 79: Field lines and equipotential surfaces are always orthogonal to each other.Thusafield linecannotcrossanequipotentialsurfacetwice. Challenge 85, page 83: See Figure 172. If the cable is resistance-free, most of the energy flows justoutsidethetwoconductorsandparallel tothem.Ifthecabledoeshaveresistance,thePoynting vectors point slightly towards the conductors. For the case of a transformer, which can be deduced fromthecaseofthecablevia theanalogy sketched inthepicture,seethebeautiful paperbyF. Herrmann & G.B. Schmid, The Ponyting vector fieldand the energy flow withina transformer,AmericanJournalofPhysics54,pp.528–531,1986. Challenge 90, page 86: Theargumentisthesameasfortheincreaseinentropy:reverseprocesses arepossible,buttheprobabilityissolowthattheydonotappearinpractice.Theextremely low probabilityisduetothefluctuationsinduced bytheenvironment. Challenge 91, page 86: Justdrawacurrentthroughacoilwithitsmagneticfield,thendrawthe mirrorimageofthecurrent andredraw themagneticfield. Challenge 92, page 87: Other asymmetries in nature include the helicity of the DNA molecules Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net
challenge hints and solutions 347 Vol. V, page 233 making up the chromosomesand many other molecules in living systems, the right hand preference of most humans, the asymmetry of fish species which usually stay flat on the bottom of theseas. Challenge 93, page 87: Thisisnotpossibleatallusinggravitationalorelectromagnetic systems or effects. The only way is to use the weak nuclear interaction, as shown in the chapter on the nucleus. Challenge 94, page 87: The Lagrangian does not change if one of the three coordinates is changedbyitsnegativevalue. Challenge 95, page 88: Theimageflipsup:a90degree rotationturns theimageby180degrees. Challenge 96, page 88: ImagineEandBastheunitevectorsoftwoaxesincomplexspace.Then anyrotationoftheseaxesisalsoageneralized duality symmetry. Challenge 97, page 91: Theangular momentumwasputintothesystemwhenitwasformed. If we bring a point charge from infinity along a straight line to its final position close to a magnetic dipole, the magnetic force acting on the charge is not directed along the line of motion. It therefore creates a non-vanishing torque about the origin. See J.M. Aguirregabiria & A. Hernandez, The Feynman paradox revisited, European Journal of Physics 2, pp. 168–170, 1981. Challenge 98, page 92: Show that even though the radial magnetic field of a spherical wave is vanishing by definition, Maxwell’s equations would require it to be different from zero. Since electromagneticwavesaretransversal, itisalsosufficienttoshowthatitisimpossibletocomba hairy spherewithouthaving a(double) vortex ortwo simplevortices. Despite thesestatements, quantum theory changes the picture somewhat: the emission probability of a photon from an excited atominadegeneratestateisspherically symmetric exactly. Challenge 99, page 92: If the conservation of linear and angular momentum are taken intoaccount,thereisnoambiguityofthePoyntingvector.See,forexample,W.H. Furry,Examplesof momentum distributions in the electromagnetic field and inmatter, American Journal of Physics 37,pp.621–636,1969. Challenge 100, page 92: Theemitted radiationisstronglysuppressedbecausethesizeofthedipole(theplug)ismuchsmaller thanthewavelength ofthefield. Challenge 102, page 92: No. Neither electromagnetic motors nor coils have been found in any living system. Muscles, the most powerful actuators in biology, are mainly made of large numbers of electrostatic motors. The fundamental reason for this difference is the low efficiency of microscopicelectromagneticmotors,whichcontrastswiththehighefficiencyofmicroscopicelectrostaticmotors.Atmacroscopicsizes,theefficiency advantagesswitches. Challenge 104, page 99: Inevery caseofinterference,theenergy isredistributed intootherdirections.Thisisthegeneralrule; sometimesitisquitetrickytodiscoverthisotherdirection. Challenge 105, page 99: The author regularly sees about 7 lines; assuming that the distance is around20μm, thismakes about3μm per line.The wavelength must besmaller than this value and the frequency thus larger than100 THz. The actual values for various colours are given in thetableoftheelectromagnetic spectrum. Challenge 107, page 100: Thedistancelbetween thelinesofaninterference pattern isgiven by l=λd/s,wheredisthedistancetothescreen,andsisthesourceseparation. To learn more about interference and theconditionsfor its appearance, explore the concept ofFresnelnumber.Forexample,theFresnelnumberallowstodistinguishthe‘farfield’ fromthe ‘nearfield’,twosituationsthatoccurinmanywavephenomena. Challenge 108, page 101: He noted that when a prism produces a rainbow, a thermometer placedintheregionafterthecolourred showsatemperaturerise. Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net
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ChristophSchiller MOTION MOUNTAIN t
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Editiovicesima octava. Proprietassc
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DieMenschenstärken,die Sachenklär
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8 preface PHYSICS: Describing motio
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10 preface Your donation to the cha
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12 contents Do we see what exists?
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Light, Charges and Brains Inourques
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16 1 electricity and fields F I G U
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18 1 electricityandfields F I G U R
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24 1 electricity and fields TA B L
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34 1 electricityandfields F I G U R
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42 1 electricity and fields Oersted
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44 1 electricity and fields Vol. IV
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48 1 electricity and fields Ref. 24
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50 1 electricity and fields Page 21
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Vol. IV, page 231 Chapter 2 THE DES
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Chapter 3 WHAT IS LIGHT? Ref. 57 Pa
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96 3 what is light? Electric field
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98 3 what is light? spark transmitt
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102 3 what is light? primary infrar
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104 3 what is light? Page 84 gases
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106 3 what is light? Fre - Waveleng
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108 3 what is light? Challenge 110
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110 3 what is light? incoming light
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112 3 what is light? Ref. 70 Challe
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114 3 what is light? F I G U R E 69
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116 3 what is light? light Ref. 72
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118 3 what is light? light Challeng
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120 3 what is light? momentumLis gi
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132 3 what is light? The forerunner
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134 3 what is light? vocabulary. On
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138 3 what is light? B B Beam in A
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Chapter 4 IMAGES AND THE EYE - OPTI
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142 4 images and the eye - optics 2
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144 4 images and the eye - optics C
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Chapter 5 ELECTROMAGNETIC EFFECTS R
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236 7 the story of the brain F I G
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248 7 the story of the brain Vol. I
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254 7 the story of the brain ∗∗
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Chapter 8 THOUGHT AND LANGUAGE Ref.
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260 8 thought and language Vol. VI,
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268 8 thought and language Vol. IV,
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Page 388 and 389: CREDITS Acknowledgements Many peopl
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406 subject index A units 328 Aplys
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408 subject index C classical class
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414 subject index I infrared photog
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426 subject index W Wien’s Wien
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MOTION MOUNTAIN

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