mgeie
idd
tintad
h acole circit is ehased
in
amymannen,
lucecl in te circit is gvperticnd
to ttu see
he clisection
cinj it. 7le aboe lwe aws
oorlen cam be"
metic Dmchuttien
incliued in aclosedciritir
(Hatenant ’The En
tins
Howin tae
cloyecl ci rccit is Such thatt oppu chanse
nelueel ina
cail'laiN hoo tu n is clihecttypptivnd
turny
fouadaienNdo
ts
clt
d
Assun
Sit
tat tte ceils
usned ie,N!
V
V- -df
nctosed toil,veltaje is gitnby V,je.cli
wee
E=21 echic field rteniy
Ah tl clesecd line intsaleqitsojn
Tnteyratien,
e
4
tine
giuy
,
onoCn
fox
.T-`
tield,
equstiContintiy
atcordinyto
Howevtr
Aere's
a
in
pomtiad
gence eliver Taeyng
on
icles
tosether,
amd field tltctic
both
’
’7he
bor ieldmsnehic
tte gheseguatin
abe
le
t
.
Now
auwin Fanaclays
asown
’1lis
is
onFne is is
astte
yiltesm|
clt
metic
do
y. Sueesie
ral Ag.tine
moviges.
T: és.
elncdesiy.
dt
t,
mato
m-
ol, mobili
veCHon
-[
fed
Apeue's
a
get
Con
is ir
m isic
oli
we
t
dlomi
t
(y.D)-
ze0
vector
is
of
sideso
sides
gaiom (
both clirenie
on
cletmtneo
and
las,
tor
i ptible
ie.qutidn0
moclify
the
tine pplieadte
for
be
temto
tilds,
we
oTlr
to
itmeke
not
t s wlert,
Ja
77lus,
Lwe
add_ca
sApues
la
1uw
1°3
Tuis is ttu conluckiem clm clousiy.
(2) Dis lacet Cumt
(onsider a
al i,
5 ut
Cclu)
th be te tote
Capity Cliarge
On posth pl cle,
Hemce, i,t : dcty
clt
clt
cl
clt
Tw cliplacenet cumet closi
s,
Diplaceeteln
cleaiy
clisolacenet eutut toy acloe
ae is,
Tus,tle cliplaceuttceut doL notstptoaut
He ale ct wica to toechange tate plae fpom
atecboele o e tethole in te ete-nal cisit.
Hence,
mzwell
qve<ni
elechic &nasneie qildsin to one set
d feur lquations, wih coplily dsttbeste
bi haviour or amy elechonmete fiel.
is e}eed toas
the istneneoy tos m..e we can clescibete
time &spac ].
’Tu term o t e qunti
is
lso
ue wn as G1aysao
Tu point torm
leeoostatie.
o
by
loted
*e tofay elecbit displacenetthgauy
a vounii eg ual totutofalelay
sttie
lasfor
toitlin tu roineiste naws
dgene
thattl
esipli
The
.
eleds
eltchie fi
Suraee doesnot (orntein
overpes
AV>0
e
iplies tat te elechic fltinesae
ame terminale at- e charl.
equatiem
ven by,
tom
The intera tor i qn by
(unet
mageticte
emenyig
toyhang
closed sur tae is
ze,
-’eg2'ipliethat te nunberd mamehc
tue tinwe force tuleg amyesion must
outotet
gion.
oignae cme end any wte,bit aw continouy,
’7uis is tle Crauss laio tr static magneticfild',
wih cotirmstte non eistne ol mametic,
monopole.
fonacayiao
-neic Dmcuction. 1lupoint tomis
lectoa
clt
-fe elechom oti e ore alndalsual
close
Lanetine deivatie ol, asntic lisplatnet
thongh anyura e boun ded bythe pat
atien(&itrlay the majntic &elrcbie fiele
t shouw s that a fine vargd magmte
Can produ e an electic dd.
ne
n as
u pomt yormis giun by,
tomir
by,
-’(le masmn etomotive forcelmm) ayound aaclosed path
is eqral
boumd
tu tomcuetion cn plwte tiedeiv
by tut at.us is the moelijii Apt
dartime vanyis fieldi
’eq"e( abo sinifies hat the Cbmelucioncln
elechi d
chngi
V
tlecbotahc, Staic 2lychic field.
Stetic hmenetie
tield.
at
masmeic ield campaoduu am fl chi pield.
Plctat
otrplatts at folr times,tr tierdalay
beins mtpotnd to spae separtttom
Comstitwey a wae.
agatiom
-
Vangiy scurtw (iln 2chanse) inte tomqe
d: atemuahen cowttat
Nerem
109
Oitos mplane yary
A wue ssaid to be plene
fna plene peremciculr othe clirc ion o|, wre.
Alane ware is Said to be aunikurs plemewae i
it getitiu the asoetwo (on ditio
anl
it)Eamd H
ho
onet unitorm inthe plane perpomelia
tote oliion of popagaton, (it. Eamd AVary
oyinta clirechion ol popqation)
’ An e lechroopn etic wawe
i h hay no elrchie o
manetie tiald cowponintnte cire chon ol
Ppondiudor to tu elirection o npaatien )i
cauee a tamrnse elechnapnetic CT¾m) wae.
3 Solitiom ol, ware lquation t r Unijom plae
tue popagatism
Cowider fine-hmoic
4E5 prec -> umitorm
plene
’ 1u unitorn ple wae has
tild,whid
Can be sipli
Has)
(E2g,
orponut
Ony twld
wae.
ple
Unitm
gien
te
in Zoie ctioy
itd fo
I2s(y) az
Now Es
Hs = Hs 4) a
jt
Hes
popeties o Em wase.
Sne, Ezs amd Hs at
-in pe yial de iva lie ar.t?y becomes aa pue
deivave.
solutiony
Ezscy)= EEe
theeced
E2e
Wave
-Caijp)y
idd.
y oy wafneti
H,ee'f+H,eyieY
’
Hzs)
(E,E, )Ort (omStet (lechic hiald oplitucle A
Cntmenad tidd soltioy obtained ine&6
Con be cdetnrinec by inyesigai
ndiny iwtadeneous fields?
be tocu d oo tiy bot
t (oep
hae sayne clhanacentiies
Ez0yt) = Re
E
E,et
= PeE(ttpy)
Eje
Aplitud & wttfy=phae
1t g2ows in tay cirction decoysin -ay clivection
as= Alitude
wt-By pase
t grows in ay livechonk decoyy into cirecion.
’ fo tle ild to be finite at inpiih,tbeg uind
tuat E 0, Hene,the ELet E=fo
ld'eanbe wstten as,
sune
E,(9,=Eoecoslewt-ßy) a2
Z-cllreten)
in
is
field
E
e
incueled,sin
La is
’y, H- idd cam be oitty as,
Hay,y= Hoe
Cos (ot py)
A
atulich the plve o
wane
at
iped
te
also
is
Tt
ce
Spa
pagals in
wane rarel;. Vpw A4
O envelope ol, t
midiu
is
nown as
wve)prpgals h g
Groyreloc,o wa.
-’ T is te veloly vith whidh t e engy propasa
Hene it is abo nown ay emenjy velod.
Vp
-Lntinsic upeclenel1)’ The intie tuprcae
o teware is cluineol
ond mapnette Htd phaos (omplie amplide)
Dernt
media
plae wae Cmd derie till Ez(y,ondta
al tue mediumyi each meium)
Thuy, i the wane ttropasas alos eliniom
so that te ete chie kiud E has only z Conpomt
teld
Hu, te solutom o te wane esgien,
fzCy,t)= Eo eoslwt-py) a
twhre, h= Eo/Ho Cos(wt-f)
- rbiaicfprclameotaneli
our mmecium
i o y Dieleetieneliu
t) Peeet Dilechi'e hmecliu
Ty Condu cti g melium.
Dielechic
w pepgtiog
tor esy cdieloctc meclium
r
w
2
2
2
2
2weee
(we
2 eu'p2
d: w
plase Cowsteutis
iven by
2
2
24
)
fupeclauley
ntiyte
eOa
the cowpomt
iwpclaee
tor
ctic' elieli adossy
asa
19eloci,o
wave
propg
Qmont
o,
losis
to
clilect
Small
Hence
’Dntinsic
clue
slity
te t
ehhect'
åo
-’The
e
peeet
elouy
te
is
2
meelym
otfware 7veloày
lony
ie propagatinm
A
atu
Cortion
cho elle
Sma clielechic.Tle
small amount as
dosi
Cos
(eot -py) ar -Ez)
dy
Cos (ot-fyê) a-fHu)
for a p,tct oliele chic mecium, 6Eo
, Atkmution coet is gien by,
’phsc towstt s giem by
x2
vlocis
Tntinsic Dupecleue is gi by,
jwA
Qtjwe
aq 6)amd ) are
H
moclilid
(tt2)
watpps te
mPcium
dielectic
tor a putect
[tine ds o
ane inple
with ea ch otei
for
-The atnation (owttis gien by,
2
-’pha (otat
ien Ly
f=woto
Tws, edod
o wae
Tatiic hjeclae
o -|207372n
E= Eo cos (wt -py) a
n- Ho Cor(ot-fy) ax
Eo tos(ut ) n
(-E)
(H)
without
is an elechoniagmetic wwame.
we can say tatEii
se,te electic kietd andmapncie ifd are in
puase with each otues.
Wane
[inood tomycts)
in by,
Now popa geton Con ta
we
Hene
o|
)
e
Conpaiyitwith
22
2
wo
2
2
'yo(xA)-JE
ot
set
we
ole, lLý
by
muuir'yi,
bott
Jt
euaionyarwlls
4cL] (modl:'Jfi
by
’Deuivation
amemengy
of Comsenreono
htte
poit.
n
pouen clireciono
atanla umit
owis
that
pY
that
tvr
atS=EyHmohct,
Tofoymtig
electic
coc good
ctrr
ayfio magmehe
os(t-yaw
On)
(wtfy)
{o
’Ît
st
thbehind
e
-(ls,
ain
tos
eeHof= and
dy
we leuow that,
Thy,
JH
in (
we qet
edE-9.(Exi)
Dteszyoer a volume, weset
(Arplyi
Divagene heorm ote second ttom on
bouneinJ
susae
eyclosd
'sis
Here
’
sqin bys
Volume V. Tuy of
otal pou
Eney
in
se
Ohaic powen|Pateo
uinte álny
LDisipatd) stordin the.& mafed
futautameoug
(ie.tLe
uled
cissip
emejy s beiný
totel volune Vlis
powen cli sipeted)oituin
Senealisation o Joues Law,
l20
whih the ste
prtseut He time ad
energy i
electic fHud enity aned masield
V.
wittin the volmie
tem
deccai
the nale at which enengy Sis esCaping deai
the voume Vth ough the closee sufae s, Tu
follovs tom thelas
Poyn iuwtor
AZ
Pognteetor
Yorapla
Stoed
Out
9lechil
ane
emegy
ste
magneic
fouse in
ii fowe Balamutor Em
It is dekined as
whe,
Ex F
elct
>7uus, poynty vec peneti te eneajyf
ol on eecbromagnetic twene
ie ateh
(14 is invetl by Boitieh physieist jon ten)
foyty
Poyntig
for insulaling
uorty or Imulagmlin
eolium, T-o
rom e (6) dk eriows oletion, tuget,
I24
Jtv
V
E.(-bu clv
EyDiegene
heorem,
du
-uis is
on
Theorem.
0.