992 N Agar do chag

equal hai toly

UnparfoJCe
Slectbestatics Eo Pesmitiu iby (ree Space
vacvum)
max
togego)
Slecic decto t Stahics (ais ox

chabge attesfE &oK = 8 pesmiHutty of ony imedtum -

is

TOo onducto dieletyity

Coyitoi
K = Eo8 = Eym Relatve pesnitiv thy ef

when temiral vol tage =o Ony mediu n

4-)eaal /unchasgad conducing bdy &o = 8-85x6 c DimenSion aiT

No potong = No eleconu
Less PE
m Higkty
Nn
tablekairlvocvum inutahor O

Na Ywr put -ve choJq& on body,

Na Kcondoctos
hen maS$ body woud
T ei3 demoved
Electc charge
A physical quantky
muss

ohich hos ptopouty

ll dect eO0e:
+ For any medium 3

to intact wh
ano het fotce Reld a
Frmediwm Fais

chaxge is called electic fed o Potce feeld I delectaic Aued

is
eack choge Tt q2
is Jeen expeximentol wy Complekely Aled
chages ae 2 tyees tve d -ve
Sl unt Coulomb (c) Dinpe o&ton LaTJ Fmcd- = Fair/K
- Main Poan of chatges Pasntially gilled
J ree chotge fee electon In a conduc, F= L 42
the valence e ott loogely bound ed witR theit LMEo (-t)+takJ
prent nucleus due egs eleco 8tahe
to PRINCIPUE SuPER PoSiTION
o otttacHion

Conduchon
8ecaue
f heat , g theSe

choge, cuttent
e, fode
Hhe ptocesr

wil be .93
OF

poßsible in conductos,ie why e ae olso

caled CasHetS
choge
Tndusgd chat neutaol body baoght PoSIT LON OF EQULI B RIUM
dole then elechic field ines
would beak bond blw ve
(a-x)
2 -ve charqe
-The tedstaibutn of chasge in an uncitigcd A f8
poßttion
Conduchng body in pae Sence chaigedl
Conducting body is called ihdoced chaoge
Phenomenon (a duction:

3] Šxess of chasge (tygpatiehieal concept ) a

Jdeal batH esy
t Psopethes electic chaage

D ike chasqes sepel Unteke attact

To find net fooce ( vectos )due
to
2) Eledic chasge scalan quantrty gothex chages
3) Conservative in natu de
G33) (b3)
(42 Ftnd Faet
Slep 1 isre foxce
hai

2=tne (ne)
nikalna
3Con q2 opat a40w heud
Chadge is quanhsed
Pgas n e ntrges, matab Slep2:Rq92()
bod pe ve chatge exist kaoegn duning te. Foek = (-s)43) K(sus)
s) Aqox do conducting body ko wide se onnec
jab tak unjea
magnifode L2c +SC Sign )
kiya, Chasqe tob tak gow kasega Find Foet on

potenhial same na ho jaye Foce gf intesoctn blw

ch 3C t3c chage
(Gi-8,1)
> COuLOMB'S LAW2ixe d
ditecty
chasges
poaonal is
point
pos ine qonog de= 6f4
F to paodoct o mogntudc• hgher ma d 31-125
K(6) (:)
42 Squose dstance bl
4Rem
 9192 N Agar do chage
tel
equal hai

UnparfotUe
Slectbestatics Eo Pesmitíoiby
vocuum)
&uee space max
tag ego)
Slectc>tecto t Staies (ois ox
charge
is atteat EoK Epemiiuthy f ony medtum
Tno ondvco
Covstont Gny nedium
when temial vol toge -o
eukal /unchasgad conducting body
Eo = 88G x\6 c Dionen Sion$a'iT
No- paotong = No elecaon mj Highky
N

Less PE Stoble ais/vocvum

1

Bwr puf -ve chole& on

body
Na
en mase bocy woud Kconductot
incese. Tl demove
mass yll deceo0e
es
Eleckaic chaxge i
For ay medium $
A physical quankty ohich hos ptopoty
to intoact wt aro Mer fotce Reld a
chaxge is called elechic fred o¥ Poce feeldJ
f eack choqe
T dielectaic is eled
q2
Tt iS Jeen expeximento! ay Complelely Aled
chages ae 2 types tve d -ve
SI un Cowomb (c) Dimenaion LATJ
- Main Roorm f charges Paxtially gilled
J Free choge fee elechton In oa condoc, F= 42

the Valence eat

loogely bounded with tieit LME (-t)+tRJ
parent nucleus due to less eleco 8 tatt Poce
>PRINCIPLE OF SUPER PoSiTION
otkacion Because these he
f heat,choge,
e, ptocesr

13
Conduchon uttent wil be
poßlible in conductos, ic whyease olso
colled choe
] Indusgd chage
f'a neute! body i bsought
clole then elecbic lield ioes
OF EQULI B RIUM
would beak bond blw +ve (a-)
2 -ve charge
The tedsbibutn o| chasge an A,
in unchittged
Conducing body in pre Sence chaged fsom Qi
Conducting body iscalled indutedchasge
Phenomenon is índyction:

3 Exess of chasge & (Hyp:theheal concept )

s ef

Dike
Jdeal

Paepees
chasqes
batey
eleckaic
Jepel. Unltke
chasge:
atac
qQil2
em cson't
odr
be
undike, psition
bdu the 2 chosge
of

but erthes on

2) Elesic
left or aight of he 2chote sy lem. Asoy Jtom
chasge soalan quanhty

W
Conservatiue

Chatge is
ih

qvanhsed &
natuse

2=ne (né I)2

8 3
red
chadged
poist choyges

paticle is
ane

aloays
like , potikn

kchuen
chey
d

Hhe
eg m

Pgot n e ntrges,maHalb in liae

body pe vo chabge exist kangn qunig he 2 chag and awey fum hgler
s connec
s) Agax do body ko wide
conduching magnode change
kiya, chage tob tak &lou Kasega
tak unka

polenhial Some na ho jaye Force g intesoct^blw

ab
g 2fred chages are unlike , posrfion e

>COuLOMB 'S LAW

to pooduc
2ixe
is disetty
d point chavges
poo poa Honol

o mignitu de •l
Iine qoinig
chasged
He
phcle
2 choges
is aluiay s
and
cutsde the

higher magnitu de of chosge

to
42
Rem
 (or any
NATURE Of EQUILBRIUM ait whsle aylem is dipped
in lq
Ghes men)
wikh dielectaic cost. K.
nalore fesce aching ua 3 chesged

portcle is apulsive,then naluse d ey

along ine of acion ond unslable TBino = Fe

IS dtable

along h. Buoyang tane = _Fo

H naure foce acing on 3td chaged
Tose
K(mg- 6)
paakcle ts attactve, nohuse i9

ungtoble along ne achon

eq

& stoble
K=
gion of
The Qvsaunding
GENERAL ANALYIS ELECcTRIC
unit tue eot
FEUe charged pachde a in uhck
Q (0,a) o chatge. a wnit tue test charged parhee

distance n then net Fotce .Q7E=F expeierces an Sleckaostalic force

is inlesachon.
(o.y aching on the
2FCose erther
choh d
Fosce feldl & magni tede chage.
O away ftom mnear podit^ Elechc fied
d chatge density
dependisg cn netue ed chatge.
QcG,-a)
Nolt/mele
oFret - Foestaiog
= 2Fos o -(2ago
by tel chored paatide Sence
a?t e)3/2 Fotce expesricnced in poe

choige ke jegell
xing erge toh 2 nah ayega
o force is max at n =t a N2
Pabce feld a, qo ko B ke Reld me le jke
uaki feld disteob kasns kadegi

o SHM only when, <n< a To find actual feld a, we can take, oo

FNCR V/m

T= 2T mas 1 lecbic feld due to point chasge

ma
Hlong veco
F=o F=o

Net fosce l-l

=
fnet FaJB chog, Frel
ue to ctHhet

lixed chabges
2(2Ji+1) 2
F

Eleclaic freld due

magnitude

to unifodmy chaged
ditecio

Whese,F= Ka= L KQt thin dod

dineat chatge denaiy
a
a) Along oxial position.
PITH BALLS 2,QL (as1=atL
untfodeL

Tine = Fo E= KQ E = KAda
alatL)
tan = Fo
mg
as>L, a +L a E = KQ
ASineTSine

det A=o
Nb mates what maga hvde o eah choige is,

(mt e4)
 b) Along
JESino
bisecto

dn
line.

Tos
of
Far

Fel3
unymmelaico
chas qe d
symonelaical

is

Jed
1-D
pattion
Sxten Sion

&rlension

Exlension
]
3
E - 2RKA =

R
KQ
R²
2
TT

RA
(-5)

()
Feld is 2-D E = 2K)
R
aaecic eld due to conducig thin
Sphestcal Shell Solid sphese
any genexal positon. a) If x>R E = Ka/y2

my
E
tHodigonlal

Vestical
K Tos
rold

Geld
o - CoS O2 ) b)

Ir<R
9 8lectac feld
R E = KQ/R
E-

due
o

to
Emax

R
Ey = KA
b
Sin e,- SineJ non- Conducing sphete.
a) y>RE= PR = KQ
3 &o&2
b) &= R E = R = KGa= Ema
PR
3Eo R

3] Slechdic field due to gini tely lodge

3&o
line
charge
io] Electaic Beld due to unfomly chaged
non conduching ylinder
a) >RE= PR
4)Elecic freld doe to semi ignite
2 Bo

line chage. b) t R E=PR

En RA Ey = KA Emax
=R
c) &< R E = Bx 2£o
2 &o
S)Sledsic feld due to uni fornly chaged n sletic freld in caae vaaiable
a,R chasge densthy (Applical ian o yoass
QA 8phese chatqe tadius R cadties a tretolem)
chasqe whose volume chosge density depeds on distanE
& Rom bal's centte as
= tREmax {I-)whese
e Po is const
ing: At x
Po

a) magatde g electic feld ao foncin o diglance

J Sleckaic feld due to unifo Outside the gphee
d

dqz P()(urad) Fasl fnd chatge tnclesedy

chaged dhsc by Sphese.
2Eo
i2

28o Now, Lng

Ecentse
2£0 b) Electic
S:fhex
E- vesy ladge
8heet is

ot
q unl
Sheet disc
2Eo
o sheet
cbject
ose to
is vely
Ex
)ma.o Value
T
dueto oo
Sheet
due to
(-o)
disc

1 Sletic held dve to citulad asc iS

Fot Ena€
E- 2K Ra6l2 = KQ Sih ol2 (-
aE(g(roa ) Cod 36)
R R o/2
2o 2Eo
 2 -)
b) Alona bisector line. Symnmelacal
Fo Sxten Ston
E = 2 KA = KQ
JESinO
R²
Feld 18l-D Srlension 2)
Foy untymmelaiol potiton
R
d
d
of chasge d Jecl Exlension R
Feld is 2-0
E= KQ
E 2KR ?
a ektic ield due to conducing tin
sphetcal shell olid sphese
any gene al positon. a) If xR E = Ka/s?
JESine
m Hodigonlal Rreld
b) tR E = KQ/R
Ey = KA [oso- Cos0] c) r<R E o
Ema
b
my Vettical Reld 4 Slectaic feld due to R

Ey = KA Sin e,-Sin e] non -

Conduchirg sphese.
t= Ea (-)+ E,(A)
b
when 6r, a Acw
a) y >R E= PR= KQ
3&o&
b) &= RE 3Eo
R = Ka-Emox
PR

3 leckdic field due to

line
nfinitely laage
3&o
R² 3

chatge
Ey = 2KA = o] Slectic feld due to unifoamly chaaged
non con ducing cylinde
a) >R E= PR
Electaic eld doe to semi 2 &ot
(gfinite

e line c^asge. b) RE= PR

Ra = KA Eman
E Ey
c) t< RE= B
=9R
2lo
2&o
S) Eledtic field due to uni fotrmly chaged i Elecaic in case q Varable
chaage density (Ppelicalian yuass
E= RQ2 QA 8phee q choatge tadiws R casties a tre tolern)
chasge whose volume chasge density deperds on dstanee
& Rom as R- o (I-}whede
At a = tR
N2
Emax
bcl's cenlse Po is const.

a) Magmtode d eletaic Jield ao oren of digtance d

J lectic field due to uni foamly [outeide the sphee
disc dq P() (uTrd)Fis1 nd chatge enclsed
chaged
2£o

Now,
R 2
ng yuasA theotem.
2&o
3
Ecentse
2&o b)Elecatc frel [incide the
Sther gheet ig sphese

2 Vedy ladge ot

) -/5
Eo
object is veby
0o heet loge
g dstonce dmatshi
1 Sletdic feld due to citulad ae
Value
1S

Fa
max.
Ena?E-
JE
d&
elecnè

=0 ke
Red
andat
intenity

da

R R 0/2

n
 FoRCE ACTING ON FINITE IRE my Uon- unifodm feld ines

DUE TO 0tY LARAE LINE CHARAE

fa9.EA
F= Aid laXotL
2TSo PROBLEMS BASED ON UNI FOR M

2To ELECTRIC FIELD LINES.

work done by leeld=
CASE-1]
2T12on yon in KE
yre (1€)s =muo
ELECTRIC AIELD LINEs ELECTRIC
LINE oF FORCES lev = li61X(bT
The locus patt a ttgjecty Jollouwed by a v, Sthe
= Vo
test charged feld d gien chasge
CASE -2 v'CosG
posticle in Te, v'cose
called elecaic dreld lines or elecksie lme. d torces
J lecdrc Jicld lnes doe to izolaled cassel m
tane = qEt
pattice. Slecsie doeld lines move

wIn staight lne due

to
deviat'on

an isolated charged
2 m y= 2L9E
m Vo2
particle

t,
tue chaqe Eqvaion of tajectoy
chasge
sink of ield ELECTRIC POTENTIAL DIFFERENCE
&reld lneg ines The amount wora done by an er temal agcnt

J Electic dreld ines due Eo On e

a

point
nit

to
tve

ano
ot chage vey lowly
her n agiuen ed
uke charges Condition Roo neutial pornt&

2
JC aR VolE

Q ELETRIC PoTENTIAL The amount

3 Blechtic field due to unlike chadges

done by an extesnal aget io bsinging akeof hage

Neutacd point Ig ya

Ve-O =
hga Depends on

mognitude f chage. 90 +J pokentia s asked,

PROPERTIES OF ELECT RIC FlELD fipd eok done.

) LIN ES
Ciqinale from tue chae & leminak to -ueRELATION
chaye ELE CT RIC
Blw
atoo, Vb-0

ELECTRIc
(Vecog)
FIELD
PoTENTIAL (Scalan)
Uo0
&
k) Dibetn
Cusve is
eledzic
guen by
ed
slope
lines at ang poind on
tangentto thet pant E= -dV
dx
my Ro enkta!

gtadient
+ In ditection
value cd
ef fela
Dolenkal dekaases
i)2 Eletic eld neves iatessect each otke
lines

non unitotn
IV:Tn a sgion, the pleahal is depseseniel

i) Neves fem close loop except

magneie reid. Vis in volts A g, z ase in metes,

v) Alauaye move h to equipofentiad

a
sface The
chasge
eleclsic

2 cowloumb
e eA pesenced

gituaed
byy
af
a
point
ui) vo f electre field lnes nognitule
(,,)is
ut) Elecic feld lines l chasge in Side
chotge
a 2

Conducor is always gero Hence, Conduvctot is

Called ehie ld ohen electic e line wil entee E=- (6-&)f - 8a-846z)$-(6y)R
GY leove onductoy it oil do it h to Susce. E-C2)1- (-i6)fF(e)k
TYPES OF ELECT RIC RED UNES
36
-

foxm Aeld tines (montude daecton

Uni
d kield iaes is
Same
 FoRCE ACTING ON FINITE WIRE
DUE To oLY LARaE LINE CHA RAE

2T S PROBLEMS BASED ON UNIFORM

dF dqE = da
2T8% ELECTRIC PlELD LINES
work done by leld =

ELECT RIC FELD

LINE
The locus
OF FoR CES
LINES | ELECTRIc
CASE
yorn

bgrelu
KE
z(1€)s
in

2
mu'o

patt od tdgjecty ollowed bq a

test choged potticle in feld d given chasge
CASE-2 v'CoS = Vo
caled elecic dreld ot electaic
lines (me toces v'ae q€t -

J Sleckarc dield lines doe to m

i8olaled chosfel
padticle. Electtie deld lnes
tane =qEt
move mvo
n shaght ine due to deviaton
an isolote d chaged m h=vyt yL46t
m 2 m Vo
panticle
tue chayge
chovg.,
sink f
ELECTRIC
Eqvalion f taojeckoxy
ield lneg
reld
PO TENTIAL DIFFERENCE
to,
&0,
lines

3 8lectic teld lines de

E

E0
The

n bithg
amount
ingq a wnt tve
work done
foot chage
by an ertenad
vey tlowly
qqcnt

uke On e point to another in

charges Con diton Rot neutsal

2
paint8
(om

VA -=ELECTRIC
Wagont = -AU JlC oR Volt

Q POTENTIAL The ameunt fwok

3 lectaic field due to unlike chadges
done by an extesnal ogent in bàigg a teo
o< Neutaal poit Itya pastiede om
Q, < given dhae

on
V-O = AU
hga. Derends
magnitude d chage 1o +TJ polentia is asked,

PRoPERTIES OF ELECT RIC FIELD find locsk done.

) LIN ES
Cagiaake

k) Disectn
.

foom

o electeic ed
tue chasge & teminal to
chaye
~ue>RELATION
ELE CT RLC
Blw

POTENTIAL
ELECTRIC FIELD
(Scalan)
&

Cusve
r)2 lectic
is guen
Reld
by

linea
slope

neves
lines atang point
tong

inkes sect eoch

entto that punt

ofha
on
E= -dv my
dx
Polenkt'a!

gtadient
+ In clitecton
value
ef fel4,
potentil decseases

) Neves fetm clo8e loop except non uniton

magnetic Beld.
v) Alauaye move k to equipotential suface:
dx dy dz
ui) No f electre feeld lines rag nikude
vT) 8lectic eld Chotge
ine S chage inide Ne-Vi=- (EEs+Ezk).(dattdys + dzk
Conductor is aluays gero Hence, lonductos is
called sheld- then electic el4 line wil ente
G& leve oncucto t wl do it h to Susbce. fEadx - fEg dy -Ezde
y

TYPES OF ELECTRIC AEID INES

Uni fom Aeld tines (Montude
ditecten
y
dfield ines is
SameJ
 ELECTRIC POTEN TIAL DUE TO
c) x <R V K
PoINT cHARaE IN 1TS ELECTRIC
dwRqo@d
R
FLE LD
4+VConst Eo
F d
Kqo 9 lecdtie polenkiol due to untbtrnly chasged
non condufng phee. 43Vs (2.
saegth
my Elecic potentPal Ka) Eleckaie polenhd

SR
a) &>R
field & force wche velol quenlaty,' natvse d chasge
Veut KQ PR
not mentioned But, for elec toic polential 3Eo x
d chadge must be menlioned.
nghuse
b) 8= R Vs = R?
3&o
X
t<R
A c)
Vin- Vs= -[o dr- -5 3E%
(R )
6&o

Yan = R(3R-) Veenbse

2
3fR
3E
b)

)
-Vs
2 2
ELE CTROSTA TUC PoTENTIAL ENERGY
Conducdig ang (chaageunifasmy --Re total amt uwosk done n atleadt
bringnA
dislaibued)
2 point chages vey slocaly Jhom oo to he fredd
Ycene = Ka & ech o Rer to fom a elem
R attally q
too at oo

b) Ingulating ing (Casge non unitoamy

distaibute d) PE G isolated yotem
Vcenhe = RQ chaxge
R patlicle = o

t (entse hg,even for non unitotm dighibotn = Kqigz

on
dig, polenhal wil be tame T quq aMe lke
uincteaseie Ussilen 0

Electtic potential due to along ik 4T q93 ane uni ke u decs eases te: Ugyskem 20
axis
hing
dv= kdq
need
As for unlike

extenal
U1 to do
oil atoac q2,
coNk
no

Jn co0e 3 chatged pankces

disc. Q3equa q ase atcosnes f

)
chaages placed
ilectoic potential due to
equilotet al ide a

dv= oR (2Trdd) /NtR

on A

Find PE chatg e Jystem b) Caleulale cu'k

Aeg. to deaeaoe gide d a to a/2 c) Ifcheyso
2&o
Veentye
=R2&e hoo dome mass m, fnd
uwhentfey
lie oh A
Bpeed
de 2a.
each pashele

3 ko' 2Ui
8 Elecdic potental due to con ducting thin A 8u ace
which
u
o b) a12

and conduchg solid sphere

at pi
shell
spherical
Ih caje ) osk done by ayslem = SK
2a
Yout KQ dogs in PE = yaun in KE

24
bY=R Vsutlace
Ka
 ELECTRIC PoTEN TIAL DUE TO
ELEC TRIC c) 8 <R Vi = KQ
POLNT cHARaE IN ITS R
FLELD dw=kqoQdr 4+Vconst E0
F J
diyen x lecdtie polenlial due to uniBtrnly chasged
Qe cppo in

non condung sphere.

A3Vs (2
shegt.
my Elecbic potental KO)x Elecail polenhd

A Va=- Kq 8-R
X a) &R
field & foe wese vecos quonkhy,. nahvse d hasge
not menhicned But, for electhic polenhial, 3 Eo &
natuse chatge

VA =
muot

Kq
be mentioned.

+ Kqz + k-93)
) b) &= R Vs = PR2
38o
X
A
2 t< R
,L
3&o

Yn =R (3R-)
6&o
Venbae = 3PR
2 3Eo
b) b

) Conducdi

Ycente
sog (chageuni feamy,

KO
R
dislaibued)
-The
ELE
total

2 poant chages
d
atoo
ech otRer
2
CTRO8TATIC
amt

to
vy
fom
wosk done
slocly
a
2
POTENTIAL

syelem
n b inging
fom oo to he
ENER GY
atleast

dd

) Ingulatfg aing (Cabge non unitosmly

disaibued) PE f isolated
Vcenbe = KQ
R
chaxge
=o
492 Syslem

paricle

centae hing, even fox non unitotm digtibutn = Kqig2

BH

on ding, polential will be ahe T qq2 ae Uke uincteases ire

UsgilenO
E|Electic polenhial due to ding along ik
TP q93 ane unlike u decbeases e. Ugysem <O
axiS dv= kdq As for unlike choxqes, 9 wil at sact q2, no

need f extesnal ogext to do wosk

n cae
d3charged pantdes
a
T lectic potential
dv=
due to disc.
oR (2Trdd) /NR
a

Ycenbe aR
2&e
2Eo
. for n'

EQuIPOTENTIAL
no f chasses , no sysom
SURFA CE
=
= n (n-)
due con duclng thfn 2
8 Elecic
Spherical
potenial

shell and conduckng

to

solid sphexe
A

at
Buj ace

Tn
which

case
wh d

polenfial

d paint
is

at
t
evey
choag
to electaic

poin t is
feld
Same .
liney

a x>R Vet KQ
susface
equipoten Hial
Sphexical

b) X=R Vsukkr KQ
A uni Poam y choged hg tddiuo a 2
 VVd cylindaic al

Suxface-,
equrpolen ial

sEx Aaea of yaussian susface = qenclesed

Eo
AENERAL AVALYSS BASED ON
In cage fa aheet aAUsS
fos Bymmelhica potihion
Planas equfpolenhal A chagefox ong (inked
Sutface Plux Po each nth part 3
44
PROPERTIES OF EQUIPOTENTINL n Bo

SURFACE
i Ameunt
partcle
wrk done th
ftom one point
mowhg
to anothe
a ctha
Hhoaged
on
equipolential
Foo chageouthidFox unaymmetical poaihon
hr Youton gujoeehasge pas a giuen sugae
Enleing lux <o
Plur cil aliys be 9/£
.
g
Cnked

Susyoce is gedo tolal lux enterg (eavig -EA +EA

i Fsum on cquipotential gwace,
=0
ii As
always moue
electic eld
h to Guxface
electrc
.dv-Ed
eld ines

THROU
FvY DUE
aH A
To
DISC
PoNT CHARAE
linos nevet Pnlea Set, 0
tquipolenlal suyfoCd neves ntessect each ohes
GAUSS THEDREM o= Q(-Cos ox)
2&o
AREA VECTOR

ee tufo CAUITy IN CASE OF UNIFOR MLY

CHARa D NON - CONDUcTINa
SPHERE LINDER AS s pe we
SOLID ANGLE do = dA /2 chosge hai,
antior
Atany
3to 3 &o

2
poiat i
=
3€%
3(7-) Tnside covtye
Cauity chaged
it Cc untbsmly
non conducka

FLUX tre product d any pgcal qvadiy 3&0 wll be unifodm

Liaked wifh any paztiwlar giuen and non zeto
>ELECTRIC FIELD DuE oo'y
Pqar given oteo Pe eledac feld ne Elecic LARaE CHARaE &HEET
O

,rana?
lux
gauHian Susloce ylncles
EdA As this is oo'ly lage,choqe
g) abx5
dislalbuhon

wil behaue
is unifdm
ao
2 this Sofoce

)
= equipotential
dinked lux Rtough Sufeae

= EA o E
30 to

baaythaough the
PindRux, E must pass
adea of suaface
wved part =0

ood |heet EAtEA =

feld lineo

A/So E
moue

=
h

Sl2
Sm ofor 2 sheet
jdg = f(2n43). sdh given

kept paallel28, ElSo

-Tus Reld
Acentte cube Alov

=4As
one Jace

, it
whateve
Pout = EL'os o = E
capaatos oube 9
68
Dio = E-A = 10 Cod 180 = -l0L2 ELECT Chegge placed at cotnes ube.
Pnet = bin t oat = -IaL + loc = o Asume thot l culbf

i8 Sunou nded by
Slalement yau8 Reotem PLATE
E
The total linked Plux wikPh a dosed Sus face bg cube.

E Hrough 3 focea infon,

total chatge
is equal L times the
24 &o
enclosed.
 Tn car he choage x Z4enclesed

d cylindical equipolen Hal

Suxface >Ex Aea cf yausgsian susface = qenclesed

Eo
ENERAL AnVALYSIS BASED ON
In cage fa theet aAUsS
fox Bymmelhicl potitton
linked
Plana equpolenhal 93 A f chage for ang
nt prt 3
Sut face Plox Por each

44
PRoPERTIE S oF EQUIPOTENTINL
Fos chage outidFox unymmetaical potihon
SURFACE for sufae ,nked
{he ypouin bujo hasge a given
i Ameuef wctk done ih moung a ctaaged Plux wil aliaye be? 9/Eo
panktle from one point to anoker on equipolenip olal flox enteig- evig - -EA +EA
Suyfoce is geso. =0
iiFsum an cquipoential unace, electit eld linesAU DuE To PoINT CHARAt
always moue h to tuxface dv-Erda THROU aH A DISC
cld ines neves 0
iii As
equipoenlial
electhic

suyfos heves ntes

PnlesSek,
sect eoach otheg JateTR = Q(- Coso<
28o
)
GAUSS THEDREM
AREA VEC TOR Alwaye h ouside OF UNIFOR MLY
CAvITY IN CASE

SOLID ANGLE da = dA/2

CHARaED
SPHERE | NON
LIN
- CoNDuCTING
DER

38o 3 &o
As dscpe we
chosge

-ve
ha,

= lmg UT iesadian.
polat in =R(i-) Tnsde cevikye

cauity unibtmly

FLUX e
inked
prduc
wifh
d any
any
phghcal
pazthiaular g'uen
quadihy

>
3&0
ELECT RIC FIELD DuE
wil be unifotm
and non zeto
T0 ao'y

LARaE CHARG E &HEET

orea Re elecie feld Cneo Electc
Pgas given
pas kosg glux
As tRis is oy lage,
unifodm
choxge
Su loce
dslalbuhon is this

wiu behove as equipotential sufoe

3) b = abx5 dinked flon tRaoug

=0
Reld lines moue h

wved paat
iac
= EA Co 30°

E= fa3)pthsough
the
to find Aox, E must pass
adea o susface
o Fo
ot
| Sheet
2 sheet
EA +EA = SAlSo F

given
f(2nt3).sd kept paxall el
-Tuis feld is independent dis lance; So,

.t
whateve Re distonce blw plales
capaatots, the freld wil be 8ame

= 10L = -l0L2 ELECTRIC FIELD DUE TO

io = E-A (o 180
UNFoRMLY CHARGED FlNITE
PLUATE
Stalement yau 8 Reotem
lux wifRPn a dosed sus face
The total linked"

is equal times the total chatge to ooly

Compored
enclesed. chaged
 Bofh shee dhon Ône
Dep endo upoh
Find Reld at PRs. But Torq ue
dopote
oentaton
Field at P- geo

RAt RAS =
230 Sine

io diechion shoUJn. t= qE(2Sfn e) = PE Sin e = PxE

Couple acting on dipole ma ( pE) when dipo lé

is
ELECTRIC DIPOLE ohen 2 equal & h tofield omin (o) wken d'pde i8 pazallel

oppoite charges placed ae by a vey Small

os ankipatallel to freld
distance (measured in f) then Hr type
Fos dmall 0cilatiun, Sn e e
staoctuoe is called an electtit dipole

ELETRIC PoLE MoMENT

e PE =o
Di
da moment
Itis a ueclar quanlity
eilie chosge &' leng
dglined
L them:
as pbdac PE 4T-27 PE
Alwaus Fom -ve to tue chage wORR DoN E AND LOSS I
-q +9
4x2 ùnit& Coulumb mete PoTENNTIAL E nIERaY (n ROTAInNa A
-2
() Dimenion & LALT DIPOLE INM ELECTRIC
ynIFoR FIELD

ELECT FIELD & PoTENTIAL

RIC Opeld = PE(CosG-Cog e,)
DUE To gmALL DIPOLE ALONG8 Te = q0° 2 ,=, then,
--PE Cos e
Sde on Gx axal posthon
(Usya <o)
syslem = -PE Stable
PRBs-2) Jatchage iEl>El equilibaium
Payhde.
-q 2R T e blw pa E qo<e<i8o> Unsta ble

equil bium
poikon, eqn (pE=tue)
2kp Una toble
(Uiys>o)

/ table e, (PE= -ue)

2| Boad on ox equatoztal disechon f dipcle ACT|n Blw 2 DI PoLES
position moment FORCE
= K(-p) FoR ORIENTIATIONS
P DIPPEREnNT
EA Code

+9
eçuatoyal

F= -6R PP
-9
B Vequatral =0 -ve &gn indicate Pose is a Haachve in

nohe
Aeuabral potilion, disechien E is oppoSile But far
to disechon dipcle moment
Enio =-2E equateaial

gereal pofnt F= + KPB

n'e
Eaxd Pos
Etyuatait

Enet KP+3Cose > ORCE ACTInG 0N DIPoLE PUACED

LNN Uond unifoRM ELE C TRIC FIELD
= tan tan e
* when a dipble s pfaced în non unifos

2 electai Ric field rt expeaien ceS toxque 0d uel

PSioe
V= KPCase 4 o> Due ho
aA taanslatonal fote

Due to A'B'
F= PdE
TORQUE ACTING oN SMALL
OIPOLE PLACED i AN UIFoRM
ELECTRIC AELD
 PRESSURE EXERTIoN EFFECT
P= dF = Dueto mutual
dA Eo sepulsion
chovge on a bady
sujoce,
an
evey part d bidy expeiendes
outword pse*sude whch scalled
electic Ptess ue
> PROPER TIES OF CoN DUC TOR
(
chage & feld Rstde a
always a emaind gero)
condochig kndy
Chasge at contse
Distaibution d
chotge net at
..Non
cenhe
Unífoam
i) AE elechao&latic tate chog Jig fai butíon indide
,eld Pnde a and innex &usfou
Con ducto
become gedo. &o fhese wrl But uniPoom outtide.
uni Pom.
movement be
ang tue o -ve ion This
phenomenon is caled
thielding
.
ec.
no
i8

AS elethc fcd entes inthe

Conductox, Re loond blu tue
2-ve break & -ve Come ih
oppo diection f elecaic field
Due to dstaibuton
in6de charge
Conductor,elecitic freld is gene
wthth tated indide
move fom
tve to -ve called E
Thege boR int

Conel out each o hee'

L hence net
electnceld in&ide conducto o
Slectic Pield nes move h to 8ufoe
conductoy

) The elecdtic
Conductor is E=at
feld
G
Eo
sufoce the

iv) The electzos tatic polential ha he 3ame

voe on the Suface and inside fhe
Con ducto

y Suyfae den siky chage is dien

at dillexent poin s.
DISTRIBUTI N

Choxge dasihy is invesely ppasional to

te todius Cuvatu se

OK 8 = Conytanf