Abs ac
A simple and p ope explana ion o elec ici y and elec o-magne ic
wa es.
Keywo ds: elec ici y, em wa es
1
Demys i ying elec ici y and elec o-magne ic
wa es
M. Ljubičić (Amenoum)
108. b igade ZNG 43, 35252 Sibinj, C oa ia
(comple e ela i i y.o g) [email p o ec ed]
Oc obe 8, 2025
1 In oduc ion
Much con usion and alse unde s anding exis s in public abou elec ici y and
elec o-magne ic wa es (and basically abou mos hings in science), e en among
educa ed people. I doesn’ help ha he educa ing sys em eaching basics o
such phenomena is o en ac ually lying in o de o keep hings simple. This is
an a emp o cla i y some hings.
2 T ans e o elec o-magne ic ene gy (elec ic-
i y)
Elec ic cu en is usually associa ed wi h mo emen o elec ic cha ges, ypically
elec ons. Howe e , ca ie s o elec o-magne ic o ce a e pho ons and hey a e
he ones ansmi ing ene gy. Conside an elec ic ci cui consis ing o a ol age
sou ce and a ligh bulb connec ed o i by ex emely long wi es. Indi idual
elec ons mo e much slowe han ligh , so i he elec o-magne ic ene gy would
be ca ied by elec ons i would ake much longe o powe up he ligh bulb
han i does. The ene gy is ansmi ed a he speed o ligh so he ligh bulb
appea s o be powe ed ins an aneously.
Elec ons do ca y kine ic ene gy, bu i is no uni o m a oom empe -
a u es and a signi ican pa o i hen ge s ans o med o hea . Thus,
no only do hey no di ec ly ca y elec ici y, hey impede i s ans e by
ans o ming i o hea . This is, howe e , usable in elec ic hea e s. Any
indi idual elec on in a wi e will no ca y ene gy long dis ances (e.g.,
om he ol age sou ce o he ligh bulb), ins ead, hey will ans e he
ene gy o o he nea by elec ons. Thus, ans e o ene gy/momen um
2
h ough he wi e is simila o he ans e o ene gy/momen um in a
alling s ack o dominoes. Fo an al e na ing elec ic cu en , howe e ,
mo e accu a e analogy is he New on’s pendulum.
Why a e he wi es needed hen? They’ e no , bu wi hou hem he ene gy
would simply be dissipa ed in all di ec ions and ha dly any hing would be ab-
so bed by he ligh bulb, especially i i ’s no elec ically cha ged. Wi es a e used
o es ablish an ene gy channel, a wa eguide, ha will guide elec o-magne ic
ene gy owa d he ene gy sink - ligh bulb, in his case.
Wi h su icien ol age, a wa eguide can be c ea ed e en wi hou wi es. This
is e iden in ligh ning, whe e cha ge is usually ans e ed om a cloud o he
g ound (usually nega i e). A ligh ning s a ing in he cloud will usually b anch
sideways a i s , bu once he main b anch eaches he g ound, he ionized
ai channel e ec i ely becomes an elec ic conduc o , h ough which all he
ene gy is hen ans e ed o he g ound. B anches occu due o di e ences in
po en ial ( ol age be ween he cloud and molecula clumps in he ai ), bu his
di e ence is g ea es be ween he cloud and he g ound. Once he wa eguide
be ween he cloud and he g ound is es ablished his becomes he pa h o leas
esis ance, so no mo e isible b anching occu s. An equi alen phenomenon can
be obse ed on small scale as well. I he ligh bulb is b ough close o he ol age
sou ce so he con ac s a e almos ouching, spa king will occu and ligh bulb will
powe up. This ligh bulb will s ay powe ed as long as he wa eguide emains
undis u bed. E en hough ene gy is ca ied by elec o-magne ic wa es, i is
ob ious ha he wa eguide is o med by unbound elec ic cha ges (ions). Thus,
good cha ge conduc o s a e usually used o ans e elec ici y due o highe
e iciency and lowe ol age equi emen o c ea e he wa eguide.
This seems o sugges ha he mo ion o cha ges in he wi e is unnecessa y,
all ha is needed is accele a ion o cha ges a he sou ce and a wa eguide which
will guide gene a ed pho ons owa d he ligh bulb. Howe e , he wa eguide
is made ou o ions so i is impossible o a oid ion mo ion (as hey abso b
he gene a ed adia ion). One could cons uc a wa eguide o ligh ou o
an insula ing ma e ial (like an ib e-op ical cable) bu his would be e ibly
ine icien o ene gy ans e (i can be, howe e , an e icien way o ans e
in o ma ion). The p oblem is ha he pho ons gene a ed a he ol age sou ce
a e low equency pho ons, so hei ene gy sp eads ou , no only as , bu o e
la ge dis ance, while he ligh bulb is ypically oo a away and has e y limi ed
dimensions so i won’ be able o abso b any signi ican ene gy - ei he as an
an enna, o an gene al abso be o elec o-magne ic adia ion. Conside he 50
Hz ol age sou ce. I gene a es em wa es wi h a wa eleng h o λ= c/ ≈6000
km. Thus, one would need a ligh bulb he size o he Moon o abso b ene gy
co ela ed wi h pho on equency. Howe e , he emi e ( ol age sou ce) is also,
due o small size compa ed o wa eleng h, e ibly ine icien he e - con e ing
mos ene gy o hea /capaci ance. Thus, e en i he ligh bulb would be designed
o ecei e ene gy in his o m, i wouldn’ eally wo k. Elec ical appliances
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don’ usually cap u e ene gy in his way, hey ca e mo e abou he in ensi y o
adia ion (p opo ional o cu en ), no equency. Howe e , e en i you gene a e
a lo o pho ons a he sou ce (inc easing in ensi y), ene gy densi y o ha
adia ion is alling o wi h he squa e o dis ance. So, again, he ene gy cap u ed
by he ligh bulb would be e y small. And ha is he eason why mo ing cha ges
in he wi e a e necessa y in p ac ical applica ions o elec ici y. Pho ons c oss
in ini esimal dis ances when ans e ed be ween one elec on and he o he in
he wi e. The e o e, he e is no sp eading o ene gy and in ensi y o adia ion is
he same a he elec ical appliance as i is a he ol age sou ce. Can one s ill
ans e signi ican amoun o ene gy using pho ons alone? O cou se, bu no
wi h con en ional ol age sou ces, a he wi h de ices ha can p oduce cohe en
high- equency pho ons (some hing ha lase s do) whe e ene gy is less sp ead
wi h dis ance. I s ill d ops o wi h he squa e o dis ance, bu wi h a di e en
cons an o p opo ionali y - smalle han π, as he ene gy dis ibu ion is no
iso opic. All pho ons ac ually sp ead iso opically (in all di ec ions) as sphe ical
wa es bu , depending on equency and cohe ence (in case o mul iple pho ons),
he ene gy is mo e o less localized owa ds a speci ic poin on he sphe e. In
ex emely high equencies he localiza ion is so high ha pho ons e ec i ely
a el as pa icles and he poin o localiza ion can be in e p e ed as di ec ion o
p opaga ion ( om he e e ence poin o he emi e ). Rega dless o equency
(amoun o localiza ion du ing mo ion), howe e , pho on abso p ion implies
comple e localiza ion ([sphe ical] wa e o m collapse) o he poin o abso p ion.
The p obabili y o pho on abso p ion a any poin on he p opaga ing sphe e
is p opo ional o pho on ene gy densi y a ha poin . Thus, pho on is mos
likely o be abso bed in he di ec ion o p opaga ion o he poin o localiza ion.
3 T ans e o elec o-magne ic in o ma ion
Elec o-magne ic wa es always ca y ene gy bu hey also ca y in o ma ion. I
he aim is o con ey in o ma ion, a he han ene gy, i is much mo e e icien
o use wa eguides, o media, which a e good elec ical insula o s, a he han
conduc o s, o ans e his in o ma ion. This is because conduc o s abso b/a -
enua e elec o-magne ic ene gy and may e lec incoming wa es.
As hey a el, elec o-magne ic wa es induce di e ences in po en ial
in elec o-magne ic ields. This di e ence can be in e p e ed as p es-
su e ha can be el by elec ic cha ges. I is highes a he peak o
an elec o-magne ic wa e. In ai , whe e cha ges a e igh ly bound in
a oms and molecules, his p essu e, especially in case o lowe equen-
cies, is usually oo low o signi ican ly a ec hem and hus ans e
ene gy o hem. This is no he case in good conduc o s o elec ici y,
whe e cha ges can low mo e eely. Fo igh ly bound elec ons in a oms
p essu e om adia ion in ensi y is p e y much i ele an , wha ma -
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e s is equency. They a e insensi i e o low equencies because hey
a e con ined o a omic o bi als which ha e a diame e on he o de o
picome es and nanome es (depending on he elemen , and how exci ed
he a om is). Since wa eleng hs o low- equency wa es a e much bigge
han he space elec ons a e con ined o (o bi als), mos ene gy o he
wa e simply passes h ough.
Conduc o s a e used only a he ecei e and ansmi e , as an ennae. A
he ansmi e , a conduc o is used o c ea e adia ion by mobilizing cha ges
(accele a ing cha ges c ea e elec o-magne ic adia ion), while a he ecei e
end a conduc o is used o abso b elec o-magne ic adia ion and mobilize he
cha ges. Because elec o-magne ic ene gy is, bo h, in he conduc o and he
ex e nal medium, a elling (sp eading) a he speed o ligh , he op imal leng h
o an dipole an enna is 1/2 o he wa eleng h.
In eali y, a di e ence ac ually exis s be ween he speed o p opaga ion
be ween di e en media, bu his is usually negligible.
T ansmi e dipole la ge han he adia ion wa eleng h will in oduce p ob-
lems (wa e dis o ion, noise) unless he leng h is he in ege mul iple o hal he
wa eleng h ( his will wo k bu will p oduce addi ional lobes in he signal, cancel
i in some di ec ions, and lowe e iciency).
In p ac ical applica ions, i is also impo an ha he impedance o he
an enna ma ches he impedance o he ol age sou ce. Impedance is he
measu e o esis ance o p opaga ion o elec ic cu en which also ca -
ies in o ma ion on phase di e ence be ween ol age and cu en ( his
phase di e ence a ises due o p esence o induc i i y and capaci ance
in elec ic ci cui s, in oduced mainly by coils and capaci o s, espec-
i ely). One e minal o he ol age sou ce is connec ed o one pa o
he dipole, he o he e minal o he o he pa , so he cha ges (and as-
socia ed elec o-magne ic wa es) a e oscilla ing be ween dipole ends and
he ol age sou ce. Ma ching impedance enables he elec o-magne ic
wa es o a el eely om one end o he dipole o he ol age sou ce.
In case he impedance is misma ched, wa es will encoun e a discon inu-
i y be ween he dipole and he sou ce, esul ing in e lec ion, and hus
educed powe ans e o he an enna.
In ensi y o adia ion is p opo ional o o he numbe o cha ges mobi-
lized (which is p opo ional o ol age applied o he dipole), bu i is mos
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Figu e 1: Elec ic ields p oduced by a dipole an enna1
concen a ed in a plane ha ’s passing h ough dipole midpoin and ha is pe -
pendicula o i .
Ob iously, an al e na ing ol age sou ce will usually be used o gene a e
elec o-magne ic wa es. A DC sou ce will only gene a e a single elec o-
magne ic pulse once connec ed o he dipole.
Figu e 2: Re lec ion o an em wa e1
High- equency wa es ca y mo e concen a ed ene gy and wi h inc easing
equency inc easingly beha e mo e like pa icles han wa es (a pa icle may
be in e p e ed as a localized wa e, o localized wa e ene gy). Thus, hey ha e
a lowe ange and a e mo e likely o be abso bed and e lec ed. A e lec ion
o a wa e encoun e ing a conduc ing su ace is illus a ed in Fig. 2. Once
he incoming wa e encoun e s he su ace i will accele a e a cha ge wi hin
he conduc o . This will c ea e a new wa e and adia e i in he di ec ion
o he o iginal wa e and in he opposi e di ec ion. The pa emi ed in he
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opposi e di ec ion o he o iginal wa e can now be in e p e ed as a e lec ion
o he o iginal wa e. No e ha he c ea ed wa e is shi ed in phase by 180◦
ela i e o he o iginal wa e. The e o e, he pa emi ed in he same di ec ion
as he o iginal wa e ( o he igh , in he igu e) will cancel he o iginal wa e.
This is he case o a pe ec conduc o . In eali y, some ene gy will unnel
h ough, and a e lec ion will no be pe ec (in ensi y o wa es will be lowe ).
Good conduc o s a e good e lec o s and a e hus used in Fa aday cages - me al
enclosu es designed o insula e ce ain space om ene ge ic (high equency)
elec o-magne ic adia ion. Ob iously, i he leng h o a dipole (su ace, o size
o a Fa aday cage) is much lowe han he wa eleng h o he elec o-magne ic
wa e, only pa ial e lec ion is possible - as he ene gy o he wa e is sp ead
ou o e la ge dis ances han he cha ge cu en in he conduc o is ee o
mo e o e . This is why low equency wa es will usually pass h ough s anda d
Fa aday cages wi hou much loss.
In o ma ion is encoded in em wa es h ough a ia ion (modula ion) o e-
quency, pola iza ion o ampli ude (in ensi y) o adia ion, bu i can also be
encoded in modula ion o he equency o emission - implying in e mi en
(pulsed) emission o adia ion.
An em wa e is pola ized when i is no oscilla ing along a andom di ec-
ion o when ha di ec ion is no changing andomly. A wa e pola ized
in a adially-symme ic ashion (e.g., e ical, ho izon al) is an example
o E-mode pola iza ion as he mo ion o [ adia ion p oducing] cha ges
is usually induced wi h linea elec ic ield oscilla ion (as in a dipole
an enna). A wa e pola ized in ei he a clockwise o coun e clockwise
ashion is an example o B-mode ( o a ing) pola iza ion, usually induced
by magne ic ields on smalle scales, and g a i a ional wa es/lensing on
la ge scales.
Re e ences
[1] In oduc ion o Elec ici y and Magne ism: MIT 8.02 Cou se No es Re ised
(2013), P. Dou mashkin e al., Pea son Lea ning Solu ions: Bos on, Chap e
13
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