MOTION MOUNTAIN

28 1 electricity and fields
Challenge 12 s
Challenge 13 e
Vol. V, page 117
Challenge 14 s
Challenge 15 s
This mathematical relation, calledGauss’s ‘law’,* from the result of Coulomb. (Note that
in the simplified form given here, it is valid only for static situations.) Since inside conductorstheelectricalfieldiszero,Gauss’s
‘law’ implies,forexample,thatifachargeqis
surroundedby an uncharged metal sphere,the outer surfaceof themetal sphereshows
thesamechargeq.
Do uncharged, neutral bodies attract one other? In first approximation they do not.
But when the question is investigated more precisely, we will find that they can attract
one other. Can you find the conditions for this to happen? In fact, the conditions are quite
important, as our own bodies, which are made of neutral molecules, are held together in
this way.
Pumping charge
Owing to the high strength of electromagnetic interactions, separating charges is not an
easy task. This is the reason that electrical effects have only been commonly used for
about a hundred years. Humanity had to wait for practical and efficient devices to be
invented for separating charges and putting them into motion: to use electric effects,
we need charge pumps. Some devices are shown in Figure 11. Can you explain whether
batteries or any other of these devices are sources of charges?
Of course, every charge pump requires energy. Batteries in mobile phones and the ion
channels in living cells use chemical energy to do the trick.Thermoelectric elements, as
used in some watches, use the temperature difference between the wrist and the air to
separate charges; solar cells use light, piezoelectric elements use stress and dynamos or
Kelvin generators use kinetic energy.
What is electricity?
The answer to this question is:Electricity is more the name for a field of inquiry, and less
the name for any specific observation or effect. Electricity is not a specific term; the term
is used to refer to the effects of electric charges, of their motion and their fields.
In fact the vocabulary issue hides a deeper question: what is the nature of electric
charge? In order to solve this issue, we start with the following question.
Can we detect the inertia of electricity?
If electric charge really is somethingflowing through metals, we should be able to observe
the effects shown in Figure 12: electric charge should fall, should have inertia and should
*Carl-FriedrichGauß(b.1777Braunschweig,d.1855 Göttingen)was,togetherwiththeLeonhardEuler,the
mostimportantmathematicianofalltimes.Afamouschildprodigy,whenhewas19yearsold,heconstructed
the regular heptadecagon with compass and ruler (see www.mathworld.wolfram.com/Heptadecagon.
html).Hewassoproudofthisresultthatheputadrawingofthefigureonhistomb.Gaussproducedmany
resultsinnumbertheory,topology,statistics,algebra,complexnumbersanddifferentialgeometrywhichare
partofmodernmathematicsandbearhisname.Amonghismanyaccomplishments,heproducedatheory
ofcurvatureanddevelopednon-Euclideangeometry.Healsoworkedonelectromagnetismandastronomy.
Gauss was a difficult character, worked always for himself, and did not found a school. He published
little,ashismottowas:paucasedmatura.Asaconsequence,whenanothermathematicianpublishedanew
result, he regularly produced a notebook in which he had noted the very same result already years before.
Thesenotebooksarenowavailable online,atwww.sub.uni-goettingen.de.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net