MOTION MOUNTAIN

344 challenge hints and solutions
Ref. 16
Page 53
Page 62
Challenge 25, page 47: Only boosts with relativistic speeds mix magnetic and electric fields to
anappreciableamount.
Challenge 27, page 48: Thedualfield∗Fisdefined onpage75.
Challenge 29, page 50: X-rays production needs high concentration of energy; such levels are
impossibleinbiologicalsystems.
Challenge 30, page 50: Electric waves of low frequency are produced in nervous systems, and
inbrainsinparticular.Asmentionedabove,variousfishcommunicateviatime-varying electric
dipolefields. But no communication via radiowaves has ever been found. In fact, there is little
hopethatsuchsystemsexist.Why?(Hint:pondertheinvolvedfrequencies,theirgeneration,and
thephysicalpropertiesofwaterandair.)
Challenge 33, page 53: Almostall neutral particles are made of charged ones.So theargument
holds for them as well. There is only one exception: neutrinos. For them, the argument is not
valid.However,evenneutrinoshavechargedvirtualparticlesaroundthem,sothatthemaximum
speedalsoappliestothem.
Challenge 28, page 49: Scalar products of four vectors are always, by construction,Lorentz invariantquantities.
Challenge 34, page 53: Asexplainedearlieron, foranobserverwhofliesalongthewire,theentranceandexiteventsforcharges
atthetwoendseventsdonotoccursimultaneouslyanymore;
the wire is charged for a moving observer. Thus there is a magnetic field around a wire for any
movingobserver.
Challenge 35, page 55: The illumination of the sun changes the ionization in the upper atmosphereandprovokes
convection intheionosphere.Thetides move theionsintheocean andin
the atmosphere. These currents lead to magnetic fields which can be seen in sensitive compass
needles.
Challenge 36, page 55: If you find such an effect and are able to demonstrate it, publish it in a
didacticjournal.
Challenge 37, page 56: Usually,thecablesofhighvoltagelinesaretoowarmtobecomfortable.
Challenge 38, page 56: MovethemtoformaTshape.
Challenge 39, page 56: Hint:ashiningbulbishot.
Challenge 40, page 56: For three and more switches, on uses inverters; an inverter is a switch
with two inputsand two outputs whichin oneposition,connects firstand second inputto first
and second output respectively, and in the other positionconnects thefirst input to the second
output and vice versa. (There are other possibilities, though; wires can be saved using electromagneticrelay
switches.)
Challenge 42, page 57: Blond children tend to have the thinnest hair, thus giving the greatest
effect. Dry weatherisneeded toavoidthatthemoistureintheairdischarges thehead thuspreventingthehairtoraiseatall.
Challenge 43, page 57: Itispossible;however,thesystemssofararenotsmallandaredangerous
forhumanhealth.TheideatocollectsolarpowerindeepspaceandthenbeamittotheEarthas
microwaveshasoftenbeenaired.Financesanddangers haveblockeditsofar.
Challenge 45, page 58: Gluetwomirrorstogetheratarightangle.OrwatchyourselfonTVusingavideo
camera.
Challenge 46, page 59: Thisisagainanexample ofcombined triboluminescenceandtriboelectricity.
See also the websites scienceworld.wolfram.com/physics/Triboluminescence.html and
www.geocities.com/RainForest/9911/tribo.htm.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net