All rights mztrttcd with Fut1iahTc:tthuok Board. Lahtwc.
Appmvud by tht: Federal Minis-‘try t;:['E,|;1u|:;|Ii0r|_ [5I;g|1-;aI;t3d_
‘Vida Letter I'~lt:|-I-'.lIi-4-I'Zl]'|]21' b-.5) dalmzl IT May, 2003
_ __
Guftarnmenl 0|" Pttltislan. Islamabad-
Sr. Ha.
12.
13.
14.
Chgpter
Electrctstattcs
C‘.-urre nt Electrictty
Electra-magnetism
|=-Q9;
1
3,1
55
15. .
Electromagnetic lnductiflfl
E1
15.
1?.
13.
Altemating Current
Physics of Solids
Electmnics
111
135
154
19.
Dawn uf Mun‘-arn Physics
1 T5
20.
-21.
Atomic Spectra
Nuclear Physics
3433
219
1.
Glossary
360
ii.
Btbliu-grap hy
iii.
"---
'
25.4
Index
255
-
.
PM Br. llln. l"dI1'.i| Saint-mi
_ Eillrl-I-|l11lil-L|h'|..'\:-'t~FaI:ct:ht.
Pm-I. Dr. M-Ttl1,g]1I-1-lrn1|ll:
I-lltrin Btttt
__ .
mt. Mnhdnmnd Mi-Silhid
I-:1:-i-F|¢p¢lg|
mt. Sh. Allah nttma tum.)
Fmf. Nu-nr Aland QIu1'r.1hl{ll|d.|
Pnul‘. 5. H.Altl1lnr[Rld'.j
Pmll IHIIII-tltrll-d Niflr
Prof. Dr. ljn Mujubn Ghuri
l"rnf- Dr. Muhammad Fllfiq
Dr. Muhammad lhflq S:hl{RI:|.]
PI'fl|'- Muhammad l"itI\~"lr Khan
Pmfl Yl'lttl1ltluIld.|l|.l_iSl1:hid
|'*.ruI. 5l1_.I|.l't|i1-.~\l1m|-d {ll'.ld.j|
l:u.1'.~|-F|.au:¢|||
_
. Prqt Bf. Mn. I"u-tlzil Sllulni
S";-ll‘!-i-|fl1|I-lLI|'iil'rir|:I.i‘.|2Ili'|I
'
\-I. |'|.1ttr§-|tt.\.
J’
-
fllliscrfillccrn
Putalllhnl by: Mum-II Brdl:l'IirlJlhIum.
I; ,1 :1 - _ I
Prin-tldhyrz
" " ' "
Zahid BI:hlt'F'I'|l‘|lfl'l'! I_ahm-
flflqgflidrllng
Euluu-n Imptld-1-|dII\
“H mu,
" 151
1-1,.
Nu-fllfirpill
PI'lfl'
noon
mm
12
_- --_
—
Attlreehdofflrlc dreptertheshrdsnlswllhedale to:
Understand and d-ee-clibe C~eu|r.trmb'e lew.
'
-.‘ "£" '!"'-":!"‘
.
‘F'l‘*F" "!-"'
Deccrl-hetl1ert__achergehesal‘lelrle1tcroeeieundit.
Uniderslendfietcsofllkeandunlllteclurges.
rec-lehlh ' 'leef' ‘t ‘nlsrssncl rtctcstsl
‘eras-ens llcetlenot‘
filroateflophenernenfipnmme'. Inna D"
p
mm
pp
Etrplcinflteelectrtclnteneltylnalreeepeoeend In other media.
‘Slate end prove Gs-|.|ss's law.
_'
'
Appreoletelheepplice1icnsctGsuss'slew.
_
heleclrtc
t‘ let
'|' rerrneotwcrkrioneInl:' '
mama
eunllcoslllve
9-
mcrgeaph hcmlnfinpltE,r‘t.r;1fl[|?atpe?nf.°m m
Fteleteelectric field strerrgthencl potential gradient.
1|}.
Ftnd Expression [DI potentislste lil'fliI'll!d|.|e!.c1a pcinlcharge.
11.
Elsscrih-s and ccrivethe value o1eleo1ric_r':herge by Millil-tan's met:-ice,
12.
11
14,
' 15,
Cielrnalatc the cspscitanceof parallel plate capacitor.
Reccgnlzclhie elfect eldielectriccnthecapccllsncecilpereltel plate capecilier.
Llnderstartrt and cleectihe electric pelerizelion ofdielerzhic.
gacw mergtrgaegfinefacgtaefigggralmd discharging c1 e cececltor through e resistance
1B-
Find energyerrereeeierrefecherged capacitor.
'
!~|e study of electric charges at rest under the ectien of electric forces is ltrrctrm as
ec1rcstalics.An electric leroe is the force which holds the peoilive end negative chargeslhal matte up atoms and molecules. The human body is composed entirety ol etcms sntl
rrtolecutes.tl'tuswe owe cur ettislencclolhe electric force.
'
We l-tnow that there are two l-tinds ot charges. namely,
positive and negative charges. The charge on an electron is
assumed to be negative and charge on a proton is positive.
Moreover. we also learnt that lilte charges rep-al each other
and urllilte charges attract each ether. Now we investigate
the quantitative nature of these forces. The first
measurement ol the loroe between electric charges was
made in 1BTtl- AD by Charles Coulomb. El Frert-tat military
engineer. Clrt the basis ol these measurements, he deduced
slew ltnowrt as C‘-oulorrtt:|'s law. it statesthat
.n teen-in-|; nun
:
.*.'¢.
'F.":'...-.-. '--—I'-r*---''.-'1I -f1‘Iit
.
I-+ l-4!,-:3-I
i. '
-.-.|
!_‘l.l|-.__;.____1.t-._..,|_,_|t
,
-. . -, ". .- . -. .1I‘... -_.-t_
'-it-_T---;".i.r1:r_;'["_§_g-i": ‘5?T;.=;.ii=-._-is :.'.".'L.,"rt-'.'.‘-.'-.'-',,-=-'{?.f!'1.---
..;-.1.--E‘-1-I-cl-t';'l,,{.‘1;_flfi.'-§.F-:1*1..";'E: "1 '
:.:,- :1-r
t_t:.--:_.1"itsI
it--'
;.u_..---|.-'
.--.-.-_-;1,
Fetiiigl
er
F.._t¢@
'
-151
;.j_-;._ L:
E7-;'- _--..t_-._ital.._ -.15
_ ...I_.'.-.j-'-t.rj
.F.:,.e|_-:_i-r:_,'€.;:‘-rf_|_.__ _L,__-_F_-_._I-_f all-I-.-__—_--||t'd.|_i.t:-._---. .-_ ._
-
_ 7 __ _
........ -.
'-
,_
112.1;
F
Where F is the magnitude of the mutual loro-E that acts on
F,‘
"It.
‘II.
F_
-l—-I ---- -~-3--l~
r"
i=-r-
“ """ ' '1'
r=,,
|=,,
‘It. j_§.----.q_-J-c.
|t:.
F.
-t------------>
each cri the two pcrnt charges qr, , q_. and r is the distance
between them. The torce F alwatrs acts along the line joining
the two point charges (Fig. 12.11, lr is the constant til
orooortionalittr. its value depends upon the nature oi medium
betweorl the two charges and system oi units in which F, q
and r are rneasured. It the medium between the two point
charges is tree sea-so and the system of units is SI, then it is
represented as
it
_
121 tlt lhoulutvtt hrou
bttilirltt llltl cltlriel Ind [hit
lltmthe lttteto ltehveert unlit:
dun-on
5"];
........ ..
[t2.2i
where t:_ 15 an elactrtcal constant known as |;t-err'n|tt|~.'|t;,r of
tree space in 5| units. its value is B B5 I 113" hlt't't'C'
Eubslttuttngtha value of: the constant
it 4% =s=-=1o*r~.|m-t:Thus Cctutornlzfs force in free space is
F H ____i__ 951 ........ ..
em,
'1
er-
'\
tu
nae;
-he stated eainier. l1o|.tlomtis‘ force is mutual force. it means
Ihel it ti. eiterts at foroe on o,. than q, also etterts an equal and
opposite force on o.. lfvre denote the force cttertedoncghy e.
arsF_.. and thaloncharge o. dueto e_.as F.,. then
F,--t=,,
t.
{tat}
The magnitude ol both these two lioroes is the same ani:t is
given by Eg. 12.3- To represent the direction ol these forces
we introduce unit vector-s.'lf |'-,, isthe urtitv-actor directed from
r.]I,toe,ar'|t:l|i,,istl1aunitve~ctori:Hreote'dfro|nq,tog,.flten
_ 1
g .
_ t=,, -Etta,-r-r._.,
‘Li
J
I
F
-'
_." r
qt
12.51:}
§
1".
t=,,-;—;;5f_§1ie
r J‘
-
If I
ll-lit
so
ti
qt
,"
taste}
The tproes F,. and F._.are shown in Fig.12.2 l_a 8. D]. ltcan he
seen that i,. =-i.,,scEqe.12.sras cisnewit-lat
J
'||
tot
ng :2 :r
For = ' Fl:
The sign cl the charges in Eqs. 12-5 ta 8- ti] determine
whether the forces are attractive or repiulsive.
We shell now consider the ettect oi medium oetweenthe me
charges upon the Coulomb's force- ll the medium l5 an
insulator. it is usually retened as dielectric. It has been fflqmfi
that the presence or a dielectric always reduces the
electrostatic loroe as compared with that tl'l tree space by e
certain lactor which is a constant for the given dielectric. This
constant is ttrtown as relative penhitlivity and is represemed
bye. The values ofrelalirve permittivityo-‘i difierent dietectncs
are given in Table 12.1
Thus the Coutcmtzrs loroe in a medium cl relative permittivity
c, ls given by
F =LEt
‘fl¢,Ef ri
..........
.
"2 E}
ltcan be seenin the tabtethel r._ forairls 1.tZiiJtZti;'i. This valuets
so close to one that with negligible error. the Eq. 12-3 gives
the electric toroeln air.
!h'It1th11fl: t2l'ugecq,=1DlIl_pl3mdq,f5Dpt3at'e
lomldhtry-phtedpctilornr, =10] u'ii:lr,=-it.tItltmier:-firttly.
3
Iii
E
|:,.
vnctun
'
1
I .tH'1I It'll]
I
‘l.{IIfl-
ii
Bllttilttrl
't'iilt'|'ltIit.|tt't
31:
him
I2-35
5-1-B
2.28-I
1!
'.-‘Mu
3-1.5
P-itfl paper
E
Flltllfll
Flttttiillt‘
Tilttti
Tfitfl‘ H
5.-ll}
2.9!
2.1
2.1
't\'ii|rllflIcl|
I'll
nlrerefliedialmseseremeaeumdinmelresfiaiuflateflwe
ferceer\e,[Fig.12.3}.
3-fill-I’flen:
"
q,é100|.1C.
q,=50|.|G
Feaiticrrvqrserefcirelefivelfler
=r,,Ir,-r.I-4-l-Bl
.r=n1egnltud|eh',.I J
\,\
--
.I.
ME.‘
‘H
"
-
‘Q1
F n1q.-
~
- »r~\
Q.
r,l~l.0l
Fla 1::
is
i':||:|!—-“Ina:
5
MEI
hl|l lil|,""
DI-_- - 1*;
_ _
=.'5n1
_ *- 4--=..-f
-
.-\.
3 _9_:r ie'_r~r_|ifc:'-’ 1_ rec I111‘ cs ms 1e"c 1 4 r- s 1
F"
'
'
rs in?’
.-.
-
s
at
=1-rHi-'l.lJBi
"ins-;,|i1r|u<issr|§,.=F=,,lr| .-14; ’ + r-r-es]»' = |.s er:
DlreclicnefF,.= tan"
_
I,
1.44;
-3T"wilh:r-axis
,
I:
-
Han-ten's urivsrsal gs-uitaliensl law and C-eulen'|l:'s law
enable us ie calculele the magniluee as well as the clireciisns
eflhe grerritetierral and eleclricferces. respect?-sly. Hewaver
one may q|.|es1ien. ta} W'ha1 are the eriglns cf lhese fercee?
{bl Haw are these [areas lransmlttec frem ene mesa leanelrisrnrlrern ens snargsle anether?
The ansn-er‘ In [is] is slil unimmvn: lhe eirlslense of lhese
forces is accepted as il is. Thal is wlw ll'ie{|' are called basic
fereesefnslure.
Te describe Ilia mecnanlsm by which electric ferce is
iransmlliacl, Michael Faraday [1?91-186?} lntrerlucecl the
eense|:tefanaisr:|risfis|d.Ai:sereinglehlslrierir1r.ltls1he
iruiinaiserepertyelnelurelrrataneiscuicfisidsisstshflne
space erer.mn:l err electric charge. This electric field la
censiceredteb-eafereefieltllhelexeriaefereeenefliar
charges plecercl In that lleld. Fer example. e charge e
preeusee an electrlr: field in the space surreunting ii. This
4
field exists whether the ether charges are present in space er
ncil. Huweuer, the presence el field cannpt be tested until
anelher charge q_, is l:irciug1'i| irtte the field. Thus the field of
charge e interacts with qi, lie prccluce an electrical farce. The
interactlen between g and g, is accomplished in twp stepe:
{at the charge e produces a field and lb) the field interacts
with charge g,_te preduce a leree Fen cu. These tiuesleps are
illustrated in Flg. 12.4.
In this figure the density cl clets is prep-nttienal te the strength
crl the field at the --arieus paints. We may define electric field
etrenglherelectric field intensity-Ealanp peintinthefield as
|=
E - qp
-
[Ill
l12.1 I
where F is the farce eitperlencecl by a peslllire test charge pi,
placed at the pcilnt. The test charge -rt, has te be uergismalse
trial itrnay net dlslertlhefield which ilhaslc measure.
Since electric field intensity is tcrce per unit charge, it is
mee5t.tre-cl in newton perceutemlzi i1 SI units. lt is a vectorquantity and its directien is lhesameasthatefthe fierce F.
The fence BlqJBl'iEl'lCE'l1l by a lest charge c, placed in the field
cl‘ a charge g in vacuum is given by Eu. £12.33.
Eq. 12.? n
be used tc evaluate electric intanslty due tci a
paint charge g ata peint distant rt'rcijn IL Place a peeitivetest
charge qr, at this paint. The C.‘-eutnrnl:i's Terce that this charge
will experience due llci q is
F =_"_‘?'l'
‘mu ?-P-r'
..........
rthet
_,'.
'
--. F=I-c|_E
llll tilt
H
_
1:I}miI_—'I.I'I*'fl-!
whereiis aunll -recterdlrected tremlne pelntchargeg te the
test point where qr, has been placed. l-e., the petnl where the
electric intensilyis teheevaluated- By Eq. 12.?
F
1 qq . 1
t g.
Eiqaflinc F39-rlqiihzn Fit’ ........ ..
H19}
:_-I.--'..".~
-'—'- -.
_'_____ _ --,3;-'--..-.
___..._.._:,.
-__'.
-|u='.-;=. -1 _ 5
.
--.-.
.
.
_ -,..
_ .. .. '-..:_ 2:11-. ,. '1];
Iu
-5--4
..!i"=‘,-‘l1'l'-,.""'T.
I"'.'i;I'_T!§",I‘. ,' -. :- -l-ti-'
Ir
._._, ,
I-lI|-u-|_
{I1-.'l—'
'l'lI."
-I I
_-|—
-_t
‘-.
II:-.
1'.‘
-;
"|1'i!'tT_'IL‘J'*!
i-5'
.P|- In.‘ .__
-I
--.15
' _,_ :
'15-‘!-2:‘
I-.t-1-:
|l
L
-1'!
1
|';:t.-J:-TI|l':l l I:
.?#-:1:
. P7‘'III:J". .- ‘l Iii--=5-lei. .'.=.*.*l~'tl.'-rd
:-I-
__l|t~|E-l‘
I
;-|'
'l--fI:"'
-_ ll.- 1'5
1
-1|---ll-Ir 1-»
5
“I I
I
Q. "al F
.¢.
41"---2]-.I}n-t----'ll'
sures
em
relfievnerelecteelit-eeclcieoiaelltthiilhifite
.1I~\ sta- ii,’
.-55
J
'l
'l
-u
Flg.t2.5.iettrtedIstencedtPtrorng,bert.--
ME
E_nEh
"
t
.f-.-‘HQ!
r
*¢|
1'‘it’.
.
"
"lib
‘qr
We
ll, ll‘
\\’/..
"T
rs
r
1'
+\\*~.
'
l
rg.t:_ag1!ltlI=iII'rtrHIdlltI*rl.
as cl-rt" est’
.
.
u
'-F‘
i
'==‘.=:i-TE
; ;l=.;
--It
-
1B.fltt“tlll"C 4.'D:r'..’llIl"G
""'i1.i=i;——
d
or
irir-an-;a-o. hilicltglvea trlgl-_1;i_ii_i;=s'ii-.f_
e+e -"ea
-
-
W
i;""-.H.__1£|"F_.iI"'li‘
l-ll
q‘, =1‘ ‘it -q
-
I
It =1-;;
|||.qj{|;lil|'|-'!_|;l_|gg1j'|qr| .:§5 ;'§:t' tiitt
E: I;_..§
.._l.!_
. .. ...."..-_
There are htiio peeslttle _ir_a1ues of cl,
oor1'es|:iondetoeiocati:inot'ItotlierlghtoIhottt;trie_et1u1gpe
urheren1egniti.ideeofE.and E.ere eorrltfl-hut"dlmcIp|@s~are
sante.li1tt\iseeeeE,endE_,iitonolc=eneeletfliea|:_irtt‘l§lie
positive velieccrroet:icnde'lici"tIte.-iioatton shoinrr'1n=flipu'I'iB.
ertdlstherterofieldlocetlor|,henee.d¢=+1.tlrrt,.;_==-5:~15!-
a
rlwisual represantaliion cl‘ lheelectric field can be obtained in
terms of electric field lines; an idea proposed by liilichael
Faraday. Electric field lines can he thought cl a ‘map’ that
provides iitlorrnalicirii ah-out the diection and 51.l‘Bt’lgl.l't of ll'ie
electric field at various pleoea- As electric field linea provide
defile:-:i'ld'in'ip|le.i|i-iiterllrieei information about the electric force etrerted on a charge. the
I tqtrtfltil tense tilcld H11cllrwd.-._|I'rIdeth'i:%l'lllII lines are commonly called ‘lines oliorce".
in-use nu-iy =-mutt Inn rut To introduce electric field lines-. we place posi'li'ire lest
neiilhIircI1l=I1IaI*~ccharges each ofmagnitude q,,at ditterenlptaces out at equal
distances froth a positive charge +q as shrnvn in the figure.
Each test change will experience a repulsive force, as
pHildl'i1ililrl'iII|ll'|IilliclfllItill
-\-
\. l/3?”
ll"l2ll.t,‘sfllfEd by enztrws in Fig- 12.E[a]. Therefore, the electric;
field created by the charge +o is directed radially outward.
Fig. 12.6 {bl shows corresponding field lines which showlhe
field direction. Fig. 12.? shows the electric field lines in the
vicinity ol a negative charge -e In this case the tines are
directed radially ‘inward’, because the tdrce on a positive
test charge is new or attraction, indicating the electric field
pointsin-ward.
__j
it
“Tn H‘/"'ti:
\ - ll
Figures 12.6 and 12.? represent two dimensional picture-sot
the field lines. However, electric field lines ernarge from the
charges in three dimensions. and an infinite ni.irnb-er of tines
couldbedrawriThe electricfield lines ‘map’ also provides information about
ti
the strength oi‘ the electric field. As we notice in
Figs. 12-5 and 12.? that field lines are closer to each other
near the charges where the field is strong vthie they
continuously spread outindicating a continuous decrease in
thefieldstrength.
‘|rii|i|-lie;-ll
-_-
‘I.
.1
--Il'I
1
__
I!|,-l_t-_-l"'_|_-
"i
.
"
i
;" -§*‘"'lr " "is" 1
-I
-I
;
l|
identical negatively charges irril be eiteclly the same, The
midcle region shows the presence ot a zero field spot or
--..
"
.-
itii
.’r'
The electric field ices are curved ln case oi hvo identical
separated charges. Flg.12.B shows the partem ot lines
associated virith two identical positive point charges of equal
magnitude. lt reveals that the linesin the region brB'l;1i'tl$Bt'lt'r'r\l;t
lilte charges seem to repel each other. ‘I1-ie behaviour i;i‘itwp
.p
_1
L
U‘-.
_.-rl .. ‘-
neutrelzorie.
The Fig.12.9 sltovrs the electric field pattern cl hvo opposite
charges oi same magnitudes. The ileld lines start from
positive charge and end on a negative charge. The electric
field at points suoh as 1, 2, 2 is the resultant otfietde created
by the two charges at these points. The directions or the
.4‘
IIII
W
gs, ‘--.
't¥i-atI.-'. .|r~_;—__5'_
lxlufi
'-.~-_
|
I
,.-'
"ti.
|
_.
equally spaced.
We are new in a position to summarize the properties
oteleciricfieldlinee.
ti
Electric field lines originate lrom positive charges
and end on negative charges.
2]
3]
til
The is-irigettt to a field line at any point gives the
diireclionotthe elactricfieldatthat point.
The fines are closer vritere the field is strong and the
linesaretanherapehnheretrtefialdisvieah
No two lines crosseach other. This is be-muse E has
only onedireclionatanygiven point. tithe lines cross,
Ecould have more than one direction.
T
It
‘
_
resultant intensities is given by the tangents drevim to the field
linesat these points.
In the regions where the field lines are parallel and equally
spaced. the same number or lines pass per unit area and
therefore, field is uniform on all points. Fig. 12-11] shows l'.l1e
field lines between the plate-sot aparallel plate capacitor. The
field is unil‘orm in the middle region where field lines are
tr
-1;
i
” Tl il 2>i
y
"
i
I
<lcl lg,last
ttltlfliglr-§
i[||
Jtorography[Photo-copier]
Fig.12.11 illustrates a photocopy machine. The copying
pa-grain-bocopled-la-oodcrirrrn
M
_
larrip
__
lens
lortorooifirrdge
ocrritl-nrrtg bleolt
lonerrhrst
:,lr—I"'I
i
—
urdr-rial
hqggigji-gigy,
papero-n'rIr11lcl'it1~rI
irrtngets-prritrl-d
t'.'*.."-...t'...’“s'f.‘;."L'l.t'..."°“"""’.....,..ll2.'.tt'..."’.......""""...':‘..'tt.t'.';'.,“s%'t
iII'lIHII'.TIlIII'fl'-Irililfir-W.
_
' fl
'_" ,2
process is celled rrerography. irom the Grreelr word 'xeros'
and ‘graphosf, theaning "dry writing", The heart of machine
is a drum which is an atuminrum cylinder coated with a layer
, ol selenium. Aluminium is an excellent conductor. CI-n the
other hand, selenium is an insulator iri the clarlr and becomes
a conductor when exposed to light; it is a photoconductor. As
a result. if a positive charge is sprinltlad over the selenium it
will remain there as tong as it remains in darir. if the drur'n is
exposed to light. the electrons from aluminium pass through
the conducting selenium and neutralize the positive charge.
It the drum is exposed to an image oi the document to be
fry; rig ||-q “yaw pg it
li-hsl lltrl hp or’ I'lrl|iidl.IlI' ‘l'IIor.rrgh
the
the orirrirroi
muin-are
H, aniii-tit
M mm
In ,,,or
“'°""““”"'“““"
copied, the clarlt and light areas of the docuntent produce
corresponding areas on the drum. The darlt areas retain their
positive charge. but light areas become conducting, lcse
their positive charge and become neutral.
In this way, a positive chargelmage of the document remains
on the selenium surlace. Then a special dry. blaclr. powder
called ‘toner’ is given a negative charge and spread overthe
dn,im,1.rrl'1ere itsticlrs to the positive charged areas.
The loner [rem the i;ln,.im is translerred on to a sheet-bl paper
on which the document is to be copied. Heated pressure
S
rollers than nri-air the toner into the paper which is also given
arr e’-tlcess positive charge to produce the permanent
impresrsion oftha document.
Ill]
lrl!-Ijcl Pr‘ r'rl.r2-I";
An inltjet printer {Fig 12.12 a] is a hrpe of printer wfiripit uses
etaotnc charge in its operation, while shuttling tiaclt and forth
acroae the paper. the initjet printer ‘ejects’ a thin stream or
inlr. The inlt is forced outcria small nozzle and breaks up into
etttrarrtel-;.r smalldroplets. Dunng their flight. the droplets pass
through two elaotrioal components. a ‘charging electrode‘
and the "deflection plates‘ [a parallel plate capacitor). When
the printhead moves over regions or the paper which are not
to he inlted, the charging electrode is tart on and gives the ink
droplets a net charge. The deflection plates ditrert suott
charged tlrepsintoa gutter and in this way such drops are net
able to aaadt the paper. Whenever ink ire to he placed on the
paper, the charging control. responding to con1ooter.turnsol‘f
the charging electrode- The uncharged droplets fly straight
through the deflection plates and sirilte the paper. Schematic
diagram ofsu-ch a printeris shown by-Fig.12.12th}.
rflnarprr-5
Ht-II-HJI
Ilr'l-|I.l-:1 to-I‘-I1
i
II-IJIIIIIIIFIIF-I
"t
...;'"-H
titEl53$ii?iiilit‘
moan-glddrnshllannimlernei-nnooon
lnltjel printers can ate-D produce coloured copies.
at
when we place an element oi area in art electric field. some
ortheiirtes olforca pass throughitt_Fig. 12 t3al.
The number of the field lines passingthrough ecertain element
or area ts ltnoir-n as electric ltutr through that area. It is usually
denoted try Graelt letter ¢'. For tell-Bmplre the flt.|:-I otthrough the
areartin Fig. 12.13 ratisd wlhletlteflutr Irlrrough Ei is2.
In order to gitra a quantitative meaning to flux. the field lines
are drawn such that the number or field lines passing through
‘ti
i i?/'
l
—r-
ll
—-+
—-n
l
i-:__L_i-J..
.\._-.- .-
—+
1--|__,.,_,_._-I
-.|»._
-
.
qr.
_.r
s unil area held perpendicular lo field Ines at a point
represrerttthelrttenslty Eolthe llald aluial paint. Suppose at
a given paint lha tralue crl E is -rill’-ill‘-". This means that ll 1m‘
area is hsldporporidlculartolleldllheeatli-tiepolrit,4fiaii!
inaswilipessutrsugltlt.ihordertaeslahiishrolstion
bohrrean elactriciluttrlli. electrlcinlensit-;rE and area rt. we
rnrtsidar the Flg-12.13 r[lfll,¢.d] triiltieit shows the three
tllrhertslrllrtfll representation of the electric field lites due to a
u'iilor'melech1cfieldoli1lensil1rEIn Fig.12.13 (bl. also is hold perpendicular to the field lines.
lhenErt_. lines pass fltrrougit ll. Tl'te1'lu:rtlll,ln ihlscasais
l—-ii
—'-it
——Ir
s
-“.- t-1==+*=-t»ir- Eli?
. _.
"--'
ll
-' '
-
_,
-
trrhere A_t:lttr'id1iee that the area is held perpendicular to field
in Flg.12.13lc},a.rea A is hel-dparallaltofiaid lines and.
*4 lino-s.
aslrs-ch»v'it:iushelinerscroesllisaraa, aatl-|atrt1nrrp_ir1 this
ii
-"'—Ir
in
caseis
.
vrhera A, indicates that A is held paralal to the field lites.
Fig.12.13{dj|shorrrsthec=aserrrhttrrtr1ls-neither perpenrzlioular
nor parallel to field lites but ls inclined at angle El with lzha
lines. in this case we have-to find the projection ol the area
tahiclt is perpendicular tie use field lines. The area at this
prcrlectlon_{Flg.12-13d}isAeee£l.Ti-ie fluxtbin lhiscaqnls
Lflfli
Fl|.12.1'! up
1iI_=EAoorsEl
Usualtrlltoalamantolaraoisrepresantsdhyavectorareah
ruhosomsrgniltrdeisequeitodtesurtacearea.-tiorll'vs
slomsntt_tind1t1'rosedlrectlcnlsdirectianefnorntaltothe
area. The electric llutt ttr, through a patch ot‘ flsl surface in
lotrrtsolEandill.istl'tangirrenl:iy
tmerareisutaartgiaoettvaonlltefleldllnesandtlterramtalte
theema.
Eleotric11r.ttr.traing ascaiarproduct. is a scalar quantity. its 5|
urtitiel~lrn’C'*.
L-etuscelculatell'ieelec1|icfluttU1r'ougltsdrosedsurfsoe.irt
shape ole sphereerradiusrdua loa point charger;
Ill
placietl at this oantre of sphere as sriorri-n in Fig. 12.14. To
applrrthelonhttla lil,= Ejlilorttiaootrqsutalioitoleleotitcflita.
tlteaurlacia qreasltoultlb-all-sl. Forthi.eroeaonl1'ielr:i'tol
strfaceareaofthesphoroisdiviiadirrionsrriollpahttltssuriht
areas olntagrtlttrdaa M..M,M, ......i|iliil..,-lfn is vary large.
each palchtrrr:|r.|ld lsa'aIoteiiernentolorere-'l'l1ie
oorreaponding tractor areas are dull... fliig,
respiectivel1r.Tha dlractionoleactttroctorareaia
parpenticular drawn outward to the ooirrespondi 3
Tliaater.ttt1cin'r-ansitiesatti-ieoentraeolrractor
iii
£|.illi..£irli.,.
E,. E, ---.----E_respecti-reigr.
According to Eq.12.12. the total 'l’I.t:tr. passing through the
_I . _. .|
.|_
--.-_cioisadattrfaoais
“l I...,1
T'l
_.:..'.I
.; . ‘iJ-,,.-_.-.._.
.
-' --
-_
.
_-
__
_
_ -
_
-
.
‘_J_T.,.T_.L
._1t'1;.; ;~
.1-i.i_
_
__
Thedi|'ectiono1alectriclntenailyarid\recloraroaisaatrtoat
eecltpatr:h.liloreovar.bacatraeolspltar1cda';immatr3r.atllto
surfaosolspriere.
-
--
-
.i.ti.._
J-1'
-
>t-.~"-=- 'r_i
fr-':1
"1""'l
..:I'.'_
‘-'r-__ "-lbs-, tn
-_..
-
..
5"t;-'_--5.2- .-:-7
.- -2
-
ll‘.
ll-
J-
__r.:
__;|:
'-."-j:ir1
3
=. .
‘Ur
._:
_ |-T-£153
tli,IEo.-i.+Eo.A,+E.oA,+ .......+Eil!iA,.
=IEtt[.ilL-li,+.ilii.ll,+iM,+ .......+a.it.t
=Ett {total spherlcelsurlacia area}
1
H
3
is_
‘I _. ._f_.-.
1..-.__. E-1|! 3'
-1 "I-i .!rI 1... 1."
‘-"I“f-',;;:E-“.4
.-_:_i. ._
i----——‘fit, :3! 4 IF
.
_
_1. _
I‘.
F‘..
. _|
"r"
'-\1'
\ .-,4
'.:.-.
__
t=tq,t:_ta
lrlowlniaginetltataclossdsurlaioafiisarioiositgltiasphare.
llcanbeaeer1lrtFig.12.1EithatthallutrtlIooghlhoolosorr:l
surlacefiietlteeameasthatthroughthospltartetsottrooart
ooricludelzhattortalfluttdt I'll"-ill haclosadsurlaroadoasnot
dEflrEl'tdU[II1|hBShE|3EDfQflflfl1D'U'§'Dffl1IdflGId5lJffIOl.ll
depends uponlhiemeditrn and lhiecriargo enclosed.
Suppose poiint charges qt, rt, qr,
. rt, are arbitrarily
distdhutad it an arhltt'a|1,rahaped closed aurla aaahorirrrt in
Fig. 12.15. Using idea giren it previous section. tlte electric
ltuiipassinglliit:tug|h1ltac:iorseidsurlaioe_ls
-.
---J-I‘:
_ -. -T
HI H 1-
(Q-=gL |.
Ea
q
E:
.| HI". ;, 1'1
E-U
ED
1
at-_= —.'r[q, +13, +41, -........+q,,)
1
5“
c,=__— at flclat charge enclosed byclcsec surface]
re
1
~it,=—I'D
........ ..
(12.15)
EU
where D = q, + q_. +q-_ + .... .. +q,1, is the tctalcharge ertdcsed
by closed surface. Er:|-12.'1E is mathematical expression of
Gauss's law which can bestatetl as.
-
.. ._._.
....::..
‘Iii____ . F
Gauss's law is acplleo to calculate the electric Intensity clue
to rtitlereht charge confrguraucns. in all such cases, an
imaginary clc-sect surface is considered which passes
through the paint at '|'|‘l‘ltCl'l the electric intensity is to be
evaluated. This clcsed surface is itnown as -l".-iatlssian
surface. Its choice is such lhatthe flu: through itc-an be easily
evaluated. Nest the charge enclosed by Gaussian surface is
calculated anrt finally the electric intensity is computed by
applying -t'5auss's law E-q.12.1E. We will iilustrate this
prcceclure lsyrccnsirlering scrne examples.
I
_
._.__..
_.-_
__:
11] Iriterislty u‘ Field irwsiclc a rlcllcw Chargiirt
F
Supposelhat a hollow ccncluclihg sphere cf radius Ens given
a positive charge c. We wish to calculate the iielcl intensity
first atapcrnt inside the sphere.
-r-*'+
Q
fir
-l-
-lGilLt1=llIt'l Sltiiflfi
1-
‘I
-__u_,_._
.-
-I‘
s l.
‘.1-.1‘
J
'\_
rt‘
‘\.
|'\-
.r
i
1-
,|,
1-
r"
_‘_
R.
1
Q
um’-Ir
'3-
i
4-
New imagine a sphere cf radius Fits R In be inscribed within
the i1r:l|hew charged sphere as shcum in Fig. 12-17’. The
surface cl‘ this sphere is the Gaussian surface- Let ti? he flux
through this closed surface. It can be seen in the figure that
the charge enclcseu by the Gaussian surfaces is zero.
Applying Gaussian law. we have
1'
o,= 5 = c
n; 1111
E9
Since
¢t,= EA = D as Ar Cl. therefore.
I2
E =D
Thus the int-erler cf a hollow charged metal sphere is e field
tree regicn.A.s a consequence. any apparatus pieced within
emelalenclesureis'st|ielded_'fromelecai_cfieli:ie._
_
_
it:-| Electric lnti:-risity ljtiie to an ln*iuitr- Sheet -ct 1,4
._
__
Eli:-irge
_|
,.__, .
Suppcse we heire B plane sheetcfinfinite estenten yiihich ' '
pcisltiug dflrges. are urifclnnly l:li=et1ibu'bed_ The ul'til'tJi|‘l'l'l
surface charge density ts. say. cr.Atinite pertctlhie sheet is
shown in Fig. 12.18. TocalculatellteelectricintensityEete
peint P, clcse to the sheet. imagine a closed Gaussian
surfacei-i thetermctecyiindarpessingdtrtmgltttie sheet.
whceecnetlatfcce ccnleins poi-nt PL Frcm symmetry we can
conclude that E pcinisat right angletetheend faces and
ainrayfrcrhtl'le plane. Since Eisperalteltethecuruedsurface
ciftl1ecytlnder.setharelsrrpccrrlIihulienlcfltnrhcn1tlte
curved wall of the cylinder. White it will he,
EA +EA=2EA.ihrcughtl1ehucllatandfacesofd1ec:lceed
cylindrical surface, where A is the surface area ct the fiat
feces (Fig- 12.13]. As the charge enclosed by the closed
suriaceia tr.-lt.1;l1erefcre. eccardingtc Gauss's law.
c_=£l itciiargeenc-lcsedhycdcseclsurfece
Q
_.
_
_. _- e==§-intuit‘
-
Therefore.
5,
-.
- --
.
-__-="-1;
-fi- _. ...,
-
._...
.-_1s
'1,
2E-'l=£lxeA
-
.__|
, E..L",1--=1-=3:s..::.;..--7'1=?lfesis
.-
s
.I_.
_
.
_--:---..-s_
.__,_
_
.i...-:.---'If1I"'_"u _-. _!.;' '."T‘?'t"_'
-_
1
'r_-'----_--i.-.--'.!1"-
"“'““‘“""-"'7"'- -' - E ‘is’?-.111:-s'='é-1-'.ij_i'i‘;ii'i_”t3jfififiwf
whereFisaunitvectnrnornuitcti'Iesheetttirectedawayfi'cmiL
1L|
Eiijiijttric ||‘itij!r"i:5.it'y E-r-tween Turci Clpp-:s|.'.Lly
Cliurguct F'cr._il|e-- Plates
-.' :-:- :Ies
upp-use I et | para = a I i-"l""""
~--i
infinite extent separated hy yacuurn are griren cppcslte
duarges, Under these eenditiens the charges are essentially
cchcentratecl en the inner surfaces cf the plates. The field
lines which originate on pesitiue charges cnthe inner face
pi‘ one plate. terminate en negalnre charges on the inner
face pf the ether plate {Fig 12.191 Thus the charges
-
I3
,.|
' '
_
-;i-
____;_____
__._In
,_
H."‘“
ereurilcnnlytllstrlhutedcnttielmersurfacecftheptatetna
icrmcfsheetefrcttargesofsurfapedensllyesqt.-\t_tthere.it
isthaareecfptateendqlstheamountofchergecnetthercf
Itepietes.
knsglneno\v_aGet:sslensu'facelntl'iefcn'nelehet+cwihcs
tin
wlthltstcplnsicelheupper|netai1:tetear"iditshottomlnti1e
specehe'trneentlIepletasessltcnni1F|g;12.2tl.Asthefield
lines are parallel tc the sides ct the cos. therefore, the tttltt
thrcughthas-idesis-aerc.Thettetdtlnasare urtltonnty
-_=-_.- -..-..-_--._ clistlitiiuted ch the tower bettcrn face and are directed
' ' '-'-.;.
normally to ll. It A ls the area ct this tape and E the electric
'
'-_‘_~'§'-1. tnteheRy'BtttB£ttis.1hsflLhttt1tcughitvrctldtteE.i\t.Thefeisnc
‘-
fltptfltrcughtheupp-ereridctlriehoxbecaLmetltet"e.isriefield
—
"' ihsidelhemelslplstsi.111L|$tt'ietetxIfl1|:ttIl_tl1rei,|ghtt1e
GaussianaurfacaksEA.Thecd1argeer1cdceedhyti'ie
Gaussian surfeceiaefl- Applying Gauss-‘slaw
c,-l ltfllilt
pr
;
E.-\t=—:tcut
-.
_.
___q_...|_
':1-']--'!,'-t.'"-".j-__!-__
.?".'-,
"
-
.
|;..-1' ;'1-.--r-'1
-. ' ",__ |.| -.;-
-
an-hf‘
.|_.-
-1.;-1-:33.
,
_.
4.
_. ."-s_1-H -
'
.1-u
__
.-rt-.1. --
"
;
-
-
- @.- - .| _ .
-
-_':-. _ . ',- -'.- ,
-
-_
__._s-_i
,|.
:__:_.
. s, c-_-.=._-,;r.-
-._l' --.- -:I,-..:,;. -." ""\"+1""" 1-",1.
'-:e '#'~c“-III: -= J’ it
ttlefialdittetisityisthesameataltpcittsbeheeantheptates.
thelzliecticrtctfietdisfrcrtipcstthletortegaltseptatebecause
amltpcstthecttageenyvrherebettueenttteptatesueutdhe
repelledtrcmpestliueanctattractedtcnegativeplaternd
tl1esefercesarei1lhesameclirecticn.lnvectcrlcrm
wtrereiisaunttvectprdiecaedtmmpoetfiuetpnegettyeptele.
EI-
LetLiscorrsider*apesiliuecd'iargeg,wt1ictiisallcwedtcn1cy-e
lnamelechtcttetdpreducechetneentvieeppoeilelydterged
lt-
ttriltrricuefmrncilateBtc.handwitlgelnK.E-1titlstobemeved
ficrnA.tciEl.aI1e1dsmalfcrceisneeideidtomattett1er:herge
meueagaii1sttheetectrtcttetdar|d\ttltgaitFtE.Letirstrnpese
accntltltprithatesthec:t1arIgetsn1cuedfrcm.iflitcB_itlsrricued
loeeplngetectrestatlceqiilitiriuh, i.e.,llmcueswiI1 uniferm
pal-eletphtesessticv-ninFig.12.21[e}.Ttrepcsitiuec=l1arge
Fl. 1121 tit
veicciry.1hse:rie|scnccueeesciseyecbysPnlri'learcice
Fe-quelandoppoeitetcq,Eateverypcirrtalchgitspati1
H
as shown in Fig. 12.21 (ti). The wort done by the etrternal
lorceegairisttheelectlicfietrzltrtcreasesetectrtcdpotenttal
eriergyefthec=l1ai'gelttattsmgued.
Let W.“ theworkctene tiylheforcein cenying tliepoeitilre
charge tL'tl't1tIl'l'l.Pt|t1lBti\l‘|"lt|fl keeping the charge in equilibrium.
Triediangeinitspo-tenfialenercry cl.-'=litr‘.,
it ' -
i
q
1—.|I .n.
- '"-==1 .i-_&"‘.-I-llit-"~1'l'li"i"‘='.=l:-'.*-I‘l'-so.-'.~. =1
F‘.1L21-fit
whereU..and Li,.arede1tnedt-otielheprrlieritialenervgiieset
polntsiltand B. respectively.
Tcoescrioeelech-tcfieldw-einuodi.icelrieideeofeiectr1c
potential
The potential clttererice between two
pctntsfliandfl nanetectrtcfteld istleflned as theworttdone
in carrying a unit positive charge trornnto Bwhile keeping the
chargeinequiitirium. thatis.
=--=-
- - ~*--
-5:" -1.". 1.
.
i
s
-i
i
e
t:i
?
tci
§
>!‘
~
s’
"
t%
tfiiieie
ghiffi-if, enowti', dellmic electricpotentials sip-oiinn one
r
.-
rr
|rI-llrll-I
IIIIII
I
1I'IIIlIIII
Ililr
run-run: run.-nun.-use-nu In-nnnisna
|.-noun ensue. IIIJI-I use acumen: I
It-iilllitlliiillilr-ii|-iililltlmil-rd-Blair
II
III III
IIIIIIIII-IIILIIIIIIIIII 1
IIIIIIIIIII IIII-IIIII1IIIIlIIII'IIlJ
II acneisanasnna||.na.nn|ana||.nn|i.u|
if
tI
respectively. lectric potential energy ciiference and
aegct-ac potential difference between the points-hand E are
as
-.iiss4i
Tl'mstl'iepoteritialdiffer*encebetweenlhetwopoi1ts-car1tia
defined as the difference of the potential energy P91’ unlt
charge.
PlSl'BLIi'lClP.E. lsiouie.Eq.1?_2s
pi_;iterilielcliflsrsriceisior.teperccr.licIr't:i.
-is - -.-"-1-t- I -'
i
'|E_.E*'-:71. '..;'. " '- -
That is. a potential difference cf 1 volt exists between two
points ifworlr clone in moi-ri_ng a unit poeitiye chem frornone
point toother. iteepiing equilibrium. isonepute.
In order to ghre a concept ofelectdc potential ate poii-it in an
electric field. we must have a reference to which we assign
zero electric potential. This point ls ursuatly talten at infinity.
Thus in Ec|.12.2T3. lfwetal-tehtp beat lnflnlty and choose
Vac. the electric potential at Bwllt he v,=w_..e.orcmppiig
the subscripts.
:"I
-.'c,_._
_
r
"s-
____ ._.'
if
: ‘"1
‘P11II'l11'I--‘IIl‘PI'I1‘PF'III'--'IP'l'I'I
ilrlllllllllrlll III'I'IIIIIII'IIIIII
IIIIIII IIIIIIIIIIIII-IIIII-I1III1J
nunnuin.“|.un.n|1;nna|nnn|nan.
,|.i.4\.-4-.|.|...H._.|_.4 cr--._--,.--.-sun-nu--u--run IIIIIIIIIIIIIIIIIIIII1
IIIIIIII nun 1 IIIIIII-IIIII Ilal. I lat
II
Illll --an .. -41 . -I
I.
I-|- H-an-1'
':IlIF:I
rl
III'I"|1 II'I|l:I
PI'IlrI"rIIl
-1 .tttit]'ll'III'I
'1 1:“: ..
' 'F:1':' l:H':':
, - l:::'i."'
.. _
I-:l.F:::l:ll; -:7 :3 ::Il:-::'::- iii I
..
t:;i..t:t::.ttitE|.t §ir'.'::i'. §:'t:t§i§
II‘|'III'I|'I'I1lFiI‘|I'II'
.'IrII1IIII'I'II'Il'I
IIILIIJI-IIIIII:nlIlIl-IIJ1llIll|II
-I1.
I-H I--'1-r-I-sill-r urn lllilll-I-I E ‘I
iisis itsitt
it
s='.i'-.-'-:i‘=":‘i'! ‘race--.1:?1rfii"-.:'it?‘?t*1
-—--|-
II
an
|.
r
I-I
15
t
whicitstatestltatiheelactricpotartlieiatartypeiritinat
etectricttetd is equal to worltdone in bn'ng'|1g a unit positive
charge from infinityto that ppintjsaep-irtct it in equilibrium. It is
tobenoted that potential eta point is stilt potentielditlerence
between the potential at that point and potential at infinity.
Both potential and potential differences are scalar quantities
because both Wand q.are scalars.
Elli?-ittflll--tliltfllifii
In this section we will establish a relation between electric
iitensity and potential diftenenoe. As a special case. let us
consider the situation shown in Fig. 12.21 tb).The electric
ttetd between the twocherged plates is unilionn. let tlsvatue
beE.Ti1apotentielditferencebetweeniitendBtsgivenbytt1e
equation
to-ttinlclclr-Ind
racer-tigonice
flIl{IlItIllflltlIij'l|ll'II |
i -1-
where til-',., = Fe’ = - o_,Eo' {the negative sign is needed
becauseFmustbeappliedopposi'tetoq,Esoastolieepitin
equitibnunli-ttnthtnis.Eq.12.2Tbecon1es
.
V,-‘t-",.=-E! =-Ed
We
5=' - I
L -:..i-"-':-'= 1»; ,'."=;~:-.=§.r.oc.=cit'
i'i;-'"-'; _.f.#._I.._i?.;'.';_-rl_
'i;.t;¢."
=5i=:~si-1-fl
- ---- ---|'.-,- .I- '
_ __-:i_
._
..
Poterfl
dllrilri-ct
--
_
1-,... _...1|.
his
‘I r I ' I - ‘I ‘I I?I't it-t--It--.
-...|.J.I'-:: 'l-H..s-I-s'-"-,5---r
; '"%t.='l
.
.
.'.'
_ -
r
.
--._1....|.
.-.-
_
.
Ii’ the plates It is B are separated by inlinitesirnsly entail
clistarrcad.r.tlisE.12.2tiisrncdifiedas _;
* _ _
l
;
- ..
_ '-_ __ ".1
-i___5_.._.
r=t~i-.sl1..-':*_:-J'-.r:n-.-- .|5 ‘ i."'.-" '
-I
".
|.'.
..
y-1-F_-‘IL? -'ir'----
" - "1"": -'-
'....
.
"-_.\_-:l_;q_
-1-
-'-~
"
-'-
-=
.- -- .-";;t;;..-n-.t'i'-
Thequentil-yg‘ves thema:itimum value ofthe rats of
or
change of potential with distance because the charge has
been rnovedslong alietdtinezaongwhich the distanced:
between the two plates is minimum. tt is itnown as potential
gradient. Thus the electric intensityis equal tothe negative of
the gradient of potential. Thenegative sign indicates trial the
directional E is along the decreasing potential-
Theurrit ofeiectric intensity from Eq.12.29ls voithnetre wriiei
iseoualtotitti ‘as shown below.
1i=1h."'°l"l.E1‘E ,1
metre
metre
lit
=1h
I rnetretieoutonlt
cotlomb
E||;h,";1_1'iC F'{HF1|‘|HEJiflt a Point due tn a Point
Cher 9 tr
__t,q¢m;.derb4eane:p|'esstd|1terltrepete|1tia1a1aeertainpnimin
d1efialdulapdeimrepeinld1argeq.Ttisem1beau:e|11pHhed
byhringingaunfl pueirive magefmmmflnltyleflmtpcint
Ivtflep-I fl1e|;:hargein equi|ib|iurn.Tt1elargeteanbeaet'tieved
uelngngq. 12.29 in the form av = -E hr, provided electric
ir|ta11.sityEren1airte:I:m-tentHdwe\Ieri1tl'ieeaseEvarie-e
inversely as square crf cietenee from the p-uinl I:-harge. fl 11¢
mereren'|ai1s::dnetanleuweus=ebasiepflrlciJIe-alndemptlte
maateuhidpdlantielalapei1t.111efieldiera1:Iia1esshu\m1in_
-
-.f'. ---
..-....
.3
Fig.12.22_
Lel us lake two points A and B. infimteelmally eleee to each
dthemlethat Eremains alt-ndsteenetanl between them. The
distance et pqinteh and B from q are r, and r,_ respdelivaty
and distanced!‘ I‘l'lid|JIDinh‘;ll5-FELDB interval behueennand B is
r [rem q-Then ac::erdlngtuFig.1l'-22.
_;- _. '
r,_Ir,, 1-Eur
£12.30]
-._m-'=r,-r,
F|q, 1Ll'.E
(12.31;
Asrra-|;|re5B|'|lE|'|‘|id pDi|1lDHfllBN3|bBMfBflflP\3Ild Ben
-_
,--&;T":_
'
' 112.521
Themagnitudedieleclrieinterlsityatthispninlifi.
1 1
,_
El dun r,
£12.33]-
A3 the paints A and B are very cldee lhen. as a first
B|3|Jl'I;HItiIIlBllr3l1.\\'B' can lake the arithmetic mean to be equal
tO"gB='UII'IBlfii:l'l'iEBI1\\'hi|::hg'vvB5
L_5
r, r‘
'-|'hlrl=Iure,
r.‘ =r, r,
Trtus.Eq.12.33c-‘an be-written as
.
_
1 q
_
' El --—-—
_
I .I
I
I
~
(12.34;
'
ihtlitlflilhliliflrflwlh.
H'fl'kil'I'I'liiI'§I,i-
I10-'l|1'|I-bl di L-erI|'ntH. Int In
vI|IlI1'||IijnIniudI'i-|:|\iI_-Ind-:i|'l
-dllpd pdhrnll i:fllrI|'l:\u cl thi-
mwdnumulflmbuunn
il"!"I""l'YP"l'°*llfi'-
_
£12.35}
‘Ian far:
_
Mmv, if a unit peeitive charge ls moved frem B teflt. the werh
dune is equal tufl1a putenlialdifferenee belweenhand B.
'|.|"_-L-"_,= -E[ri- 1",}
Hllfifiiiflifie
'
'lT
Suhelfluth
.~
_
..
'
aqtzas
'
'
fi'_,_;‘§,",,,"§',",§""""
Teeelcalateahedlut-updlu|1llddrpetunflulatA.p0ir|tBls
assunedl:dbohir|ltypdi1ledfl1atV,=flendhenee
'“H*u*|#
I
-
lll-1-D
ri
‘fl
'
In
_
.
111e5|enera|exp|e::idnfdre¥e:htep|dle|1l1a|\F,aladislinue
rfrdmqie.
;Pu||-u
|ln'I'CI
RBI?-P
.
_%
HUI-ll-lulfllllllfll
- §i“‘ .»..
FlBfBlTi'lQFig.12.21.WBhrlWtfl\BlIhBl1BIlGI'tlflBflHi'lBfQE
'_
-.
..
'
-.-.,.._.-,=-=..
., .n.r_'-"\":..
'
|.-
-.
.
qmweefmm pelntAwitl1pdtenl;ie| V,,tdepelntBwifl1
pdtert-fie! V, keeping eiedt|1delnfidequilbr1um.tl1eehar1gein
potanlt=eienetgy.fl.Udfperdetele.'
_
IIr|dautle|ndinrdua»e|een'I1ed'iu'ge'td'n1}i11ilhu:|L|I:rh|n.
lhtsd1ungui1FtEnppaarsi1l1afdn'ndlet'nr|gei1K.E.
Euppde-echargecarfiadbyfl1eputlcialeqIeI1.Bx1IJ”'¢.
‘hue. in this case. ttteenergy acquirer! tnytliac-t1a|=;a willbe
else =qsv=ssv-l1.a I 1o"‘t:t[eu1
»ioreo1rar.asaurnett1atM-‘=1 1-roit.harioe
oi-LE - qov={1.es1o"‘c):{1l-on;
£it{.E =(1.s=1c"'}:{cxv}=1.es1o"‘-t
‘he amount cl‘ energy ec|uatto1.E~ t-:10" J is celed cne
rlectron-volt and is denoted by 1eV. It is defined as ‘the
lmoont ol energy acquired or teat by an electron as it
raveraeaa potantiald_itieren-oeolonevoit'.Tt1ue.
it} . '-t_‘_|'1itg:.1.e==1a"J ' ........
(12421
Example 12.1: Apufldscanrinqa ctiargaolie latte
itrough e peerless dtlieranoe ol am. Calculate the energy
iaqmrsu b1_rlt.
q=ile
,
.lllll'l3.lt‘ll'
|'ltt!tH'lt2lfflt_|'l=ttlt]ltlt'Ittlltl[|t'llte|:let|1;it‘;laIi$ '
.
sic: =qev-las]ra.ow=eoav
I=$.litr1.t5::1lZl"'..i =tl.fl-:r1fl-"'J
n chapter 4, we pointed out that gravitational force is a
mnaervative loroa. that is. wort: done in a-ooh a field is
ndependent ol path. It can also he proved that C‘-oulomlata
electrostatic force is also conservative force. The electric
'oroabet\\-aentwo charges F = £211; ,issirnitarirl1‘orrn to
the gravitational force between tlle two |:l-oint rnaaaea.
= =t3-m-"':-31.Bofl1foroesvaryinverselyvdfl1lheaouareolfl1e
r
distance between the two charges or the two masses.
l-tow-ever, the value of gravitational oionstant G is very small
ea oompared to-electrical oonalant e.
It is because oi this
4115
i-act that the gravitational tome is a"u-ery weal: foroa as
ooropare-d to electrostatic force- As regards their qualitative
aspect. trreelectrcataticiioroe could beattractiveor repulsive
lvhie. on theother hand. gravitational loroe is only attractive.
Anolherdiflareooetobeno-ted iethatttiealactmstatictoroeis
medium dependant and can be shielded while gravitational
19
force laclts this property.
In 190$. FLA tutill'lr.ar1 devised a technique that resulted i
precise rneaeuremenrtotthe charge onanatectron.
C
5
.-
ri-if a
_.._
_
.
-
"."|':I:':£'d.-r
.:;.i..£:i';r,J
__
fig. lump
F. - ii!
Di mp
A schematic diagram of the htilliltan oil drop experiment l.
shown in Fig. 12.23 la}. Two parallel plates PF‘ are piece:
inside a container C. to avoid disturbances due to ai
cmranls. The separation between the plates is d. Tris uppe
plaleF' hasa snlallholeH.asst1osinintttefigore.Au-oltagel
is applledtlothe plates dueto-nhichtiieel-acizricfield Eit
setup between the plates. The magnitude of its value it
E = ea. An atomizereis used for spraying oil dropslnto the
container through a nozzle. The oil drop gets charger
because of friction between walls ol atomizer and oil drops
These oildrops are verysrnall. and are actuallyln the form o
n1iat.$oma ofthase drops happerlto pass throughtheholeir
the upper plate. Thespaoe between the pistes is ilurninater
bythe ligil coming from the souroe S through the lens L ant
Wlndthtl W',. The path oF|'|1|olion oi’ i;hes.e drops can bl
-
F.*""'l
- -sq
-- -
_ .._____l'f'f'§§1§-'_'-;§j=_j-fit;-_.r:" _
carefully observed byamiorosoope M.
-it given droplet between the two plates could he suspendec
in airiflha gravitational loroe F, I mgacilingonthedropit
aquatic the eieolricalt‘oroe F, - us. asshotrrn in Fig-12.23{t:|}
The F_c-anbeediusted equal tofibyradjtietitgttievolage. tr
this case. we can write.
_
or
'
qE=mg
ltlfisthevalt1eo1'p.d-hehveenli1eplalealorti'|is ae‘tt:ing.1her
H
Ii]
'
=
E=E
if '
wemaywrita
'il'!'=""Q
11'
humarludatalmir-H\emanamuifl'|a¢l'cplat.maalac=1‘n=
|ldbfln'aanl1apl|hu:siu'nitd'~adufl=Tlrad|'unlaIlaIIs-undurma
cliunolql-niylvaughai.nau.uln:mrninal:und\¢a1moslallhe
ifllnltI'lIlil1:lrl¢fiHdill'hi:hB5nfl'.ltilIm'iIrBl:pfildv,i$
uhmirodhyfinirlglwialnlhawnflflwaranuasumd
b§'tlnUl.$iMiIPItI‘I§iUI'¢lFdulhliri¢l.iflQ\|nMU'|idI'DQlH
fiB11itilIfi"|Qwflh¢¢|'|IiInltGflfllflI|&nild|5B£l|fll0fbiVIiQht.'
FIEnn1rv.Img
rhuarlsfluradlusnilheurup-latand :1 lsmacnalfldqmui
isnusilyfurai.lfpis-lhadansityu'Ilr|udr=n|:lat,H10h
‘E
Hfltl,
r
§1|:r‘pg=BII:\1rv,
I‘? 2 9 “H-I
I-’|-W
_
.
irumiwgihavalua olr. the mas-5 mcan tyac-abculalad by
slng Eq.{1.'?,-15). This value of mis s|.|b:|:i'oulad in E_q.12.4-I
:gel1i1uvaIuunId1a|'=g|q0nll'\udmplat.
'
Iilkmmaasuradmachargann marqdrbpsaawdlbund mm
an-I1 U1-'iI'EB was ail integral mullipla crfa rrinimurn value of
hargenqualtu1.Bx1D'"G.Ha.li1enaIum.umc|L|1uflIh=atlhla
inhummkmnlmedurgablhadwargammulecrun.
1|
Ferfltedlapietelflledtflfflflq-weheve
_. _
_
. fa _ .-R;-e_ I: _q..e_e_1g_!F_|g eea me" ire.e.rr1e'l' m_- '
v
, " : -raw =
- r
_qI3.2:r1D"'G
,0 .
I12
-
*“‘“"-
'__';- _
Acepaciler la a |:le\-'i|:_e that can store charge- It ceneiete -r
twe eenduetera piaeecl neer one another separated l:
uaeuum. air er any ether ineuleter. ltnewn as rlleleclrii
Usually lheeencluciere are it thetermetperelet ptelee. an
tltecapeiciherielgieumaeperelleiplatelapacllmwttenm
_.;,
_’_|:
1-
"
g
Fla-11-H
pareeureueneeapeeturemeenneeeumaneeeryr
voltage V|[Flg.12.24}|, iteelabli-ehee e potential clitlereaeer
Vault: between lhehllrepleles enrllltebalileryplaeee
el-large +C.len the plate eennectecl vi-ilh ite peeiti-we termim
ende charge--Den the otherplate. eennectedte its negalhr
tenninal. let Cl-aethe megnitudeelthe charge en either-elth
pletee. It iefeund that
Darin"
of .flI_GV DI‘ ‘C-"lg
"['I2.'lifl
The 1!lt‘t)|DIDfliOl'kB|H‘_|l' cenetanl C la celled tl1e eeperzitarrce 1
the capacitor. he we e-hall see leler. it e'ep-encle upen th
gee-rneu'3r'eIlne plates endthe medium between lhern. It is
rneeeure ef the eniity el capacller lle atere charge. Th
r,-apaeitanee er a capacitor can he clellner! as the arneunti
charge en ene plele nepeeeery tap raise the petential at rm
plate by ene --elt with respect te the ether. The SI unit i
capacitance la eeuipmh per veil. which beceuee at i'
3 freq I1 entuse.iscc+mmenl'y' calleell‘erer:l{F]|.elte I’ the Ie l1‘l tn.
W5‘-aw,“ .-,-,-5 Englieh S-ClBfl|fl5I..FH|'H'dH!|'.
. ““"“"".. . .""..R2"'
.-.|. . .....l“".l.l..-""""
I:~m_iFF_Wh'fl
mm_H“_,FF_w..hu
I
"1'l't|H:lplcllll'l_Bl an =-n-rare =eI1'i.n!l III;
duraealetwcentlemhqhueuuueltlrqplalee
eiepn-flflflat':'i:fic|'1:nhr.ueduc:aapeh|uh_
Censiclar a parallel plate capacieer canslellng cl twe plan
metelpietee. eeehetareaa. eepalatedby edietance in
shown in Fig. 12.24. The dielenee cl ls small ee lnal lh
electric field E between the plelee is unilerrn and eenfine
22
atrneat entirely in the raglan between the plates. Let initially
the medium between the plat-ee be air er vacuum. Then
accerdingteEq.12.4ti.
_ __ __
_
D
I G_- T;
(12171
where Ole the charge an the capaciter and 1-its the p-ctential
diflerence between the parallel plates. The magnitude E el’
etectrtcinlensltyle related wilttthetlietaneedbv Eq.12.2-Bee
' _
Er;
“I.
pa.-tat
AeQiethechergeenei1heref1tteplateselarea.ll,ttte
eurfeaedensitvetchergeenthepteteeieae I =1?-
Ae aieedtr ah-awn in sectren 12.3. the electric intensity
between tvra dppttraile-Iv ctterged plates is given by E =
Saba-ltt|.li'|glhevaltreefc.weheve
_ 1'.._'?_
-
d
ttpt-in -
'
kg
c,,-g-4’?
'
’"
t:t:t.4a;
I
112.:-at
If an insulating metettal. celled dielectric. cl relatlve
p-etmittivil-tr r, is introduced between the plates, the
capacitance at cepeciter ls enhanced by the teeter 1,.
ti?-epacitela ccmrnentv have sernedielectric medium. thereby
c,leeteeceltedaadielect|'iccenetant.
Fellcrwlng experiment give-stheettect cl insertion at dielectric
between the plates eta capaciter.
Cencider a charged cepaclterwheee plates are cennected taa vettmeter (Fig. 12.25 e). The detteclicn ct‘ the meter ls e
tneaeure at the potential difference between the plates.
When a dielepttie material is inserted between the plates,
reeelng drape
a decrease In the petential
dillerenee between the plates (Fig. 12.25 bt. Frcm the
definitien, C = O.-‘V. eince V decreases whlte O remaine
ccnetentthevalueeftilncreaeee.ThenEq.t2-5-flbectcmea.
_ _ '
c_-it?
112.51}
23
pnnlll-elllatltlilv
trill
ttrttir fttl
H
e
I
_®
Er
I.-‘<1.-'_
Ft|,i 1I.I5Efldl2IlkI'.ilSI!l1I'I
%i'HI'flIi'I
Ee.12.5tt shows the dependence oi a capacitor upon the
area oi plates. the separation between the plates and
medium betweanthem.
Dividing Ec|.12.51 by Eq.'i2.5t) we get expression tor
diatarztriccenslantias,
.
I
-
s.I%5-
i[t2.ti2}_
From Eq.12.52 dielectric co-eiticient or dielectric constant is
defined as
"._i_i
..-_I
"-"_1-'-
!"I'lte.
---.---i
'-'-. '-'-'
mt.“
i-
-1
-l"" ole
2-
_
.it-
--I.t
|i- Int. 'I_
-.
.
'
_ 1:;--“""."5'T]i'.'!"-<~i.-.=.-ii'_i‘-‘= ;.. .. -. . ‘r
iiiieerirliiriirreiriiiriiriiiiii-r_iiinirt-i The increasein the capacity eta capacitor due to presence oi
1'-'I‘KII“'lit
diatectricisduetoeiectric polarization oidielectric.
The dielectric consists ot atoms and molecules which are
electrically neutral on the average, i.e, they contain equal
amountsotnegative and positive charges. Tlmedisrnbutionot
these charges in the atcme and molecules is such that the
centre oi the positive charge coincides with the centre of
negative charge. Wltien the molecules oi dielectric are
subjected to an electric iield between the plates oi a
capacitor. the negative charges [electrons] are attracted
towards the positively charged plate cl the capacitor and the
positive charges (nut:-lat} towards the negetiiieiy charged
plate. The electrons in the dielectric iinsulatcrji are not tree to
lttcive but it is possible that the electrons and nuclei can
undergo slight displacement when subjected lib an electric;
field. As a result of this displacement the centre of positive
and negative charges nevrnoionger coincide with each other
and one end oi molecule-s shows a negative charge and the
bitter end. an equal amount oi positive charge but the
molecule as a whole is still neutral. Two equal arid opposite
charges separated by a srnalt distance are said to constitute
adipola- Thus the molecules otihe dielectric under the action
at elechricfield become dipoles and the dielectric is said to be
p-alitrildtil.
‘i'heeltectetthepclari2a'lieneti:tielactncissnonni1
14
atsit? get;tiiiti
sis
_ —'
Eas
the dielectric in contact with the nege
pieceealtiryerofpoei1iverharges.ltelactivetydeo'easeethe
flllTB'EBt3i'Bfi5i|}t'UlihEd1EIQ'BfltI1‘i|lBDiBlB'§.tl5i5li']B electric
inteneityEbettveenthepia1iesis §'.soEdect1aaseedueto
polaitzationottliedieiectrlcttisresuits-ittoedecaaseet
potential riflerencebetweentheplatesdue to presencec'i_
dielectitcasdei1'ior'rslraledbytl'ieeicpedntentdesc:i:adintha
Acapacitoris adevtceto stare charge. Fiitemattveiy. itie
peeeibtetcthlnitctecapacttcrasadevlcaiorstorlng
electrical energy. iiittereli. the chargeon the plate possesses
electrical potential energywhich arises becausewertt tstobe
donetodepositchargaen theplates- This isduelotltetact
that with each small increment at charge heiig deposited
during the tifialjiifla process. the Potential difference
betweenthe plates lncreeeae.and a larger BI'l'ttJl.ll'tiD‘iW0l'|'l is
neededtd bring upnerttlnuement ofcharge.
initially when the capacitor is uncharged. the potential
ditterence between plates is zero and tlnetiy it becomes if
vmengctiaigeisdepcettedoneactt plate. Thus, theaveraga
eeiencereisere-ieee!3%‘i=%u
.
riiereeire
as. =Energy = %e v
usiiigiiviriitauiiiii;-=cvirireipei;itiiriiiegiit
r"
i'_:|:-_.-r"'--
!-.--.;j.
..e.:...eit,p;qg,
. - ..
it is also possible to tegard the energy as being stored in
stectricfield bet'iveentheplates.ratherthenthepo'nenltal
energy ct‘ the charges on the plates. Such e view point is
usetutvihen electric Field strength behveenthe plates itstaad
otcharges on the plates causing field is to he considered.
This relation can be obtained by Etlsatiiuting iv’ = Ed and
C= Ara-.Jd in Ei:|.t2.53.'
25
_..
-.
,
_‘ _.__|__
|'__tr;".
.
'_--. - __]
CIILCII,
[jeiii-is". "_':.i'..i;_1 |
Fig. 12-H
'
R
+1; ~¢
Emm,,E[_..é._q.)5d]F
1 Ass
—iec
=1=eE1mm
I
5
Fl-E[Ad]iiu'G|umBbHWBflfl'|L|iBplEliBBBfl
A
_¢
.
. TJ. -.3. ll
"
'__..
'--'
'i".
_
E-'1.
' '|__|" II-.
. 'r
.L'_.,'_
.~:_-:-'-.
3|I
.'''_-.:E
1,"-'. IL-..:|_'.
-:|
' -‘:.''-_t
.';:-,
-.1-‘F.-.Jr;
3J‘!"‘ -_!_:..
"' .' _F,"
- -..2.
_,_
r‘-1. . .-l_ !!I
'_1'-''|-_'.
‘l'nisequa1inn isuaiidferan1_reieeb'iefieide'b'eflQfl1-
1|.-5I
.- -..1-L
--'.I
'
'l-'
.:
v'
|-I
I.
--..,."_. .'=r
Br.-n.
" "" ; Ll“
: 5'i
1-:
F1 11-H
R
.,._ -_..
L_
Many eieetlie tireiilis sensisl ei hem eeeesilbls and
nesislaers. Fig.12.2? ehe-as e resieiibr-sapacilel einmit eeiied
F!-G-c=irv::ui1;. ‘Mien the ewil1.':h S is set al tenninai A. ihe R-E
enirbineliginisebnneclied ieeheiteryeflelteee 'i-",Wi'I|-ei1
starts charging lheca|:iesitbrtl1reughlheresistnr R.
The sepecih:-r is nnl charged immedieiehr. reihel‘ eflefeee
-build up gredualy le ihe equilibrium velue ef q. = CV, The
gmwtll ef ¢l'|el'ge\uflh lime ier diiierent-resistenees is ehbum
in Fig.12.2B. Aseerclirig in ihis graph q = D at i = D and
increases gradually witi'| time lil ll reaches its equilibrium
vaiue q_, I Cifl. Thevelege Vecmss pacilnr
alarvyirisiant
.||¢.q
{
C
"'
canbenbminedbydiifidingqby G, as i-'= qifi.
5
B
A
+ A
[Ii
1?
CV.
I-lcrnleslerhnwsiewtl1esepaeitce'issharginger
dieehergirig. depends upen the predusi of ihe resisienee R
and ihe uapasiiame G used in Ihe circuit. A-e lihe uflii el
pmdu-|:!RCiBH1HfC||'fil'fl0, sethis pruduetislinuumeeiinie
censtenl end is defined as lhe lime required by the GBDB-flier
tedepesit 0.53 timeelhe eqiiilbfium charge q,,. Thegraphsei‘
Fig.1:-_*.1'.B ghewthatthaeiiarge reaeries ils equilibrium value
snenerwhenliietime eeneieniisemell.
Fig. 12.291111} iiiusirales ihe dieel1ergi1g of a capacitor
through a resislnr. in this iigure. the ewiieh 5 '5 eel ei peinl B,
seihe::i1arge+qnnt|1eieitpieiessI1flewerifi~eie-cinidse
'
5InlI'?¢
in
through ihe reeielenee and neulraiize lhe charge -q en the
right piale.
.
The grqziesin Fig. 12.29ibj|-eheurs ihelc|is|:i'ierging begins at
i= Human q = CV, and decrees-ee graduelyhcizere. E-male!
'- values uilime eensiamfl-Cieed teemererepiddiseharge.
@
26-
EJ:ampie1i.5: 'I'I'|eti'l1e00I‘IIlfl1lU|l series HG clrcuilis
I=R‘G.Vu1fyil1ateneiuI:ti|ieefe1'ediseqiivaie|'uteeeound.
: ohm‘: E~iv'iF1 iem*e'uFpnmrIE" BIIereneo"_""" ‘II
curreriuandreeisimeeflcanbeiirriitenes.
V=IR
pqum ;-qr; um gqiimni-|' unmiuu-nu h'i:eihe equelien.
v=%e
_
r
nu
M n
eleenll-llilifl-iililflill‘
wiper: ei eerl he he-use-d
l'hn'IllIIj'fl'l'!§-IQ!-li'hD.||\
“I
lillindeelqlimlieubln
HIE
Mifliflfilflfllfllfli I.Il'i1II
llilfi'.ThII'iiIII'lIll'i-'flqI:llI
Khfifi HID HI hi-if I
Q
i\fi0fll'li'lflTUBqilBlifl1lI'CV.CI¢"V
'
|IlLIliIiFi'lflil1ieequeien\ii'd1abeueec||1aiion-fives.
ifiur-a|iI:||'urIliflen.
_
-1 1
'
i-ienoe 1eh1n-x1feredI‘ieeeend_
wi'|ereoiI'nisfl1eu|it-alresietaricefi.
'
.
Tiiefiwhniflsieueieieeflietfliefnrbehememnmpeirldulgeehdheeiiy
pmpuflenalmmepudueteifliemegniudeabidwgesmdhwuueiyplupuflemih
lieequme-aili1edi:lanuebehueentherr1-
1
Eieebiefieidhmepermfidiergeetepehliscdhdehebiefilfiflrengmersledrh
flddhllnlljralfllalpditit.
e
Tl1en|||'nbe:di'1heiieidiir|eepeeehgiiu1:I.|gl1e eensinelm-'rmlde|Ie ;ilme'e'flBe
eiaic:rii:fl1ncli'Inughli'ielaree.derlbi|db'yfli.
. flreeleehiefiasfiflimiqhauectnramehhdmdesbiefiddeikdellelyiiegiuflihy
¢IE.A=Edens-E.ufl1ereBielrieangiehetweei1flnfleidihiesar|dfliene|'n1aiib
e
1
.
eurfaee area.
Gain-s'siawisetawdes'fl1eflusdIeughenyc:nsedu|fieeehiIs,flmeel1eumi
diageensiibsldhil.
Tl1einlariornIai'ueiiewci1lgedmelaienl1e|1eieefieldfieeIegi1e.
U
fl1eeieehsH¢eneIyheheu1hneeppnsinehrei'iergedpu'eleipieieeleE= t— .
flwarmumefiwlkduiehbnrighigeuritpudfluedulgehumhfldhrhepdm
ageinsleieclri<:filidisiheiiec:i:iepei:e|1iielelihetpein1.
2'7
‘I
.
fl1epeierflielieemslenimmu%rnmeghenmgienefspene.lefl1eehehicHfieH
zereernen-zeminilfleregien? spleln_ .
11.2‘ Suppnsefl1etyeuhIuuw1Hedriefieidinedueieepesifiveeei|'flfl\e:‘ge.De
eiec.-briei'ieid andlhe peteniieiirisreaeeerdeiieeee?
‘IE-3 Huiinyeu_idenfifyjthatudflc#ipiaieefacepec#ieIispeeiflveiyd1a1;ed?
111
12.4
gigs“-ginmmefermmbrmemapeflflmpbimdmrgenhmpheedbemewiperflifl
iai
wiihsintiisuandeqiiaidaerges
(bi
wilhnppnsileandequdelnarges
12.5
Eleei1'ieii1eeeffeteeneveru'nss.\|ilhy'?
12.6
Hepdrfldwlqeeelmessmismleesedinenerwfifiermeieehiefiaflwfiiifiehiries
p0|l'Iii'iQli‘ifl'ifl'B-Bi'I'iB'iii'BlZi'i;iliiIl, Wi||i;ITiB|i'H'~BrBGi|il_BflrI'flU‘liUl'l‘?
I18
isEnenes-eerily zeru-insides-ei1arged rubberbeiieun ifbeleenie spherieel? Resume
ihat charge isdisb'ibuieduniiem1l1;eveIihesurfeee.'
is_ilhnflulGmss‘sieusHmsd\mdBlmaimn|hueiHrp§_:jfe[eesu'eesfl1gany
eieeeflsurieeeiniheeuhuarddieelinnisprnpnninneite
nelpeslthrechatge
enzsnsednimhsufleee?
123
Deeiedrenemndlegehunegimeirighpelmflaiereiiewpetemiai?
111
Cenuuermgnflxndesefeieeuleflsneg-ewmennuiermsuenenunnnebiuc:
12.?
' '
~[m-ass-=1fl.Ug,el1e|'ge=2fl._iiu'C}b3re|1ifleflfieelebieI21fl'ialiepleeed 11'Ii.i]i;:n'|fmm
thefiral-{G=B.H?x1fl"‘Hm‘hg"'}
'
(Ann: fl I 5.4 :1 10"}
FI
IS
12.2
Calculate uectcrieity the net eieeireslsetic fierce en q as sheum in the iigiure.
flilflpr
I -1
i
Ii
ii
1
,_ __M
-I
I
_
I
I
Fl
---
iI--I
1
I
in
-1
1 (Am: |= = 0.050 my
I
“"2 _,_ ___m
12.3
.i.peir|tchargie e= -Ei.0:|r10“Cis|:|ieeed ettheerigin.t';eltui_ateeiett1ricfieidete
puint 2.0 tn from the eriginen the 2-esie.
|A.ns: [-1.8 :10’
12.4
Deterrrtinedteeiectficiieidettitepeeiiienr=0i-i+3]]mc=eusedbyapdint_dterge
12.5
12.0
12.?
12.5
12.5
e=5.0x10"Cpie0edaterigin.
[A.rll:-[1-I11i0i +10e0jJN 0";
T-we paint charges. e, = -1.0 s10‘C end qr, = + 4.0 it 10‘ C. are separated by e
distance ef 3.0 m. Find and iuslity the zere-feid iecalien.
tens: 3.0 mfi
Fihdtheeleetriclieid strength requiredte hcidsuspendede |:\eri:ieleefrness
1-0 ::10'kg end charge 1.0|.ic between tyi-e_pietes 10.0 cm apart. {amt 0.0 'ut't1'f|
Apelticiehevirig acttargeef20etecb'ensenitiatieltu1:ughapetentialditerer1eebI
100 ydtts. Gaiwlate theenergy acquired by itin B1001-l'1;\n\Pt:||i3l{tt"r"}I. fem: [2 0 1: 10‘ em;
in Mi|iiitan's experiment. nil drepiets ere introduced |t1i0 the space between twe flat
herizentel pieles. 5.00 mrn apart. The plate vdttage is adjusted te exactly T0011’ se
that the dmpiet isheidstetienery. The piateuelegeis switched eflendtheseleeted
drepiet ieebsenred tefeii a measured dislaneeet 1-50 mm in 11,2 5. Gi‘uen1',i1a‘|;fl'Ua
density elihe eilused is 900irg m“, end the viscbsitycfeirattaberatery temperature
is1.00:r10"i*-im"'s,caicuia|e
5;
Themess.end
a}_ Tirechergeenuiedrepiettflussume-g=0.ttms’i
[Am-: {e} 5.14 it 10'” HQ, ib} 3.20 at 10'" C]
Apretcn pieced inaunflermeiectiie iieidet‘5000 NC‘ direciedterighi is eiicmled tc
geedisiance cI'10.0cr'r|fremAte B. Deteulele
re;
Pct-entiai difference between thetwe points
q 1; 5|
were dene bythe iield
ic]
Theehengein P.E.eiprc1en
idi
Thechangein i{.E.ei'1heprnl.en
re}
tisueie-city
{mes-a0I|:r010fli51.l5?'.'t10'"lItg}
.
_ (Ana: ~5D0 V, 500 e‘i|". -500 e"-I. 500 e'u'. 3.00? 110’ ms")
12.10 Usingzere reiarenee peini ei iniiiity. determine the ameunt by which a painlcharge
01'-1.0::10"(.1eiterstheeiectricpetentia|atape-int1.2me1Ire'y.1Irl1en
re;
Chargeispesdiye
(bi _ Ctiergeisnegsttve
’
(Ans: +3.0 rt 10‘ V, -3.0 at 10' Vi
.
19
12.11 in ears atemic mcdeiethytregen Bl0i11,0‘lBB|Bi.'!0"0l'i15ifi3fl{I'|ii0iBi'lZlI|FIii11I|'lB
nuctear prctan at e distance cl 5.29 iii 10'" m with a speed -at‘ 2.10 it 10‘ nee".
-[eI1.00:\t 10'“t3.maeeeteiect11:I1 =0.10ir10"'kg]-. Find
ta}
Titeatectricpeterttiattttateprtatcarteatertsettiitedietanee
ib}
Tetaienergyefthe ateminett
tc}
Theicriizaiierl ertergytermealcmin a"u' _
[Ann +2120 ti. -12.0 av, +t3.0D av}
12.12 The eiedrenic itash attachment tar a camera contains a capecitcr fer aicring the
energy uaed ta preducethetteah. In ene such unit, ihapetentiai diiierence between
ti-ueptetaeete?50uFpaciturieseettfleterrninethaenergythetisusedte
predueethatteah.
(lu1s:40.aJ}
12.13 Asap-aeiterhasalcep-ecitaneeet2.5:r10' F. _inthecharging precess.eiecl.ransare
rernu-iredtremenepiatear1dpieee~de-ntbeethercne. Whenittepetentieidittiererice
bete'eenthepiatesis450V.hawmenyalecatat1ahevabeenharts1erred‘?
{e =1.00:-1 10"'tI‘.}
'
{il|.ne:7.0:r10"eiaclrens)
3-0