MOTION MOUNTAIN

challenge hints and solutions 345
Challenge 49, page 61: Pepper is lighter than salt, and thus reacts to the spoon before the salt
does.
Challenge 50, page 64: For a wavelength of546.1 nm (standard green), that is a bit over 18
wavelengths.
Challenge 51, page 64: Theangular sizeoftheSunistoolarge; diffractionplaysnorolehere.
Challenge 52, page 64: Justuseahighspeed camera.
Challenge 53, page 64: The current flows perpendicularly to the magnetic field and is thus deflected.Itpulls
thewholemagnetwithit.
Challenge 54, page 66: The most simple equivalent to a coil is a rotating mass being put into
rotationbytheflowingwater.Atransformerwouldthenbemadeoftwosuchmassesconnected
throughtheiraxis.
Challenge 55, page 66: Lightmakes seventurnsoftheEarth inonesecond.
Challenge 59, page 67: Therearenopermanentmagnetsinnaturethatfitinafloorandthatare
strong enough to achieve a floating height of 50 to80 cm. (Note that in one image the floating
heightissolargethatthelegsofthewomandonottouchthefloor.)Andanybodywhohastried
thiswithanelectromagnet knowsthatsuchadevicewould belarger thanacompleteroom.
Looking carefully at the images, you will also note that they are not photographs: there are
errors with the shadow and with the reflected image of the woman. And most of all, nobody
would cuthalf thebed outofanimagewithawomanonthebed.Finally, nobodyhasever seen
thefloatingbedshownintheimages.
Challenge 61, page 69: Themathematicsrequired tofindthesolutionisfascinating.Exploreit!
Challenge 62, page 69: Thecharged layerhastheeffect thatalmostonlyionsofonechargepass
the channels. As a result, charges are separated on the two sides of the liquid, and a current is
generated.
Challenge 63, page 69: Theattractionatlowdistancesisduetothe ‘imageforce’,theattraction
of a charge to any conducting surface. Measuring the distancedfrom the centre of the sphere,
therepulsionofthepointchargestartsforvaluesd>1.618R.
Challenge 64, page 69: Leakagecurrentschangethepicture.Thelongtermvoltageratioisgiven
bytheleakage resistanceratioV 1 /V 2 =R 1 /R 2 ,ascanbeeasilyverified inexperiments.
Challenge 65, page 70: The wire parallel to the high voltage line forms a capacitor. The voltage
differencethatappearsissufficienttotrigger theneonlamp.
Challenge 66, page 70: The water disrupts the small discharge sparks, called aigrettes. When a
newoneappears,itmakes asmall noise.Then,withthearrival ofnewwater,theyaredisrupted
again,and the process repeats. Aigrettes are a form of corona discharge; the also lead to power
lossesandtoradiointerference.
Challenge 67, page 70: Seeabove,inthesectiononinvariants.
Challenge 70, page 72: Themodeldoesnotworkinthreedimensions.Anattempttocorrectthis
isF. De Flaviis, M. Noro & N.G. Alexopoulos, Diaz-Fitzgeraldtimedomain (D-FTD)
methodappliedtodielectricandlossy materials,preprintavailableonline.
Challenge 71, page 72: Search on the web, for example on the pages blog.biodiversitylibrary.
org/2012/06/narwhal-oceans-one-toothed-wonder.html or narwhalslefttooth.blogspot.de/2011/
05/narwhal-tusk-debate.html.
Challenge 76, page 78: Somemomentum,usually avery smallpart,iscarried awaybytheelectromagnetic
field. Given that the electromagnetic momentum is given by the vector potential,
areyouabletocheckwhethereverything comesoutright?
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net