Christoph Schiller
MOTION MOUNTAIN
the adventure of physics – vol.iii
light, charges and brains
www.motionmountain.net

Christoph Schiller
M M
e Adventure of Physics
Volume III
Light, Charges and Brains
Edition ., available as free pdf at
www.motionmountain.net
Editio vicesima quinta.
Proprietas scriptoris © Chrestophori Schiller
primo anno Olympiadis trigesimae.
Omnia proprietatis iura reservantur et vindicantur.
Imitatio prohibita sine auctoris permissione.
Non licet pecuniam expetere pro aliqua, quae
partem horum verborum continet; liber
pro omnibus semper gratuitus erat et manet.
Twenty-h edition.
Copyright ©  by Christoph Schiller,
the rst year of the th Olympiad.
is pdf le is licensed under the Creative Commons
Attribution-Noncommercial-No Derivative Works . Germany
Licence,whosefulltextcanbefoundonthewebsite
creativecommons.org/licenses/by-nc-nd/./de,
with the additional restriction that reproduction, distribution and use,
in whole or in part, in any product or service, be it
commercial or not, is not allowed without the written consent of

the copyright owner. e pdf le was and remains free for everybody
to read, store and print for personal use, and to distribute
electronically, but only in unmodied form and at no charge.
To Britta, Esther and Justus Aaron
τ µο δαµονι
Die Menschen stärken, die Sachen klären.
PREFACE
“
Primum movere, deinde docere.*
”
Antiquity
isbookiswrittenforanybodywhoiscuriousaboutnatureandmotion.Curiosity
about how people, animals, things, images and space move leads to many adventures.
is volume presents the adventures one encounters when exploring everything electric.
e story ranges from the weighing of electric current to the use of magnetic elds to
heal bone fractures and up to the understanding of the human brain.
In the structure of physics, shown in Figure , motion due to electricity is the most
fascinating aspect of the starting point at the bottom. Indeed, almost everything around
us is due to electric processes. e present introduction to electricity, magnetism, light
and the brain is the third of a six-volume overview of physics that arose from a threefold
aim that I have pursued since : to present motion in a way that is simple, up to date
and captivating.
In order to be simple, the text focuses on concepts, while keeping mathematics to the
necessary minimum. Understanding the concepts of physics is given precedence over
using formulae in calculations. e whole text is within the reach of an undergraduate.
In order to be up to date, the text is enriched by the many gems – both theoretical and
empirical – that are scattered throughout the scientic literature.
In order to be captivating, the text tries to startle the reader as much as possible. Read-
ing a book on general physics should be like going to a magic show. We watch, we are
astonished, we do not believe our eyes, we think, and nally we understand the trick.

When we look at nature, we oen have the same experience. Indeed, every page presents
at least one surprise or provocation for the reader to think about. Numerous interesting
challenges are proposed.
e motto of the text, die Menschen stärken, die Sachen klären,afamousstatementby
Hartmut von Hentig on pedagogy, translates as: ‘To fortify people, to clarify things.’ Clar-
ifying things – and adhering only to the truth – requires courage, as changing the habits
of thought produces fear, oen hidden by anger. But by overcoming our fears we grow
in strength. And we experience intense and beautiful emotions. All great adventures in
life allow this, and exploring motion is one of them. Enjoy it!
Munich,  November .
* ‘First move, then teach.’ In modern languages, the mentioned type of moving (the heart) is called motivat-
ing;bothtermsgobacktothesameLatinroot.
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 
Galilean physics, heat and electricity
Adventures: sport, music, sailing, cooking,
describing beauty and understanding its origin
(vol. I), using electricity, light and computers,
understanding the brain and people (vol. III).
Special relativity
Adventures: light,
magnetism, length
contraction, time
dilation and
E
0
= mc
2
(vol. II).
Quantum theory

Adventures: death,
reproduction, biology,
chemistry, evolution,
enjoying colours and
art, all high-tech
business, medicine
(vol. IV and V).
Quantum
theory with gravity
Adventures: bouncing
neutrons, under-
standing tree
growth (vol. V).
Final, unified description of
motion
Adventures: understanding
motion, intense joy with
thinking, calculating
couplings and
masses, catching
a glimpse
of bliss
(vol. VI).
G
c
h, e, k
PHYSICS:
Describing motion
with the least action principle.
Quantum field theory

Adventures: building
accelerators, under-
standing quarks, stars,
bombs and the basis of
life, matter, radiation
(vol. V).
How do
everyday,
fast and large
things move?
How do small
things move?
What are things?
Why does motion
occur? What are
space, time and
quantum particles?
General relativity
Adventures: the
night sky, measu-
ring curved space,
exploring black
holes and the
universe, space
and time (vol. II).
Classical gravity
Adventures:
climbing, skiing,
space travel,
the wonders of

astronomy and
geology (vol. I).
FIGURE 1 A complete map of physics: the connections are defined by the speed of light c,the
gravitational constant G, the Planck constant h, the Boltzmann constant k and the elementary charge e.
A  
In my experience as a teacher, there was one learning method that never failed to trans-
form unsuccessful pupils into successful ones: if you read a book for study, summarize
every section you read, in your own images and words, aloud.Ifyouareunabletodo
so, read the section again. Repeat this until you can clearly summarize what you read in
your own images and words, aloud. You can do this alone in a room, or with friends, or
while walking. If you do this with everything you read, you will reduce your learning and
reading time signicantly.
e most inecient learning method is to use a marker or to underline text: it wastes
time, provides false comfort and makes the text unreadable. Nobody marking text is an
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 
ecient learner. Instead, by repeating every section in your own images and words, aloud,
youwillsavetimeandmoney,enjoylearningfromgoodtextsmuchmoreandhatebad
texts much less. Masters of the method can use it even while listening to a lecture, in a
low voice, thus avoiding to ever take notes.
U  
Text in green, as found in many marginal notes, marks a link that can be clicked in a pdf
reader. Such green links are either bibliographic references, footnotes, cross references
to other pages, challenge solutions, or pointers to websites.
Solutions and hints for challenges are given in the appendix. Challenges are classied
as research level (r), dicult (d), standard student level (s) and easy (e). Challenges of
type r, d or s for which no solution has yet been included in the book are marked (ny).
F  
is text is and will remain free to download from the internet. I would be delighted to
receive an email from you at , especially on the following issues:

 What was unclear and should be improved?
Challenge 1 s
 What story, topic, riddle, picture or movie did you miss?
 What should be corrected?
In order to simplify annotations, the pdf le allows adding yellow sticker notes in
Adobe Reader. Alternatively, you can provide feedback on www.motionmountain.net/
wiki.Helponthespecicpointslistedonthewww.motionmountain.net/help.html web
page would be particularly welcome. All feedback will be used to improve the next edi-
tion. On behalf of all readers, thank you in advance for your input. For a particularly
useful contribution you will be mentioned – if you want – in the acknowledgements,
receive a reward, or both.
Your donation to the charitable, tax-exempt non-prot organisation that produces,
translates and publishes this book series is welcome! For details, see the web page www.
motionmountain.net/donation.html. If you want, your name will be included in the
sponsor list. ank you in advance for your help, on behalf of all readers across the world.
A paper edition of this book, printed on demand and delivered by mail to any ad-
dress, can be ordered at www.lulu.com/spotlight/motionmountain.Butaboveall,enjoy
the reading!
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
C
  L ,     
Fields:amber,lodestoneandmobilephones  •Howcanonemakelightning? 
•Electriccharge  •Electriceldstrength  •Pumpingcharge  •What
is electricity?  • Can we detect the inertia of electricity?  • Feeling electric
elds  • Magnets and other magnetic materials  • Can humans feel magnetic
elds?  • Magnetism and electricity  • How can one make a motor? 
• Which currents ow inside magnets?  •Magneticelds  •Electromag-
netism  • e invariants and the Lagrangian of electromagnetic elds  •e
uses of electromagnetic eects  • How motors prove relativity to be right  •
Curiosities and fun challenges about things electric and magnetic  • Hopping

electrons and the biggest disappointment of the television industry  •Howdo
nerves work?  • A summary: three basic facts about electricity 
  T     
e rst eld equation of electrodynamics  •esecondeldequationofelec-
trodynamics  •evalidityandtheessenceofMaxwell’seldequations  •
Colliding charged particles  • e gauge eld – the electromagnetic vector poten-
tial  • Energy and momenta of the electromagnetic eld  •eLagrangian
of electromagnetism  • e energy–momentum tensor and its symmetries of
motion  •Whatisamirror?  • What is the dierence between electric and
magnetic elds?  • Could electrodynamics be dierent?  •ebrain:the
toughest challenge for electrodynamics  • Challenges and fun curiosities about
electrodynamics  • Summary 
 W?
What are electromagnetic waves?  • Light as an electromagnetic wave  •
Polarization and electromagnetic waves 
• Light and other electromagnetic
waves  • e slowness of progress in physics  •Anotherlookatelectromag-
netic radiation  • How does the world look when riding on a light beam? 
• Can one touch light?  • War, light and lies  •Whatiscolour?  •Fun
with rainbows  • What is the speed of light? – Again  •Signalsandpredic-
tions  • Aether good-bye  • Challenges and fun curiosities about light 
• Summary on light 
  I    – 
Ways to produce images 
125 Light sources
Why can we see each other? Black bodies and the temperature of light  •Limits
to the concentration of light  •Measuringlightintensity •Otherlightand
radiation sources  • Radiation as weapon 
133 Images – transporting light
Making images with mirrors  • Does light always travel in a straight line? –

Refraction  • Bending light with tubes – bre optics  • 200 years too late
– negative refraction indices  • Metamaterials  •Lightaroundcorners–
diraction  • Beating the diraction limit  •Otherwaystobendlight •
How does one make holograms and other three-dimensional images?  •Images
through scanning  •Tomography 
154 e eye and the brain: observing images
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 
Do we see what exists?  • How can one make pictures of the inside of the
eye?  • How to prove you’re holy  • Challenges and fun curiosities about
images and the eye  • Summary on optics 
  E 
Is lightning a discharge? – Electricity in the atmosphere  •Doesballlightning
exist?  •Doesgravitymakechargesradiate? • Planetary magnetic elds 
•Levitation  • Matter, levitation and electromagnetic eects  •Challenges
and fun curiosities about electromagnetic eects 
  S     
Strong elds and gravitation  • Charges are discrete  •Howfastdocharges
move?  • Challenges and curiosities about charge discreteness 
  T    
Evolution  • Children, laws and physics  •Polymerelectronics  •
Why a brain?  • What is information?  •Whatismemory?  •e
capacity of the brain  • Curiosities about the brain 
  T  
What is language?  •Whatisaconcept?  • What are sets? What are
relations?  • Innity  • Functions and structures  •Numbers 
•Whyusemathematics?  • Is mathematics a language?  •Curiosities
and fun challenges about mathematics 
  C,     
Are physical concepts discovered or created?  • How do we nd physical

patterns and rules?  •Whatisalie?  • What is a good lie? 
• Is this statement true? – A bit about nonsense  • Curiosities and fun
challenges about lies and nonsense 
253 Observations
Have enough observations been recorded?  • Are all physical observables
known?  • Do observations take time?  • Is induction a problem in
physics? 
258 e quest for precision and its implications
What are interactions? – No emergence  •Whatisexistence?  •Do
things exist?  • Does the void exist?  • Is nature innite?  •Is
the universe a set?  • Does the universe exist?  •Whatiscreation? 
•Isnaturedesigned?  • What is a description?  •Reason,purpose
and explanation  • Unication and demarcation  •Pigs,apesandthe
anthropic principle  • Does one need cause and eect in explanations? 
• Is consciousness required?  •Curiosity  •Courage 
  C    
What can move?  • Properties of classical motion  •efutureofplanet
Earth  • e essence of classical physics – the innitely small and the lack of
surprises  • Why have we not yet reached the top of the mountain? 
  U,   
SI units  • e meaning of measurement  • Precision and accuracy of mea-
surements  •Limitstoprecision  •Physicalconstants  •Usefulnum-
bers 
 C   
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 
 B
 C
Acknowledgements  •Filmcredits  •Imagecredits 
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012

L, C  B
In our quest to learn how things move,
the experience of hiking and other motion
leadsustodiscoverthatimagesareproducedbycharges,
that charges move, accumulate and interact,
and that there is a smallest charge in nature.
Weunderstandwhatlovehastodowithmagnetsandamber,
why the brain is such an interesting device,
andwhatdistinguishesagoodfromabadlie.
C 
LIQUID ELECTRICITY, INVISIBLE
FIELDS AND MAXIMUM SPEED
W
 is light? e study of relativity le us completely in the dark, even though
e had embarked in it precisely to nd an answer to that question. True,
e have learned how the motion of light compares with that of objects. We
also learned that light is a moving entity that cannot be stopped, that light provides the
speed limit for any type of energy, and that light is our measurement standard for speed.
However, we haven’t learned anything about the nature of light itself.
Asecondquestionisopen:whatiscontact? We still do not know. e only thing we
learned in our exploration of relativity was that truly mechanical interactions do not exist.
Vol. II, page 76 Indeed, all interactions are due to exchange of particles. But which ones?
e answer to the questions about the nature of light and contact emerges only from
the study of those types of motion that are not related to gravitation. It turns out that the
key to the answers is the understanding of the ways magicians levitate objects.
If we make a list of motors found in this world,
Vol. I, page 199 we notice that gravitation hardly de-
scribes any type of motor. Neither the motion of sea waves, re and earthquakes, nor
that of a gentle breeze is caused by gravity. e same applies to the motion of muscles.*
Have you ever listened to your own heart beat with a stethoscope?

Challenge 2 e (Or use, as many med-
ical doctors do now, an MP player to record your heart beat.) Without having done so,
you cannot claim to have experienced the mystery of motion. Your heart has about 
million beats in your lifetime. en it stops.
It was one of the most astonishing discoveries of science that heart beats, sea waves
and most other cases of everyday motion, as well as the nature of light itself, are con-
nected to observations made thousands of years ago using two strange stones. ese
stones show that all those examples of motion that are called mechanical in everyday
life are, without exception, of electrical origin.
In particular, the solidity, the soness and the impenetrability of matter are due to
internal electricity; also the emission of light is an electrical process.
Ref. 1 As these aspects
are part of everyday life, we will leave aside all complications due to gravity and curved
space-time. e most productive way to study electrical motion is to start, as in the case
of gravity, with those types of motion which are generated without any contact between
the bodies involved.
*ephotographofacircularrainbowonpage  was taken in  from the Telstra Tower in Canberra
(© Oat Vaiyaboon).
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 ,      
FIGURE 2 Objects surrounded by fields: amber (c. 1 cm), lodestone (c. 1 cm) and mobile phone
(c. 10 cm) (© Philips).
water
pipe
comb
rubbed
on wool
FIGURE 3 How to amaze kids, especially i n dry weather (photo © Robert Fritzius).
F: ,    
e story of electricity starts with trees. Trees have a special relation to electricity. When

atreeiscut,aviscousresinappears.Withtimeitsolidiesand,aermillionsofyears,it
forms amber. When amber is rubbed with a cat fur, it acquires the ability to attract small
objects, such as saw dust or pieces of paper. is was already known to ales of Miletus,
one of the original seven sages, in the sixth century . e same observation can be
made with many other polymer combinations, for example with combs and hair, with
soles of the shoe on carpets, and with a television tube and dust. Children are always sur-
prised by the eect, shown in Figure , that a comb rubbed on wool has on running tap
water. e same eect can be produced with an air-lled rubber balloon rubbed on wool.
Another interesting eect can be observed when a rubbed comb is put near a burning
candle. (Can you imagine what happens?)
Challenge 3 ny
Another part of the story of electricity involves lodestone,anironmineralfoundincer-
tain caves around the world, e.g. in a region (still) called Magnesia in the Greek province
of essalia, and in some regions in central Asia. When two stones of this mineral are put
near each other, they attract or repel each other, depending on their relative orientation.
In addition, lodestone attracts objects made of cobalt, nickel or iron.
Today we also nd various small objects in nature with more sophisticated properties,
such as the one shown on the right of Figure .Someoftheseobjectsallowyoutotalk
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
    
with far away friends, others unlock car doors, still others enable you to switch on a
television.
All these observations show that in nature there are situations where bodies exert in-
uence on others at a distance. e space surrounding a body exerting such an inuence
is said to contain a eld. A (physical) eld is thus an entity that manifests itself by accel-
erating other bodies in a given region of space. A eld is space that changes momenta. If
you prefer, a eld is space that exerts forces. Or again, a eld is space with some extra
structure. Despite this extra structure, elds, like space, are invisible.
e eld surrounding the mineral found in Magnesia is called a magnetic eld and
the stones are called magnets.

Ref. 2 e eld around amber – called λεκτρον in Greek, from a
root meaning ‘brilliant, shining’ – is called an electric eld.enameisduetoaproposal
by the famous English physician and part-time physicist William Gilbert (–).
Objects surrounded by a permanent electric eld are called electrets.Electretsaremuch
less common than magnets; among others, they are used in certain loudspeaker systems.
e eld around a mobile phone is called a radio eld or, as we will see later, an elec-
tromagnetic eld. In contrast to the previous elds, it oscillates over time. We will nd
out later that many other objects are surrounded by such elds, though these are oen
very weak. Objects that emit oscillating elds, such as mobile phones, are called radio
transmitters or electromagnetic emitters.
Experiments show that elds have no mass. Without any material support, elds inu-
ence bodies over a distance. Fields are invisible. To make them imaginable, we just need
to colour them. Some ways to colour electric elds are shown in Figure .esegures
are the best way to imagine electric elds: they reproduce faithfully how the inventor of
the eld concept, Michael Faraday, imagined them.
For a long time, electric, magnetic and radio elds were rarely noticed in everyday
life.Indeed,inthepast,mostcountrieshadlawsthatdidnotallowproducingsuchelds
or building mobile phones or garage openers. Still today, laws severely restrict the prop-
erties of machines that use and produce such elds. e laws require that for any device
that moves, produces sound, or creates moving pictures, elds need to remain inside the
device. For this reason a magician moving an object on a table via a hidden magnet still
surprises and entertains his audience. To feel the fascination of elds more strongly, a
deeper look into a few experimental results is worthwhile.
H    ?
Everybody has seen a lightning ash or has observed the eect it can have on striking a
tree. Obviously lightning is a moving phenomenon. Photographs such as that of Figure 
show that the tip of a lightning ash advance with an average speed of around 600 km/s.
But what is moving? To nd out, we have to nd a way of making lightning for ourselves.
In , the car company General Motors accidentally rediscovered an old and simple
method of achieving this.

Opel engineers had inadvertently built a spark generating mechanism into their cars;
when lling the petrol tank, sparks were generated, which sometimes lead to the explo-
sion of the fuel at the petrol station.
Ref. 3 ey had to recall  million vehicles of its Opel
brand.
What had the engineers done wrong? ey had unwittingly copied the conditions for
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 ,      
FIGURE 4 Visualizing what is invisible: a simple way to visualize electric fields as space with a structure,
using computer graphics and using seeds in oil. Top: the field around a point or spherical charge;
second row: two or three charges of different signs; third row: two charges of the same sign; bottom: a
charge in an external field E, and the field between two plates. The charge will feel a force F directed
along the so-called electric field lines; the density of the lines gives the intensity of the field and thus the
strength of the force (© MIT, Eli Sidman, MIT).
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
    
FIGURE 5 Lightning: a picture taken
with a moving camera, showing its
multiple strokes (© Steven Horsburgh).
a electrical device which anyone can build at home and which was originally invented
by William omson:* the Kelvin generator. Repeating his experiment today, we would
take two water taps, four empty bean or coee cans, of which two have been opened at
both sides, some nylon rope and some metal wire.
Ref. 4 Putting this all together as shown in
Figure ,andlettingthewaterow,wendastrangeeect:largesparksperiodically
jump between the two copper wires at the point where they are nearest to each other,
giving out loud bangs. Can you guess what condition for the ow has to be realized for
this to work? And what did Opel do to repair the cars they recalled?
Challenge 4 s
If we stop the water owing just before the next spark is due, we nd that both buckets

areabletoattractsawdustandpiecesofpaper.egeneratorthusdoesthesamethat
rubbing amber does, just with more bang for the buck(et). Both buckets are surrounded
by electric elds. e elds increase with time, until the spark jumps. Just aer the spark,
the buckets are (almost) without electric eld. Obviously, the ow of water somehow
collects something on each bucket; today we call this electric charge.Chargecanow
in metals and, when the elds are high enough, through air. We also nd that the two
buckets are always surrounded by two dierent types of electric elds: bodies that are
attracted by one bucket are repelled by the other.
e discovery that there are two dierent types of electric charge is due to the French
universal genius Charles Dufay (–). In a long and careful series of experiments
* William omson (–), important Irish Unionist physicist and professor at Glasgow University.
He worked on the determination of the age of the Earth, showing that it was much older than  years,
as several sects believed, but also (falsely) maintained that the Earth was much younger than geologists and
Darwin (correctly) hat deduced. He strongly inuenced the development of the theory of magnetism and
electricity, the description of the aether, and thermodynamics. He propagated the use of the term ‘energy’
as it is used today, instead of the confusing older terms. He was one of the last scientists to propagate me-
chanical analogies for the explanation of phenomena, and thus strongly opposed Maxwell’s description of
electromagnetism. It was mainly for this reason that he did not receive a Nobel Prize. He was also one of
the minds behind the laying of the rst transatlantic telegraphic cable. Victorian and religious to his bones,
when he was knighted, he chose the name of a small brook near his home as his new name; thus he became
Baron Kelvin of Largs. erefore the unit of temperature obtained its name from a small Scottish river.
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 ,      
metal wires
nylon ropes
metal cylinders
metal cans
water pipe
or tank
bang!

nylon ropes
FIGURE 6 A simple Kelvin generator; the one on the right lights a fluorescent light bulb using dripping
water (photograph © Harald Chmela).
he conrmed that all materials he could get hold of can be charged electrically, and that
all charges can be classied into two types. He wasRef. 5 the rst to show that charged bod-
ies of the same charge repel each other, and that bodies of dierent charge attract each
other. He showed in detail that all experiments on electricity can be explained with these
statements. Dufay called the two types of charges ‘vitreous’ and ‘resinous’. Unfortunately,
Dufay died at a young age. Nevertheless, his results spread quickly. A few years later,
Georg Bose used them to develop the rst electrifying machine, which then made the
exploration of sparks and the science of electricity fashionable across Europe.*
Twenty years aer Dufay, in the s, the US politician and part-time physicist Ben-
jamin Franklin (–) proposed to call the electricity created on a glass rod rubbed
with a dry cloth positive instead of vitreous, and that on a piece of amber negative instead
of resinous. us, instead of two types of electricity, he proposed that there is really only
one type, and that bodies can either have too much or too little of it. With the new terms,
bodies with charges of the same sign repel each other, bodies with opposite charges at-
tract each other; charges of opposite sign owing together cancel each other out. Large
absolute values of charge imply large charge eects. It took over a hundred years before
these concepts were accepted unanimously.
Electric eects are due to the ow of charges. Now, all ows take time. How fast is
electricity? A simple way to measure the speed of electricity is to produce a small spark
at one end of a long metal wire, and to observe how long it takes until the spark appears
at the other end of the wire. In practice, the two sparks are almost simultaneous; the
speed one measures is much higher than everything else we observe in our environment.
How can we measure the time nevertheless? And why did dierent researchers get very
* In fact, the fashion still goes on. Today, there are many additional ways to produces sparks or even arcs,
i.e.,sustainedsparks.ereisasizeablesubcultureofpeoplewhobuildsuchhighvoltagegeneratorsasa
hobby at home; see the www.kronjaeger.com/hv website. ere is also a sizeable subculture of people who
do this professionally, paid by tax money: the people who build particle accelerators.

Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
    
on the roof
in the ground
in the hall
pendulum
with metal
ball
FIGURE 7 Franklin’s personal lightning rod – a copy of Gordon’s
electric chime – is one of the many experiments that shows
strikingly that charge can flow.
dierent speed values in this experiment?Challenge 5 s
Sparks, electric arcs and lightning are similar. Of course, one has to check whether nat-
ural lightning is actually electrical in origin. In , experiments performed in France,
following a suggestion by Benjamin Franklin, published in London in , showed that
one can indeed draw electricity from a thunderstorm via a long rod.* understorm
clouds are surrounded by electric elds. ese French experiments made Franklin fam-
ous worldwide; they were also the start of the use of lightning rods all over the world.
Later, Franklin had a lightning rod built through his own house,
Ref. 6 but of a somewhat un-
usual type, as shown in Figure . is device, invented by Andrew Gordon, is called an
electric chime.Canyouguesswhatitdidinhishallduringbadweather,allpartsbeing
made of metal, and why?
Challenge 6 s (Do not repeat this experiment; any device attached to a light-
ning rod can kill.)
In summary, electric elds start at bodies, provided they are charged. Charging can
be achieved by rubbing and other processes. ere are two types of charge, negative and
positive. Charge can ow: it is then called an electric current. e worst conductors of
current are polymers; they are called insulators or dielectrics.Achargeputonaninsulator
remains at the place where it was put. In contrast, metals are good conductors; a charge

placed on a conductor spreads all over its surface. e best conductors are silver and
copper. is is the reason that at present, aer two hundred years of use of electricity, the
highest concentration of copper in the world is below the surface of Manhattan.
E 
If all experiments with charge can be explained by calling the two charges positive and
negative, the implication is that some bodies have more, and some less charge than an
uncharged, neutral body. Electricity thus only ows when two dierently charged bodies
are brought into contact. Now, if charge can ow and accumulate, we must be able to
somehow measure its amount. Obviously, the amount of electric charge on a body, usu-
ally abbreviated q,mustbedenedviatheinuencethebody,sayapieceofsawdust,feels
* e details of how lightning is generated and how it propagates are still a topic of research. An introduction
is given on page .
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 ,      
FIGURE 8 Asimpleset-upto
confirm electric charge
conservation: if rubbed fur is
moved from the first pot to the
second, the charge taken away
from the first pot is transferred to
the second, as shown by the two
electrometers (© Wolfgang
Rueckner).
when subjected to a eld. Charge is thus dened by comparing it to a standard reference
charge. For a charged body of mass m accelerated in a eld, its charge q is determined by
the relation
q
q
ref
=

dp/dt
dp
ref
/dt
,()
i.e., by comparing its momentum change with the momentum change of the reference
frame. Charge thus determines the motion of bodies in electric elds in the same way
that mass determines the motion of bodies in gravitational elds. Charge is therefore the
second intrinsic property of bodies that we discover in our walk.
In practice, electric charge is measured with electrometers.Afewsuchdevicesare
shown in Figure . e main experimental properties of electric charge that are discov-
ered when experimenting with electrometers are listed in Table .Inalldetails,charge
behaves like a owing substance; charge behaves like a uid.
Nowadays the unit of charge, the coulomb, is dened through a standard ow through
metal wires, as explained in Appendix A. is is possible because all experiments show
that charge is conserved,thatitows, and thus that it can accumulate.Inotherwords,if
theelectricchargeofaphysicalsystemchanges,thereasonalwaysisthatchargeisowing
into or out of the system. is can be checked easily with two metal pots connected
to two electrometers, as shown in Figure .
Ref. 7 Charge thus behaves like a uid substance.
erefore we are forced to use for its description a scalar quantity q,whichcantake
positive, vanishing, or negative values.
Describing charge as a scalar quantity reproduces the behaviour electrical charge in
all everyday situations. However, as in the case of all previously encountered classical
concepts, some of the experimental results for electrical charge in everyday situations
will turn out to be only approximate. More precise experiments will require a revision of
the idea of continuous change of charge value. However, the main observation remains:
no counter-example to charge conservation has as yet been observed.
Objects without electric charge are called neutral.Achargedobjectthatisbrought
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012

    
FIGURE 9 Various electrometers: a self-made electrometer based on a jam pot, an ancient (opened)
high precision Dolezalek electrometer, the Ampullae of Lorenzini of a shark, and a modern digital
electrometer (© Haral d Chmela, Klaus Jost at www.jostimages.com,Advantest).
TABLE 1 Properties of classical electric charge: a scalar density.
E

P

M

D
Can be distinguished distinguishability element of set Page 224
Can be ordered sequence order Vol. IV, page 206
Can be compared measurability metricity Vol. V, page 328
Can change gradually continuity completeness Vol. V, page 336
Can be added accumulability additivity Vol. I, page 77
Can be separated separability positive or negative
Do not change conservation invariance q =const
near a neutral body polarizes it. Electrical polarization is the separation of the positive
and negative charges in a body. For this reason, all neutral objects, such as hair, are at-
tractedtoachargedbody,suchasarubbedcomb.Generally,bothinsulatorsandcon-
ductors can be polarized; polarization occurs for single molecule up to whole stars.
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 ,      
TABLE 2 Values of electrical charge observed in nature.
O C
Smallest measured non-vanishing charge 1.6 ⋅10
−19
C

Charge per bit in computer memory down to 10
−15
C
Charge in small capacitor 10
−7
C
Charge ow in average lightning stroke 1Cto 100 C
Charge stored in a fully charged car battery 0.2 MC
Charge of planet Earth −1MC
Charge separated by modern power station in one year 3 ⋅10
11
C
Totalchargeofpositive(ornegative)signobservedinuniverse 10
60±1
C
Total charge observed in universe 0C
E  
Charges produce attraction and repulsion on other charges. Equivalently, charges change
momenta; charges exert forces on other charges. is happens over large distances. Ex-
periments that explore energy and momentum conservation show that the best descrip-
tion of these interactions is as told so far: a charge produces a eld, the eld then acts on
asecondcharge.
Experiments show that the electric eld forms lines in space. As a consequence, the
electric eld behaves like a small arrow xed at each point x in space. Electric elds are
described by a direction and a magnitude. e local direction of the eld is given by the
local direction of the eld line – the tangent of the eld line. e local magnitude of the
eld is given by the local density of the eld lines. e direction and the magnitude do
not depend on the observer. In short, the electric eld E(x)is a vector eld. Experiments
show that it is best dened by the relation
qE(x)=

dp(x)
dt
()
takenateverypointinspacex. e denition of the electric eld is thus based on how
it moves charges. In general, the electric eld is a vector
E(x)=(E
x
, E
y
, E
z
) ()
and is measured in multiples of the unit N/CorV/m.Challenge 7 e
e denition of the electric eld assumes that the test charge q issosmallthatitdoes
not disturb the eld E. We sweep this issue under the carpet for the time being. is is
a drastic move: we ignore quantum theory and all quantum eects in this way; we come
back to it below.
Page 195
e denition of the electric eld also assumes that space-time is at, and it ignores
all issues due to space-time curvature.
By the way, does the denition of electric eld just given assume a charge speed that
is much less than that of light?
Challenge 8 s
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
    
TABLE 3 Some observed electric fields.
O E 
Field 1maway from an electron in vacuum Challenge 9 s
Field values sensed by sharks down to 0.1 µV/m
Cosmic noise 10 µV/m

Field of a 100 W FM radio transmitter at 100 km distance 0.5 mV/m
Field inside conductors, such as copper wire 0.1 V/m
Field just beneath a high power line . to 1V/m
Field of a GSM antenna at 90 m 0.5 V/m
Field inside a typical home to10 V/m
Field of a 100 W bulb at 1mdistance 50 V/m
Ground eld in Earth’s atmosphere 100 to 300 V/m
Field inside thunder clouds up to over 100 kV/m
Maximum electric eld in air before sparks appear to3MV/m
Electric elds in biological membranes 10 MV/m
Electric elds inside capacitors up to 1GV/m
Electric elds in petawatt laser pulses 10 TV/m
Electric elds in U
91+
ions, at nucleus 1EV/m
Maximum practical electric eld in vacuum, limited by electron
pair production
1.3 EV/m
Maximum possible electric eld in nature (corrected Planck elec-
tric eld c
4
/4Ge)
1.9 ⋅10
62
V/m
To describe the motion due to electricity completely, we need a relation explaining
how charges produce electric elds. is relation was established with precision (but not
for the rst time) during the French Revolution by Charles-Augustin de Coulomb, on
his private estate.* Hefoundthataroundanysmall-sizedoranysphericalchargeQat
rest there is an electric eld. At a position r,theelectriceldE is given by

E(r)=
1
4πε
0
Q
r
2
r
r
where
1
4πε
0
=9.0 GV m/C. ()
Later we will extend the relation for a charge in motion. e bizarre proportionality con-
stant, built around the so-called permittivity of free space ε
0
, is due to the historical way
the unit of charge was dened rst.** e essential point of the formula is the decrease of
* Charles-Augustin de Coulomb (b.  Angoulême, d.  Paris), French engineer and physicist. His
careful experiments on electric charges provided a rm basis for the study of electricity.
** Other denitions of this and other proportionality constants to be encountered later are possible,
leading to unit systems dierent from the SI system used here. e SI system is presented in detail in
Appendix A. Among the older competitors, the Gaussian unit system oen used in theoretical calculations,
the Heaviside–Lorentz unit system, the electrostatic unit system and the electromagnetic unit system are
the most important
Ref. 8 ones.
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012
 ,      
R

A
2R
4A
3R
9A
FIGURE 10 A visualization of Coulomb’s formula and Gauss’ law.
the eld with the square of the distance; can you imagine the origin of this dependence?
Challenge 10 s A simple way to picture Coulomb’s formula is illustrated in Figure .
e two previous equations allow us to write the interaction between two charged
bodies as
dp
1
dt
=
1
4πε
0
q
1
q
2
r
2
r
r
=−
dp
2
dt
,()

where dp is the momentum change, and r is the vector connecting the two centres
of mass. is famous expression for electrostatic attraction and repulsion, also due to
Coulomb, is valid only for charged bodies that are either of small size or spherical, and
most of all, only for bodies that are at rest with respect to each other and to the observer.
is description denes the eld of electrostatics.
Electric elds accelerate charges. As a result, in everyday life, electric elds have two
main properties: they contain energy and they can polarize bodies. e energy content
is due to the electrostatic interaction between charges. e strength of this interaction is
considerable. For example, it is the basis for the force of our muscles. Muscular force is
a macroscopic eect of Coulomb’s relation (). Another example is the material strength
of steel or diamond. As we will discover, all atoms are held together by electrostatic at-
traction. To convince yourself of the strength of electrostatic attraction, answer the fol-
lowing: What is the force between two boxes with a gram of protons each, located on the
two poles of the Earth? Try to guess the result
Challenge 11 s before you calculate the astonishing value.
Coulomb’s relation for the eld around a charge can be rephrased in a way that helps
to generalize it to non-spherical bodies. Take a closed surface, i.e., a surface than encloses
a certain volume. en the integral of the electric eld over this surface, the electric ux,
Motion Mountain – The Adventure of Physics pdf file available free of charge at www.motionmountain.net Copyright © Christoph Schiller June 1990–November 2012