MOTION MOUNTAIN

challenge hints and solutions 355
Page 30
Vol. II, page 166
Challenge 216, page 223: Ideal absorption is blackness (though it can be redness or whiteness
at higher temperatures).
Challenge 217, page 224: Indeed, the Sun emits about4⋅10 26 W from its mass of2⋅10 30 kg,
about0.2 mW/kg. The adult human body (at rest) emits about100 W (you can check this in
bed at night), thus about1.2 W/kg. This is about 6000 times more than the Sun. The reason:
only the very centre of the Sun actually emits energy. If that energy amount is then divided by
the full mass, including all the mass that does not emit energy at all, one gets a small average
value. By the way, any candle or, better, any laser pointer emits even more light per mass, for
similar reasons.
Challenge 218, page 224: The charges on a metal box rearrange so that the field inside remains
vanishing.This makes cars and aeroplanes safe against lightning. Of course, if the outside field
varies so quickly that the rearrangement cannot follow, fieldscan enter the Faraday cage. (By the
way, also fields with long wavelengths penetratemetals;specialized remotecontrolsforopening
security doorsregularly use frequencies of25 kHz to achieve this.) However, one should wait a
bit before stepping out of a car after lightning has hit, as the car is on rubber wheels with low
conduction;waitinggives thechargetimetoflowintotheground.
For gravity and solid cages, mass rearrangement is not possible, so that there is no gravity
shield.
Mu-metalisanickel-ironalloy,oftencontainingtracesofothermetals,thathasahighrelative
permeabilityμ r intherangeof50000to140000;itisastonishinglyductile.Thehighpermeability
valueeffectivelyconcentratesthemagneticfieldsinsidethealloyandthusleadsappliedmagnetic
fields through the mu-metal and around the enclosed volume, which therefore is shielded as a
result.
Challenge 222, page 225: Thisisatouchytopic.Itisnotclearwhether50 Hzfieldsaredangerous
tohumans.Thereisahighprobabilitythattheyarenot;buttheissueisnotsettled.
Challenge 223, page 226: Thenumberofphotonstimesthequantumofactionħ.
Challenge 224, page 226: First,Faradaycouldhavefoundasuperficiallinkusingthementioned
tube experiment. But he was looking for a possibledeep connection. However, gravitation and
electricity are not at all connected, as one is due to mass, the other due to charge. Much after
Faraday, people discovered that gravity also includes gravitomagnetism, i.e., measurable effects
duetomovingmasses –butstillnorelationtoelectromagnetism.Adistantconnectionbetween
gravitationandelectricity willonlyappearinthelastvolume.
Challenge 225, page 226: The charging stops because a negatively charged satellite repels electronsandthusstopsanyelectroncollectingmechanism.Electronsarecapturedmorefrequently
thanionsbecauseitiseasierforthemthanforionstohaveaninelasticcollisionwiththesatellite,
duetotheirlarger speedatagiventemperature.
Challenge 226, page 226: Any lossmechanismwill explain thelossof energy, suchaselectrical
resistanceorelectromagneticradiation.Afterafractionofasecond,theenergywillbelost.This
littleproblemisoftendiscussedontheinternet.
Challenge 227, page 226: UsethewireasshowninFigure177.If theoscillationisproperlytuned
in frequency, and if the contact detaches properly at the tip, and if you touch the two contacts
withastronggrip,youwill getastrongershockthanyoucanstand.
Challenge 229, page 227: This should be possible in the near future; but both the experiment,
whichwillprobablymeasurebrainmagneticfielddetails,andtheprecisecheckofitsseriousness
willnotbesimple.
Challenge 230, page 227: No,thesystemisnotsecure.Inanysystem,thesecurityisgivenbythe
weakestspot.Andinanypasswordsystem,theweakest spotsarethetransportoftherawdata–
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net