ELECTRIC, MAGNETISM AND MODERN PHYSICS.pdf

7/25/2019 ELECTRIC, MAGNETISM AND MODERN PHYSICS.pdf

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PHY 121 ELECTRICITY, MAGNETISM AND MODERN PHYSICS

PHY 132: ELECTRICITY, MAGNETISM AND MODERN

PHYSICS

COURSE GUIDE

NATIONAL OPEN UNIVERSITY OF NIGERIA

NOUN 2


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1.0 Intro!"t#on

PHY132 electricity, ma!eti"m a!# m$#er! %&y"ic" i" a $!e "eme"ter 2cre#it", '$(!#ati$! le)el c$(r"e* It +ill e a)ailale t$ all "t(#e!t" t$ ta-et$+ar#" t&e c$re m$#(le $' t&eir .*Sc* E#(cati$!, a!# $t&er %r$ramme"

.*Sc c$m%(ter "cie!ce, e!)ir$!me!tal "t(#ie" a!#

T&e c$(r"e c$m%ri"e" 2/ "t(#y (!it" 0 m$#(le", +&ic& i!)$l)e a"ic%ri!ci%le" $' Electricity, Ma!eti"m a!# M$#er! P&y"ic"* T&e material &aee! #e)el$%e# i! "(c& a +ay t&at "t(#e!t" +it& at lea"t a cre#it %a"" at t&e$r#i!ary le)el $' e(i)ale!t +ill '$ll$+ (ite ea"ily*

T&ere are !$ c$m%(l"$ry %re re(i"ite" '$r t&e c$(r"e* H$+e)er, y$( are"tr$!ly a#)i"e# t$ &a)e a#e(ate ra"% $' 4(rt&er Mat&ematic" $r A%%lie#Mat&ematic"*

T&i" c$(r"e (i#e tell" y$( rie'ly +&at t&e c$(r"e i" a$(t, +&at c$(r"ematerial" y$( +ill e ("i! a!# &$+ t$ +$r- y$(r +ay t&r$(& t&e"ematerial"* I" "(e"t" "$me e!eral (i#eli!e" '$r t&e TIME t$ c$m%lete it"(cce""'(lly* It al"$ i)e" y$( "$me (i#a!ce $! y$(r t(t$r5mar-e#a""i!me!t"*

T&ere are re(lar t(t$rial cla""e" t&at are li!-e# t$ t&e c$(r"e* Y$( area#)i"e# t$ atte!# t&e"e "e""i$!" re(larly* Detail" $' time a!# l$cati$!" $'t(t$rial" +ill e i)e! t$ y$( at t&e %$i!t $' rei"trati$! '$r t&e c$(r"e*

2.0 $%&t Yo! $#'' L(&rn In T%#) Co!r)(

T&e $)erall aim $' PHY132 i" t$ i!tr$#(ce t&e a"ic %ri!ci%le a!# a%%licati$!$' Electrical E!ery a!# it" a""$ciati$! +it& Ma!eti"m* D(ri! t&e c$(r"ey$( +ill lear! t&at a! electric 'iel# i" al+ay" a""$ciate# +it& a ma!etic 'iel#a!# )ice )er"a* Y$( +$(l# "ee t&at t&i" $!# et+ee! Electricity a!#Ma!eti"m i" t&e a"i" $' ma!y "cie!ti'ic a!# tec&!$l$y #e)el$%me!t"#(ri! t&e la"t ce!t(ry*

T$+ar#" t&e e!# $' t&e c$(r"e y$( +ill e i!tr$#(ce# i!t$ "$me a"%ect" $'M$#er! P&y"ic" +&ere +e &a)e i!tr$#(ce# "$me !e+ c$!ce%t" t$ e6%lai!

"(5at$mic %&e!$me!a* T&e"e i!cl(#e (a!t(m t&e$ry, a!# e!ery le)el" i!at$m"*

NOUN 3


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3.0 Co!r)( A#*)

T&e aim $' t&i" c$(r"e ca! e "(mmari7e# a" '$ll$+"8 t&i" c$(r"e aim" t$i)e y$( a! (!#er"ta!#i! $' Electricity, Ma!eti"m a!# M$#er! P&y"ic" a!#t&eir a%%licati$!" i! e)ery#ay li'e* T&i" +ill e ac&ie)e# y

I!tr$#(ci!y$( t$t&e'(!#ame!tal" $'Electricity,Ma!eti"ma!#M$#er!P&y"ic" a""(9ect" $!t&eir$+!

ri&t*

Dem$!"trati!&$+t&e)ari$("t&e$rie" ca!

ea%%lie# t$realli'e"it(ati$!"*

NOUN


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E6%lai!i!"$me'(!#a

me!talc$!ce%t" i!Electricity,Ma!eti"ma!#M$#er!P&y"ic"*

E6%lai!i!t&etra!"i"ti$!'r$m

Ne+t$!ia!

Mec&a!ic" t$:(a!t(mMec&a!ic"*

Gi)i!y$("$mei!"i&t

i!t$%$""ile'(t(re#e)el$

%me!ti!

NOUN ;


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t&e"earea"*

+.0 Co!r)( O-("t#()

T%( "o!r)( )(t) o(r&'' o-("t#(), to &"%#(( t%( *) )(t o!t &o(.

I! a##iti$!, eac& (!it al"$ &a" "%eci'ic $9ecti)e"* T&e (!it $9ecti)e" areal+ay" i!cl(#e# at t&e ei!!i! $' a (!it< y$( "&$(l# rea# t&e! e'$re y$("tart +$r-i! t&r$(& t&e (!it* Y$( may +a!t t$ re'er t$ t&em #(ri! y$(r"t(#y $' t&e U!it t$ c&ec- y$(r %r$re""* Y$( "&$(l# al+ay" l$$- at t&e U!it$9ecti)e" a'ter c$m%leti! a (!it* I! t&i" +ay y$( ca! e "(re t&at y$( &a)e#$!e +&at +a" re(ire# $' y$( '$r t&e (!it*

Set $(t el$+ are t&e $9ecti)e" $' t&e C$(r"e a" a +&$le* .y meeti! t&e"e$9ecti)e" y$( "&$(l# &a)e ac&ie)e# t&e aim" $' t&e C$(r"e a" a +&$le*

O! "(cce""'(l c$m%leti$! $' t&e C$(r"e, y$( "&$(l# e ale t$8

1* De"crie t&e t&e$ry $' electricity, ma!eti"m a!# electr$ma!eticra#iati$!

2* E6%lai! t&e c$!ce%t" $' electric a!# ma!etic 'iel#"*

3* Mea"(re a!# c$m%(te electric c(rre!t i! #*c a!# a*c* circ(it*

* Ill("trate t&e %ri!ci%le" $' electr$ma!etic i!#(cti$! a" t&ey a%%ly t$$t& #*c* a!# a*c* e!erat$r"*

;* Dem$!"trate &$+ circ(it eleme!t" are c$!!ecte#*

=* De"crie t&e %ri!ci%le" $' cat&$#e ray $"cill$"c$%e, ammeter",)$ltmeter", 65ray t(e" a!# #ry cell" a" +ell a" acc(m(lat$r"*

>* I#e!ti'yi! t&e a#)a!tae" a!# #i"a#)a!tae" $' 65ray"

?* De"crie t&e "tr(ct(re $' t&e !(clear at$m*

@* Di"ti!(i"& et+ee! e$ra%&ic a!# e$ma!etic meri#ia!"*

1/* De"crie t&e terre"trial ma!etic 'iel#*

11* Di"ti!(i"& et+ee! !(clear '("i$! a!# !(clear 'i""i$!*

NOUN =


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12* De"crie t&e e!erati$! a!# #i"tri(ti$! $' electric %$+er*

/. 0 $or#n T%ro!% T%#) Co!r)(

T$ c$m%lete t&i" c$(r"e y$( are re(ire# t$ rea# t&e "t(#y (!it", rea# "et

$$-" a!# rea# $t&er material" %r$)i#e# y NOUN* Y$( +ill al"$ !ee# t$ #$"$me %ractical e6erci"e +&ic& +ill e arra!e# y y$(r C$(r"e T(t$r* Eac&(!it c$!tai!" "el'5a""e""me!t e6erci"e", a!# at %$i!t" i! t&e c$(r"e y$( arere(ire# t$ "(mit a""i!me!t" '$r a""e""me!t %(r%$"e"* At t&e e!# $' t&ec$(r"e, t&ere i" a 'i!al e6ami!ati$!* T&e c$(r"e "&all ta-e y$( a$(t ; +ee-"i! t$tal t$ c$m%lete * .el$+ y$( +ill 'i!# li"te# all t&e c$m%$!e!t" $' t&ec$(r"e, +&at y$( &a)e t$ #$ a!# &$+ y$( "&$(l# all$cate y$(r time t$ eac&(!it i! $r#er t$ c$m%lete t&e c$(r"e "(cce""'(lly a!# $! time*

.0 Co!r)( M&t(r#&')

1* C$(r"e (i#e

2* St(#y (!it"

3* A""i!me!t 'ile

* Pre"e!tati$! "c&e#(le

.0 St!4 Un#t)

T&ere are 2/ St(#y U!it" i! t&i" C$(r"e, a" '$ll$+"8

U!it 1 Electric c&are, 4$rce a!# 4iel#

U!it 2 Ga(""" La+

U!it 3 Electric P$te!tial

U!it P$te!tial '$r C$!ti!($(" C&are Di"tri(ti$! A!# E!ery

U!it ; Dielectric" a!# Ca%acit$r"

U!it = Electric C(rre!t

U!it > Direct5C(rre!t Circ(it" a!# I!"tr(me!t"

NOUN >


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U!it ? T&e Ma!etic 4iel#

U!it @ M$ti$! $' C&are Particle" i! Electric a!# Ma!etic 4iel#

U!it 1/ Electr$ly"i" a!# Cell"

U!it 11 T&ermal E''ect" $' Electric C(rre!t" A!# Electric P$+er

U!it 12 Ma!etic Pr$%ertie" $' Matter

U!it 13 Terre"trial Ma!eti"m

U!it 1 Electr$ma!etic I!#(cti$! I

U!it 1; Electr$ma!etic I!#(cti$! 11

U!it 1= Alter!ati! C(rre!t T&e$ry 1

U!it 1> Alter!ati! C(rre!t T&e$ry 11

U!it 1? T&erm$electric, P&$t$electric T&ermi$!ic E''ect"

U!it 1@ M$#er! P&y"ic" 1

U!it 2/ M$#er! P&y"ic" 11

Eac& "t(#y (!it c$!"i"t" $' t+$ t$ t&ree +ee-" +$r-, a!# i!cl(#e" "%eci'ic$9ecti)e"* Eac& (!it c$!tai!" a !(mer $' "el'5te"t"* I! e!eral, t&e"e "el'5te"t", (e"ti$! y$( $! t&e material y$( &a)e 9("t c$)ere# $r re(ire y$( t$a%%ly it i! "$me +ay a!#, t&erey, &el% y$( t$ a(e y$(r %r$re"" a!#rei!'$rce y$(r (!#er"ta!#i! $' t&e material* T$et&er +it& t(t$r5mar-e#a""i!me!t", t&e"e e6erci"e" +ill a""i"t y$( i! ac&ie)i! t&e "tate# lear!i!$9ecti)e" $' t&e i!#i)i#(al (!it" a!# $' t&e c$(r"e*

5.0 S(t T(6too)

D(!ca! T$m 01@?2 P&y"ic"* A Te6t$$- '$r A#)a!ce# Le)el St(#e!t"

B$&! M(rray 0P(li"&er" Lt#* L$!#$!*

S*M* Ge##e" 01@?1 A#)a!ce# P&y"ic"* Macmilla! E#(cati$! Lt#* L$!#$!Mce!7ie A*E*E 01@>3 A Sec$!# C$(r"e $' Electricity* T&eU!i)er"ity Pre"", Camri#e

7.0 A))#n*(nt F#'(

NOUN ?


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T&e a""i!me!t 'ile +ill e "(%%lie# y NOUN* I! t&i" 'ile y$( +ill 'i!# allt&e #etail" $' t&e +$r- y$( m("t "(mit t$ y$(r t(t$r '$r mar-i!* T&e mar-"y$( $tai! '$r t&e"e a""i!me!t" +ill c$(!t t$+ar#" t&e 'i!al mar- y$( $tai!'$r t&i" c$(r"e* 4(rt&er i!'$rmati$! $! a""i!me!t" +ill e '$(!# i! t&e

a""i!me!t 'ile it"el' a!# later i! t&i" c$(r"e (i#e i! t&e "ecti$! $!a""e""me!t*

10.0 Pr()(nt&t#on S"%(!'(

T&e %re"e!tati$! "c&e#(le i!cl(#e# i! y$(r c$(r"e material" may "&$+ t&eim%$rta!t #ate" '$r t&e c$m%leti$! $' t(t$r5mar-e# a""i!me!t"* Rememer,y$( are re(ire# t$ "(mit all y$(r a""i!me!t" y t&e #(e #ate a" #ictate# yy$(r 'acilitat$r* Y$( "&$(l# (i#e aai!"t 'alli! e&i!# i! y$(r +$r-*

11.0 A))())*(nt

T&ere are t+$ a"%ect" t$ t&e a""e""me!t $' t&e c$(r"e* 4ir"t are t&e t(t$r5mar-e# a""i!me!t< "ec$!#, t&ere i" a +ritte! e6ami!ati$!*

I! #$i! t&e a""i!me!t, y$( are e6%ecte# t$ a%%ly i!'$rmati$!, -!$+le#ea!# tec&!i(e" at&ere# #(ri! t&e c$(r"e* T&e a""i!me!t" m("t e"(mitte# t$ y$(r t(t$r '$r '$rmal a""e""me!t i! acc$r#a!ce +it& t&e #ea#5li!e" "tate# i! t&e %re"e!tati$! "c&e#(le a!# t&e a""i!me!t 'ile* T&e +$r-y$( "(mit t$ y$(r t(t$r '$r a""e""me!t +ill c$(!t '$r / $' y$(r t$talc$(r"e +$r-*

At t&e e!# $' t&e c$(r"e y$( +ill !ee# t$ "it '$r a 'i!al +ritte! e6ami!ati$! $'t&ree &$(r" #(rati$!* T&i" e6ami!ati$! +ill al"$ c$(!t '$r =/ $' y$(rc$(r"e mar-*

12.0 T!tor8M&r( A))#n*(nt) 9TMA

T&e TMA" are li"te# a" item =*/ i! eac& (!it* Ge!erally, y$( +ill e ale t$c$m%lete y$(r a""i!me!t" 'r$m t&e i!'$rmati$! a!# martial c$!tai!e# i! t&e"t(#y (!it", "et $$-" a!# $t&er rea#i!* H$+e)er, it i" #e"irale i! all #ereele)el e#(cati$! t$ #em$!"trate t&at y$( &a)e rea# a!# re"earc&e# m$re

+i#ely t&a! t&e re(ire# mi!im(m* U"i! $t&er re'ere!ce" +ill i)e y$( ar$a#er )ie+%$i!t a!# may %r$)i#e a #ee%er (!#er"ta!#i! $' t&e "(9ect*

F&e! y$( &a)e c$m%lete# eac& a""i!me!t, "e!# it, t$et&er +it& a TMA'$rm, t$ y$(r t(t$r* Ma-e "(re t&at eac& a""i!me!t reac&e" y$(r t(t$r $! $r

e'$re t&e #ea#li!e i)e! i! t&e %re"e!tati$! "c&e#(le a!# a""i!me!t 'ile* I','$r a!y rea"$! y$( ca!!$t c$m%lete y$(r +$r- $! time c$!tact y$(r t(t$r

NOUN @


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e'$re t&e a""i!me!t i" #(e t$ #i"c("" t&e %$""iility $' a! e6te!"i$!*E6te!"i$!" +ill !$t e ra!te# a'ter t&e #(e #ate (!le"" t&ere are e6ce%ti$!alcirc(m"ta!ce"*

13.0 F#n&' E6&*#n&t#on &n Grn

T&e 'i!al e6ami!ati$! '$r PHY 132 +ill e $' t&ree &$(r" #(rati$! a!# &a)e a)al(e $' =/ $' t&e t$tal c$(r"e ra#e* T&e e6ami!ati$! +ill c$!"i"t $'(a!titie" +&ic& re'lect t&e ty%e" $' "el'5te"ti! %ractice e6erci"e" a!# t(t$r5mar-e# %r$lem" y$( &a)e %re)i$("ly e!c$(!tere#* All area" $' t&e c$(r"e+ill e a""e""e#*

Y$( are a#)i"e# t$ ("e t&e time et+ee! 'i!i"&i! t&e la"t (!it a!# "itti! t&ee6ami!ati$! t$ re)i"e t&e e!tire c$(r"e* Y$( mi&t 'i!# it ("e'(l t$ re)ie+y$(r "el'5te"t", t(t$r5mar-e# a""i!me!t" a!# c$mme!t" $! t&em e'$re t&ee6ami!ati$!*

1+.0 Co!r)( M&r#n S"%(*(

T&e '$ll$+i! tale "&$+" &$+ t&e act(al c$(r"e mar-i! i" r$-e! #$+!*

A""e""me!t Mar-"A""i!me!t" / $' c$(r"e mar-"4i!al e6ami!ati$! =/ $' $)erall c$(r"e mar-"T$tal 1// $' c$(r"e mar-"

Tale 1 c$(r"e mar-i! "c&eme

NOUN 1/


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;;;;


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PHY 132: ELECTRICITY, MAGNETISM AND MODERN

PHYSICS

COURSE DEVELOPMENT

Course Developer4re# E(!(

Unit Writer4re# E(!(

Programme Leader

Course CoordinatorDr* 0Mr"* C* A* O-$!-+$

NATIONAL OPEN UNIVERSITY OF NIGERIA

NOUN 12


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UNIT 1

ELECTRIC CHARGE, FORCE AND FIELD

T&'( o= Cont(nt)

1*/ I!tr$#(cti$!2*/ O9ecti)e"3*1 Electric c&are3*2 C$(l$m" la+3*3 Pri!ci%le $' "(%er%$"iti$!3* Electric 'iel#*/ C$!cl("i$!;*/ S(mmary=*/ T(t$r Mar-e# A""i!me!t 0TMA">*/ Re'ere!ce"

1.0 Intro!"t#on

Li&t!i! a!# t&(!#er are t+$ c$mm$! %&e!$me!a i! $(r &$t a!# &(mi#atm$"%&ere i! Nieria* Ha)e y$( e)er i)e! a t&$(&t t$ +&at i" re"%$!"ile'$r t&e $cc(rre!ce $' t&e %&e!$me!a

A %&y"ici"t, .e!9ami! 4ra!-li! #em$!"trate# a" l$! a$ a" 1>;2 t&att&(!#er cl$(#" are c&are# +it& electricity* T&e"e c&are# cl$(#", +&e!#i"c&are# i! t&e atm$"%&ere, i)e ri"e t$ a reat "%ar-, +&ic& i" re'erre# t$a" li&te!i!* It +ill i!tere"t y$( t$ -!$+ t&at t&e am$(!t $' electric c(rre!t#(ri! t&e #i"c&are i" a$(t 2/A*

T&e electric #i"c&are +&ic& i)e" ri"e t$ li&t!i! al"$ %r$#(ce" a reatam$(!t $' &eat* I! a 'racti$! $' a "ec$!#, tem%erat(re ri"e" t$ a$(t 1;////C*T&e li&te!i! #e)el$%" i! a "mall area +&ic& i" a$(t 2/cm i! +i#t&*H$+e)er, a" a re"(lt $' t&e &eat am$(!t $' reat %r$#(ce# i! t&at "mall area

t&e air m$lec(le" m$)e 'a"t a!# ca("e t&e i!te!"e "$(!# +&ic& +e callt&(!#er* F&e! t&e "$(!# i" re'lecte# y cl$(#", &ill $r a!y $t&er $"tacle, +e&ear t&e r$ari! $' cl$(#"*

A )ery im%$rta!t t&i! a$(t electric c&are" i" t&at t&e '$rce" et+ee! t&emare )ery lare* T&e '$rce i" -!$+! a" electr$"tatic '$rce 0$r electric '$rce a!#i" re"%$!"ile '$r &$l#i! electr$!" t$ !(clei t$ '$rm at$m" a!# '$r &$l#i!t&e r$(%" $' t&e at$m" t$et&er t$ '$rm m$lec(le", "$li#" a!# li(i#"*

NOUN 13


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T&e "t(#y $' t&e"e "tatic c&are" i" -!$+! a" electr$"tatic* I!#ee#,electr$"tatic +a" t&e 'ir"t ra!c& $' electricity t$ e i!)e"tiate# a!#, '$r"$me time, it +a" rear#e# a" a "(9ect +&ic& &a# !$ %ractical )al(e*H$+e)er, it i" !$+ -!$+! t$ &a)e %ractical i!#("trial a%%licati$!"* 4$re6am%le, +e "&all "ee later i! t&i" c$(r"e t&at a -!$+le#e $' electr$"tatic i"

im%$rta!t i! t&e #e"i! $' cat&$#e ray t(e" '$r tele)i"i$!, i! electrical%r$"%ecti! '$r mi!eral"* Electr$"tatic l$(#"%ea-er" a!# micr$%&$!e are i!c$mm$! ("e a" +ell a" electr$"tatic %&$t$c$%yi! mac&i!e"*

2.0 O-("t#()

A'ter "t(#yi! t&i" (!it, y$( +ill e ale t$8

Di"ti!(i"& et+ee! t&e t+$ ty%e" $' electric c&are

S&$+ t&at t&e t$tal electric c&are i! a! i"$late# "y"tem i" c$!"er)e#

State C$(l$m" la+ a!# ("e it t$ 'i!# t&e electr$"tatic '$rce et+ee!t+$ c&are"

State t&e "(%er%$"iti$! %ri!ci%le

Calc(late t&e )ect$r "(m $' t&e electric 'iel# "tre!t& #(e t$ a !(mer$' %$i!t c&are"*

S-etc& t&e 'iel# li!e" '$r "$me "im%le #i"tri(ti$! $' c&are*

3.1 E'("tr#" "%&r(

3.1.1 T4>() o= "%&r()

T&e a!cie!t Gree-" #i"c$)ere# t&at amer +&e! r(e# +it& "il- ac(ire# t&e%r$%erty $' attracti! li&t $9ect" "(c& a" %iece" $' c&a'' * Filliam Gilert#i"c$)ere# t&at $t&er "("ta!ce" e6&iit t&e "ame e''ect, a!# t&at t&ema!it(#e $' t&e e''ect i" r$(&ly %r$%$rti$!al t$ t&e area $' t&e "(r'acer(e#* He +a" t&e! le# t$ t&e i#ea $' a c&are $' electricity*

D( 4ay 01>; #i"c$)ere# t&at t&ere are t+$ -i!#" $' electricity* T+$ e$!iter$#" +&e! r(e# +it& '(r e6ert a '$rce $' re%(l"i$! $! eac& $t&er* T+$ la""r$# r(e# +it& "il- al"$ re%el $!e a!$t&er* H$+e)er, a! e$!ite r$# +&ic&&a" ee! r(e# +it& '(r attract" a la"" r$# +&ic& &a" ee! r(e# +it& "il-*A!y "("ta!ce r(e# +it& a #i''ere!t "("ta!ce ac(ire" a c&are $'electricity, a!# i" '$(!# eit&er t$ re%el c&are# e$!ite a!# attract c&are#la"", $r )ice )er"a* Si!ce t&e t+$ -i!#" $' electricity ca! !e(trali7e eac&

NOUN 1


15/342


$t&er" e''ect, $!e i" calle# %$"iti)e a!# t&e $t&er !eati)e* N$te t&at t&ec&$ice a" t$ +&ic& i" %$"iti)e +a" %(rely aritrary* Gla"" r(e# +it& "il- i""ai# t$ &a)e a %$"iti)e c&are a!# e$!ite r(e# +it& '(r a !eati)e c&are*

T&e $rii! $' t&e )e a!# J)e c&are $' %r$t$! a!# electr$!

T&e la+ $' '$rce et+ee! c&are" may e "tate# a" '$ll$+"8 li-e c&are"re%el, (!li-e c&are" attract

Let (" !$+ (!#er"ta!# clearly t&e $rii! $' t&e t+$ ty%e" $' c&are"< +erememer t&at a! at$m c$!"i"t" $' a %$"iti)ely c&are# !(cle(" +it&!eati)ely c&are# electr$!" ar$(!# it* T&e !(cle(" i" ma#e (% $' %r$t$! a!#electr$! * T&e !e(tr$! i" !e(tral 0!$ c&are +&ic& t&e %r$t$! a!# electr$!&a)e e(al (t $%%$"ite c&are" 0%$"iti)e a!# !eati)e*

T&e %r$t$! a!# !e(tr$! i! t&e !(cle(" are &el# t$et&er )ery ti&tly y a!(clear '$rce* S$ "tr$! i" t&e !(clear '$rce t&at t&e %r$t$!" are (! ale t$m$)e a+ay 'r$m t&e !(cle("* O! t&e $t&er &a!#, t&e '$rce &$l#i! electr$! t$t&e at$mic !(cle(" i" m(c& +ea-er t&a! t&e !(clear '$rce* He!ce t&eelectr$!" may m$)e a+ay 'r$m t&e at$m*

F&e! t+$ #i''ere!t material" are r(e# t$et&er, electr$!" et tra!"'erre#'airly ea"ily 'r$m $!e material t$ t&e $t&er* Si!ce "$me material" te!# t$ &$l#t&eir electr$!" m$re "tr$!ly t&a! $t&er", t&e #irecti$! $' tra!"'er $' electr$!"#e%e!#" $! t&e material"* 4$r e6am%le, +&e! a %la"tic r(ler i" r(e# +it& a+$$le! cl$t&, electr$!" 'l$+ 'r$m +$$l t$ %la"tic, "$ t&at it carrie" !et

!eati)e c&are" +&erea" t&e +$$l, +it& a #e'icit $' electr$!", carrie" a%$"iti)e c&are $' e(al ma!it(#e*

T&i" %r$ce"" $' c&ari! t&e $#ie" y mea!" $' r(i! t&em t$et&er i"calle# c&ari! y 'ricti$!* I! a!y ca"e, +e "&$(l# !$te t&at 'ricti$! act(ally&a" !$t&i! t$ #$ +it& t&e c&ari! %r$ce""* It +$(l# a%%ear t&at 'ricti$! i"$!ly $rr$+e# t$ #e"crie t&e r(i! %r$ce""*

?!()t#on

T&ere are t+$ c&are# $#ie", 6 a!# y +&ic& attract eac& $t&er* K re%el" a

t&ir# c&are# $#y * D$ y$( t&i!- 7 +ill attract $r re%el Y

3.1.2 Un#t o= C%&r(

I! t&e Sy"tem I!ter!ati$!al 0SI, electric c&are i" mea"(re# i! c$(l$m" 0C,+&ic& i" #e'i!e# i! term" $' am%ere* A c$(l$m i" t&e (a!tity $' c&are

NOUN 1;


16/342


'l$+i! %er "ec$!# t&r$(& a c$!#(ct$r i! +&ic& t&ere i" a "tea#y c(rre!t $'1A*

Not(:

T&e #e'i!iti$! $' am%ere i!)$l)e" '$rce et+ee! c(rre!t"* Fe "&all "ee t&i" i"

M$#(le" 3*

A C$(l$m" i" t&e am$(!t $' c&are t&at 'l$+ t&r$(& a cr$""5"ecti$! $' a+ire i! $!e "ec$!# i' t&ere i" a "tea#y c(rre!t $' $!e am%ere 0IA i! t&e +ire*I! "ym$l",

It **3*1

F&ere i" i! c$(l$m", i' I i" i! am%ere a*# t i" i! "ec$!#"* T&e mai! rea"$!'$r #e'i!i! t&e c$(l$m i! term" $' am%ere i" t&at it i" ea"y t$ mai!tai!,c$!tr$l a!# mea"(re a c(rre!t t&r$(& a c$!#(ct$r rat&er t&a! t&e am$(!t $'c&are*

3.1.3 Con)(r&t#on o= C%&r(

I! t&e met&$# $' c&ari! y 'ricti$! 0r(i! +&ic& i" #i"c(""e# i! "ecti$!3*1, !$ !e+ c&are" are create#* T&e aleraic "(m $' t&e i!#i)i#(al c&are",t&at i" t&e !et c&are, al+ay" remai!" c$!"ta!t* Let (" "ee &$+ t&i" i" t&eca"e* .e'$re t&e %r$ce"" $' r(i!, t&e t+$ $#ie" +ere electrically !e(tral0&a)i! !$ c&are* T&ere'$re, t&e t$tal c&are i" 7er$* A'ter r(i!, $!e

$#y ec$me" !eati)ely c&are# +&ile t&e $t&er ac(ire" a %$"iti)e c&are

$' e(al ma!it(#e* I! e''ect, t&e aleraic "(m $' t&e e(al a!# $%%$"itec&are" $! t&e t+$ $#ie" i" 7er$*

T&i" "&$+" t&at electric c&are i" a c$!"er)e# (a!tity* I! $t&er +$r#",c$!"er)ati$! $' c&are im%lie" t&at t&e t$tal c&are i! a! i"$late# "y"tem #$e"!$t c&a!e* Y$( "&$(l# !$te t&at t&i" #$e" !$t mea! t&at t&e t$tal am$(!t $'

%$"iti)e $r !eati)e c&are i! a "y"tem i" 'i6e#* F&at +e are "ayi! i" t&at'$r e)ery a##iti$!al %$"iti)e c&are create#, t&ere i" al+ay" a! e(al am$(!t$' !eati)e c&are create#*

T&e c&are c$!"er)ati$! la+ may e "tate# a" '$ll$+"8

T&e t$tal electric c&are i! a! i"$late# "y"tem, t&at i", t&e aleraic "(m $'t&e %$"iti)e a!# !eati)e c&are %re"e!t at a!y time, #$e" !$t c&a!e

NOUN 1=


17/342


3.1.+ ?!&nt#@&t#on o= "%&r(

T&e "malle"t c&are t&at i" %$""ile t$ $tai! i" t&at $' a! electr$! $r %r$t$!*T&e ma!it(#e $' t&i" c&are i" #e!$te# y e* A c&are "maller t&a! e &a" !$t

ee! '$(!#* I' $!e #etermi!e" t&e am$(!t $' c&are $! a!y c&are# $#y

0e** a c&are "%&ere $r a!y c&are# %article 0e** 5%article $r a!y i$!, it"c&are i" al+ay" '$(!# t$ e a! i!teral m(lti%le $' e, t&at i" e, 2e, 3e, a!# "$$!* N$ c&are +ill e a 'racti$!al m(lti%le $' e li-e /*>e $r 2*;e* T&i" i" tr(e'$r $t& !eati)e a!# %$"iti)e c&are" a!# i" e6%re""e# a"

!e **3*2

+&ere ! i" a %$"iti)e $r !eati)e i!teer*

Y$( &a)e !$+ lear!t t&at c&are e6i"t i! #i"crete %ac-et" rat&er t&a! i!c$!ti!($(" am$(!t* F&e!e)er a %&y"ical (a!tity %$""e""e" #i"crete )al(e"i!"tea# $' c$!ti!($(" )al(e", t&e! t&e (a!tity i" "ai# t$ e (a!ti7e#*T&ere'$re, +e "ay t&at c&are i" (a!ti7e#*

?!()t#on

A c$!#(ct$r %$""e""e" a %$"iti)e c&are $' 3*26 1/ 51@ C* H$+ ma!y electr$!#$e" it &a)e i! e6ce"" $r #e'icit 0e 1*=/ 6 1/51@C

3.2 Co!'o*) '&B

A -!$+le#e $' t&e '$rce" t&at e6i"t et+ee! c&are %article" i" !ece""ary '$ra $$# (!#er"ta!#i! $' t&e "tr(ct(re $' t&e at$m a!# $' matter* T&ema!it(#e $' t&e '$rce" et+ee! c&are# "%&ere" +a" 'ir"t i!)e"tiate#(a!titati)ely i! 1>?; y C&arle" C$(l$m, a 4re!c& "cie!ti"t* He $"er)e#t&at t&e electr$"tatic '$rce et+ee! t&e t+$ "%&ere i" %r$%$rti$!al t$ t&e

%r$#(ct $' t&e c&are" a!# i" i!)er"ely %r$%$rti$!al t$ t&e "(are $' t&eir#i"ta!ce a%art*

C$(l$m" la+ may e "tate# i! mat&ematical term" a"

4 :1:2

r2F&ere 4 i" t&e electric '$rce et+ee! t&e t+$ c&are" :1:2, #i"ta!ce r a%art*Fe ca! t(r! t&e a$)e e6%re""i$! $' %r$%$rti$!ality t$ a" e(ati$! y +riti!

4 :1 :2 *3*3r2

F&ere i" a c$!"ta!t*

NOUN 1>


18/342


1 *3*

F&ere t&e c$!"ta!t #e%e!#" $! t&e material "(rr$(!#i! t&e c&are", a!# i"calle# %ermitti)ity*

Not(

Fe "&all "ee later t&at it i" a#)a!tae$(" t$ &a)e t&e a##iti$!al c$!"ta!t i!a!y "y"tem &a)i! Q"%&erical "ymmetry i*e* a!y "y"tem i! +&ic& e''ect" aret&e "ame a!y+&ere $! t&e "(r'ace $' a "%&ere*

T&e %ermitti)ity $' a )ac((m i" #e!$te# y $ 0%r$!$(!ce# a" e%"il$!!$(&t a!# i" calle# t&e %ermitti)ity $' 'ree "%ace

$ ?*?; 6 1/512

C2

N51

m52

Fe ca! al"$ +rite

1 ?*@? 6 1/@Nm2C52

0$ a!# al"$

4 @ 6 1/@ :1:2r23*;

T&e %ermitti)ity $' air at "ta!#ar# tem%erat(re a!# %re""(re 0"*t*% i"

1*///;$* T&ere'$re, +e ca! ("(ally ta-e E$ a" t&e )al(e '$r air*

Fe "&all "ee i! M$#(le 2 t&at a m$re +i#ely ("e# (!it '$r %ermitti)ity i" t&e4ara# %er metre 04m51*

Y$( "&$(l# !$te t&at C$(l$m" la+ a%%lie" t$ %$i!t c&are"* S(5at$mic%article" "(c& a" electr$!" a!# %r$t$!" may e rear#e# a" a%%r$6imati! t$%$i!t c&are* I! %ractice t+$ "mall "%&ere" +ill $!ly a%%r$6imate t$ %$i!tc&are" +&e! t&ey are 'ar a%art a!# t&ere m("t !$t e a!y c&are !eary t$#i"t(r t&e (!i'$rm #i"tri(ti$! $' c&are $! eac& $' t&em*

E6&*>'(

A c&are 1, ;*/c i" %lace# 3/cm t$ t&e +e"t $' a!$t&er c&are 212c*F&at i" t&e '$rce e6erte# y t&e %$"iti)e c&are $! t&e !eati)e c&are

So'!t#on

1 ;*/c 2 512c

NOUN 1?


19/342


3/cm

C$(l$m" la+ i)e" '$rce $! !eati)e c&are #(e t$ t&e %$"iti)e c&are a"'$ll$+"8

4 1 1 2$ r2

4 0@ 6 1/@N m2 C52 0; 6 1/5= C 0512 6 1/5= C0/*3/m2

5= N

T&e mi!(" "i! "&$+" t&at t&e '$rce i" i! t&e !eati)e 65#irecti$! t&at i"t$+ar#" +e"t* T&ere'$re, it i" a '$rce $' attracti$!*

3.3 Pr#n"#>'( o= )!>(r>o)#t#on

I! t&e la"t "ecti$!, +e c$!"i#ere# t&e electr$"tatic '$rce" et+ee! t+$c&are"* T&e (e"ti$! i" &$+ #$ +e calc(late t&e electr$"tatic '$rce $! ac&are 1#(e t$ t&e %re"e!ce $' $t&er t+$, t&ree $r m$re c&are" T&i""it(ati$! i" "&$+! i! 'i(re 3*1

2

413 3

1

4i(re 3*1 41 412

Fe ca! "till calc(late t&e '$rce et+ee! #i''ere!t %air $' c&are" ("i!

C$(l$m" la+* T&e t$tal '$rce $! 1+ill e t&e )ect$r "(m $' '$rce" $! 1#(e t$ 2a!# 3i!#e%e!#e!tly* T&i" i" t&e %ri!ci%le $' S(%er%$"iti$!* I! t&e$t&er +$r#", t&e 'act t&at electric '$rce" a## )ect$rially i" -!$+! a" t&e

%rici%le $' "(%er%$"iti$!*

T$ ill("trate t&e %ri!ci%le, let (" $ t&r$(& t&e '$ll$+i!

NOUN 1@


20/342


F$r-e# e6am%le

E6am%le2 2*/c

41

1/ cm 412

413 3 */c 1 51*/(c

2/cm

'i(re 3*2

I! 'i(re 3*, 1 1*/c, 2*/c a!# 3 */c* 4i!# t&e electr$"tatic '$rce $!1t$ t&e t+$ $t&er c&are"* Y$( "&$(l# e6%re"" y$(r re"(lt a" a ma!it(#ea!# #irecti$!*

So'!t#on

T&e t&ree c&are" are l$cate# at t&e c$r!er" $' a ri&t a!le tria!le* T&e%r$lem ca! e "$l)e# ("i! t&e "(%er%$"iti$! tria!le* T&e %r$lem ca! e"$l)e# ("i! t&e "(%er%$"iti$! %ri!ci%le*

T&e '$rce $! 1#(e t$ t&e c&are 2i" i)e! y412 1 1 2 $ r2

0@ 6 1/ @ Nm2 C52 051 6 1/5= C 026 1/5= C0/*1/m2

1*?N 0attracti)e i! t&e )e 65#irecti$!

Similarly, t&e '$rce $! 1 #(e t$ 2i"

413 0@ 6@ Nm2 C52 051 6 1/5= C 06 1/5= C0/*2/m3

/*@/N 0attracti)e i! t&e )e 65#irecti$!

NOUN 2/


21/342


Acc$r#i! t$ t&e "(%er%$"iti$! %ri!ci%le, t&e re"(lta!t '$rce 41acti! $! , i"t&e )ect$r "(m $' t&e '$rce" #(e t$ 2 a!# 3* T&e ma!it(#e $' 41i"

V0/*@/2 01*?2 2*/1Na!# it ma-e a! a!le ta! 5101*?/*@ ta! 512 =3*;W +it& t&e %$"iti)e 65

a6i"*

3.+ T%( E'("tr#" F#('

A! electric 'iel# i" a rei$! +&ere a! electric c&are e6%erie!ce" a '$rce, 9("ta" a '$$tall 'iel# i" a! area +&ere t&e ame i" %laye#* I' a )ery "mall,

%$"iti)e %$i!t c&are i" %lace at a!y %$i!t i! a! electric 'iel# a!# ite6%erie!ce" a '$rce 4, t&e! t&e 'iel# "tre!t& E @al"$ calle# t&e E5'iel# at t&at

%$i!t i" #e'i!e# y t&e e(ati$!*

' $r 4 E **3*;T&e ma!it(#e $' E i" t&e '$rce %er (!it c&are a!# it" #irecti$! i" t&at $' 40i*e t&e #irecti$! $' t&e '$rce +&ic& act" $! a %$"iti)e c&are*

T&(" E i" a )ect$r*

3.+.1 C&'"!'&t#on o= t%( E'("tr#" F#('

I! $r#er t$ mea"(re t&e electric 'iel# i! a i)e! rei$!, +e i!tr$#(ce a te"tc&are a!# mea"(re t&e '$rce $! it* H$+e)er, +e "&$(l# reali7e t&at t&e te"t

c&are e6ert" '$rce" $! t&e c&are t&at %r$#(ce t&e 'iel#, "$ it may c&a!et&e c$!'i(rati$! $' t&e c&are"* I! %ri!ci%le, t&e te"t c&are "&$(l# e "$"mall a" t$ &a)e !$ "i!i'ica!t e''ect $! t&e c&are c$!'i(rati$! t&at

%r$#(ce" t&e 'iel#*

E(ati$! 3*; "&$+" t&at t&e electric 'iel# i" mea"(re# i! !e+t$!" C$(l$m 51

0NC51* Si!ce 4 i" a )ect$r (a!tity, E +ill al"$ e a )ect$r* I' i" %$"iti)e,t&e electric 'iel# E &a" t&e "ame #irecti$! a" t&e '$rce acti! $! t&e c&are* I' i" !eati)e, t&e #irecti$! $' E i" $%%$"ite t$ t&at $' t&e '$rce 4*

Let (" c$!"i#er t&e electric 'iel# $' a %$i!t c&are* Fe alrea#y -!$+ 'r$m

c$(l$m" la+ t&at i' +e %lace a %$i!t c&are 1at a #i"ta!ce r 'r$m a!$t&er%$i!t c&are 1t&e '$rce $! 1+ill e*

4 1 1 **3*=

$ r2

NOUN 21


22/342


Si!ce t&e electric 'iel# i" '$rce %er (!it c&are, +e #i)i#e t&e '$rce i"e(ati$! 3*= y t&e c&are 1 t$ $tai! t&e 'iel# #(e t$ at t&e l$cati$! $' 1*T&at i"

E 4 1 **3*>

$ r2E(ati$! 3*> i)e" t&e 'iel# ari"i! #(e t$ t&e c&are at a!y l$cati$! +&ic&i" at a #i"ta!ce r 'r$m *

F&at i" t&e "it(ati$! +&e! t&e electric 'iel# i" #(e t$ t+$ $r m$re c&are"T&e a!"+er i" "im%le* Si!ce t&e electric '$rce $ey" t&e "(%er%$"iti$!

%ri!ci%le, "$ #$e" t&e electric 'iel# 0'$rce %er (!it c&are* T&ere'$re, t&e'iel# at a i)e! %$i!t #(e t$ t+$ $r m$re c&are" i" t&e )ect$r "(m $' t&e'iel#" $' i!#i)i#(al c&are"*

E6&*>'(

A! electric 'iel# i" "et (% y t+$ %$i!t c&are" 1 a!# 2 "(c& t&at1 52 12 6 1/5@C a!# "e%arate# y a #i"ta!ce $' /*1m a" "&$+! i! 'i(re3*3* 4i!# t&e electric 'iel# at t&e %$i!t" A a!# .*

E1

. =/W E. O

/*1mE2 /*1m

52C 1 A

/*/m /*/; /*1m

4i 3*3 e6am%le 3*

So'!t#on

0i At %$i!t A1t&e electric 'iel# E1#(e t$ 1i"

NOUN 22


23/342


E1 0@61/ @ Nm2 C52 12 6 1/5@ C0/*/=2

0@ 6 1/@ Nm2 C52 6 12 6 1/5@ C3= 6 1/5m2

3 6 1/NC51i! t&e )e 65#irecti$!

At A , t&e electric 'iel# E2, #(e t$ 2i"

E2 0@ 6 1/@ 6 0512 6 1/ 5@ C0/*/2

@ 6 1/@ Nm2 C52 6 12 6 1/5@ C 6 1/5m2

=*>; 6 1/NC51i! t&e )e 65#irecti$!

T&ere'$re, t&e !et electric 'iel#, E1at %$i!t A i" i)e! y

EA E1 E2 03 =*>; 6 1/NC51

@*>; 6 1/NC51

At %$i!t ., t&e electric 'iel# E, #(e t$ , i"

E1 0@61/@Nm2C 52 12 6 1/5@ C0/*1m2

1*/? 6 1/NC51i! t&e #irecti$! "&$+! i! 46, 3*

Similarly t&e 'iel# E2#(e t$ 2i"E2 0@61/@Nm2C522 0512 2 6 1/5@ C

0/*1m2

51*/?6 1/NC51

0T&e mi!(" "i! "&$+" t&at t&e electric 'iel# %$i!t" #ia$!ally#$+!+ar# t$ t&e ri&t

START

N$+ +e &a)e t$ a## t&e t+$ '$rce" )ertically* I' +e re"$l)e E1a!# E2i!t$ c$m%$!e!t" al$! t&e 65a6i" a!# y5a6i", it i" clear 'r$m 4i* 3*3t&at t&e y J c$m%$!e!t" $' )ect$r" E1 a!# E2ca!cel $(t a!# t&$"eal$! 65a6i", i*e* .O a##* Y$( +ill $"er)e t&at t&e a!el et+ee!eit&er )ect$r a!# t&e 65#irecti$! i" =//eca("e t&e tria!le '$rme# y.11a!# J2i" a! e(ilateral tria!le* T&e #irecti$! $' t&e re"(lta!t'iel# i", t&ere'$re, al$! .O a!# it" ma!it(#e i" i)e! y

NOUN 23


24/342


E. 01*/? 6 1/c$" =// 1*? 6 1/c$" =//

1*/? 6 1/NC51

3.+.2 F#(' '#n()

A! electric 'iel# ca! e re%re"e!te# y electric 'iel# li!e" $r li!e" $''$rce* T&e li!e" are #ra+! "$ t&at

0a T&e 'iel# li!e at a %$i!t 0$r t&e ta!e!t t$ it i' it i" c(r)e#i)e" t&e #irecti$! $' E at t&e %$i!t* T&i" i" t&e #irecti$! i!+&ic& a %$"iti)e c&are +$(l# accelerate*

0 T&e !(mer $' li!e" %er (!it cr$""5"ecti$! area i" %r$%$rti$!alt$ E*

Y$( "&$(l# !$te t&at t&e 'iel# li!e i" imai!ary< t&e re%re"e!tati$!"er)e" $!ly t&e ("e'(l %(r%$"e $' all$+i! (" t$ -!$+ t&e e!eral'eat(re" $' t&e electric 'iel# i! t&e e!tire rei$! at a la!ce* T&eta!e!t t$ t&e 'ile# at %$i!t A i! 'i(re 3* "&$+" t&e #irecti$! $'electric 'iel# at t&at %$i!t* T&e 'iel# li!e" are c$!ti!($(" a!# e6te!#"t&r$(&$(t "%ace #e%icti! t&e electric 'iel#*

EA E.

A .

4iel# li!e

F#!r( 3.+ An ('("tr#" =#(' '#n(

Si!ce a 'iel# li!e" i" al"$ #e'i!e# a" a %at& al$! +&ic& a 'ree, %$"iti)e, %$i!tc&are +$(l# tra)el i! a! electric 'iel#, it i" al+ay" #ra+! +it& a! arr$+&ea#i!#icati! t&e #irecti$! $' tra)el $' t&e %$"iti$! c&are*

NOUN 2


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F#!r( 3./ F#(' '#n() !( to & >o)#t#( >o#nt "%&r(

Si!ce t&e #irecti$! $' a! electric 'iel# i" ta-e! t$ e t&at $' t&e #irecti$! $'t&e '$rce" $! a %$"iti)e c&are, t&e 'iel# "(rr$(!#i! a %$i!t %$"iti)e c&arei" ra#ially $(t+ar#, a" "&$+! i! 'i* 3*;

F#!r( 3. 9&

F#!r( 3.9

4i(re 3*=8 T&e !at(re $' 'iel# li!e"

0a T+$ (!li-e c&are"

0 T+$ li-e c&are"

+.0 Con"'!)#on

NOUN 2;


26/342


Y$( &a)e !$+ $!e t&r$(& t&e 'ir"t (!it $' t&e c$(r"e J electricity a!#ma!eti"m* T&e m$"t ce!tral %$i!t %ertai!" t$ t&e electric c&are* A" y$(+$(l# "ee t&e c$!ce%t $' electric c&are c(t" acr$"" )irt(ally all a"%ect $' t&ec$(r"e* Y$( &a)e al"$ lea!t a$(t t&e electric 'iel#" #(e t$ a "i!le c&area!# t&$"e #(e t$ a "y"tem $' c&are"* D$ !$t '$ret t&at t&e electric '$rce ca!

e attracti)e $r re%(l"i)e*

/.0 S!**&r4

T&ere are $!ly t+$ ty%e" $' electric c&are a!# t&ey are aritrarilycalle# %$"iti)e a!# !eati)e* Li-e c&are" re%el a!# (!li-e c&are"attract eac& $t&er*

T&e (!it $' c&are i" t&e c$(l$m 0C

C&are i" al+ay" c$!"er)e#* T&at i", t&e aleraic "(m $' t&e c&are"i! a cl$"e# "y"tem #$e" !$t c&a!e

Electric c&are i" (a!ti7e#, $cc(rri! $!ly i! #i"crete am$(!t"*

T&e '$rce et+ee! t+$ c&are" i" %r$%$rti$!al t$ t&e %r$#(ct $' t&eirc&are" a!# i!)er"ely %r$%$rti$!al t$ t&e "(are $' t&e #i"ta!ce

et+ee! t&em* T&e '$rce act" al$! t&e li!e 9$i!i! t&e t+$ c&are"*4 1 012

$ r2T&e )al(e $' 1$ i" @61/@Nm2C52

T&e electric 'iel# at a %$i!t i! "%ace i" #e'i!e# a" t&e electric '$rcee6erte# $! a te"t c&are %lace# at t&at %$i!t*

E E

T&e electric 'iel# $' a %$i!t c&are i" i)e! yE 1 r

$ r2F&ere r i" a (!it )ect$r %$i!ti! 'r$m t&e %$i!t c&are t$ t&el$cati$! at +&ic& t&e electric 'iel# i" ei! calc(late#*

T&e electric 'iel# #(e t$ a #i"tri(ti$! $' c&are", acc$r#i! t$ t&e"(%er%$"iti$! %ri!ci%le, i" t&e )ect$r "(m $' t&e 'iel#" $' t&ei!#i)i#(al c&are" ma-i! (% t&e #i"tri(ti$!

NOUN 2=


27/342


E 1 ! r! ! $ r2!

Electric li!e" $' '$rce are $!ly a )i"(al +ay $' re%re"e!ti! a!electric 'iel#* T&e ta!e!t t$ a li!e $' '$rce at a!y %$i!t "&$+"t&e #irecti$! $' t&e electric 'iel# at t&at %$i!t*

.0 T!tor M&r( A))#n*(nt)

=*1 T+$ c&are" e a!# e are 'i6e# at a #i"ta!ce a* A t&ir# c&are i"%lace# $! t&e "trai&t li!e 9$i!i! t&e t+$ c&are" "$ t&at i" i!e(iliri(m* 4i!# t&e %$"iti$! $' * U!#er +&at circ(m"ta!ce" +ill t&ee(iliri(m e "tale $r (!"tale

=*2 A.CD i" a "(are $' /*/m "i#e* C&are" 1= 6 1/5@, 51= 6 1/5@

a!# 32 6 1/5@

c$(l$m are %lace# at t&e %$i!t" A, C a!# Dre"%ecti)ely* 4i!# t&e electric 'iel# "tre!t& at %$i!t .*

=*3 A "mall $9ect carryi! a c&are $' 5;61/5@C e6%erie!ce" a '$rce $'2/ 6 1/5@N i! t&e !eati)e 65#irecti$! +&e! %lace# at a certai! %$i!ti! a! electric 'iel#*

0a F&at i" t&e electric 'iel# at t&e %$i!t

0 F&at i" t&e ma!it(#e a!# #irecti$! $' t&e '$rce acti! $! a%r$t$! %lace# at t&e %$i!t

.0 R(=(r(n"() An Ot%(r R()o!r"()

P&y"ic"* A Te6t$$- '$r A#)a!ce# Le)el St(#e!t"* T$m D(!ca!B$&! M(rray 0P(li"&er" Lt#, L$!#$! 1@?2

Electr$"tatic" i! 4ree S%are J PHE5/>* I!#ia G&a!#i Nati$!alO%e! U!i)er"ity * Oct$er 2//1

A Sec$!# C$(r"e $' Electricity* A* E* E* Mc-e!7ieU!i)er"ity Pre"", Camri#e 1@>3

NOUN 2>


28/342


GAUSSS LA$

T&'( O= Cont(nt

1*/2*/3*13*23*3

I!tr$#(cti$!O9ecti)e"Electric 4l(6Ga(""" La+A%%licati$!" O' Ga(""" La+

NOUN 2?

UNIT 2


29/342


3*3*13*3*23*3*33*3**/

;*/=*/>*/

S%&erical SymmetryT&e Electric 4iel# O' A S%&erical C&are Di"tri(ti$!Li!e SymmetryPla!e SymmetryC$!cl("i$!"

S(mmaryT(t$r Mar-e# A""i!me!t"0TMA"Re'ere!ce" A!# Ot&er Re"$(rce"

1.0 Intro!"t#on

Ga(""" la+ e6%re""e" t&e relati$! et+ee! a! electric c&are a!# t&e electric'iel# t&at it "et" (%* It i" a c$!"e(e!ce $' C$(l$m" la+* Alt&$(& itc$!tai!" !$ a##iti$!al i!'$rmati$!, it" mat&ematical '$rm e!ale" (" t$ "$l)ema!y %r$lem" $' electric 'iel# calc(lati$! 'ar m$re c$!)e!ie!tly t&a!t&r$(& t&e ("e $' C$(l$m" la+*

I! (!it 1, y$( lear!t t&at electric 'iel# at a!y %$i!t i" i)e! y t&e '$rcee6%erie!ce y a (!it %$"iti)e c&are %lace# at t&at %$i!t* I! t&i" (!it, +e +ill#e)el$% t&e c$!ce%t $' 'l(6 $' a! electric 'iel# a!# t&e! arri)e at t&e Ga("""la+* Fe +ill al"$ "ee &$+ t&e a(""" la+ all$+" (" t$ calc(late t&e electric'iel# 'ar m$re ea"ily t&a! +e c$(l# ("i! C$(l$m" la+*

2.0 O-("t#()

A=t(r )t!4#n t%#) !n#t, 4o! B#'' ( &'( to:

relate t&e electric 'l(6 t&r$(& a!y "(r'ace t$8

0i t&e 'iel# "tre!t&

0ii t&e "(r'ace area

0iii t&e $rie!tati$! $' t&e "(r'ace relati)e t$ t&e 4iel#

+rite relati$! et+ee! t&e electric 'la6 a!# t&e c&are e!cl$"e# +it&i!t&e "(r'ace*

c$m%(te t&e electric 'l(6 t&r$(& a!y cl$"e# "(r'ace %lace# i! t&eelectric 'iel#*

("e Ga(""" la+ t$ c$m%(te electric 'iel#" i! t&e ca"e $' "%&erical,li!ear a!# %la!ar "ymmetry*

NOUN 2@


30/342


3.1 E'("tr#" ='!6

T&e !(mer $' t&e li!e" $' '$rce cr$""i! a!y "(r'ace #e%e!#" $! t&ree'act$r" J t&e 'iel# "tre!t&, E, t&e "(r'ace area, S a!# t&e $rie!tati$! $' t&e"(r'ace relati)e t$ t&e electric 'iel#*

S X

E

F#!r( 3.1

T$ "%eci'y t&e $rie!tati$! $' t&e "(r'ace, S +e #ra+ a %er%e!#ic(lar t$ t&e"(r'ace* I' i" t&e a!le et+ee! t&e electric 'iel# a!# t&e %er%e!#ic(lar a""&$+! i! 'i(re 3*1, t&e! t&e !(mer $' li!e" $' '$rce %a""i! t&r$(& t&e"(r'ace ra!e" 'r$m ma6im(m t$ mi!im(m #e%e!#i! $! * T&at i"

F&e! /< t&e !(mer $' li!e" $' '$rce cr$""i! t&e "(r'ace i" ma6im(m

F&e! @//, t&e !(mer $' li!e" $' '$rce cr$""i! t&e "(r'ace i" 7er$*

Fe ca! !$+ "ee t&at t&e !(mer $' li!e" $' '$rce cr$""i! a "(r'ace i"%r$%$rti$!al t$ t&e %r$9ecti$! $' t&e 'iel# $! t$ t&e %er%e!#ic(lar t$ t&e"(r'ace, i*e c$" 50N$te c$"// 1, c$" @// /*

P(tti! t$et&er (a!titie" $! +&ic& t&e !(mer $' li!e" $' '$rce #e%e!#"i)e" t&e relati$!"&i%* N(mer $' li!e" $' '$rce cr$""i! a "(r'ace ES c$" E * S J 3*1*

F&ere E i" t&e electric 'iel# )ect$r a!# S i" a )ect$r +&$"e ma!it(#e i"e(al t$ t&e area $' t&e "(r'ace a!# +&$"e #irecti$! i" t&at $' t&e

%er%e!#ic(lar t$ t&e "(r'ace*

T&e (a!tity $! t&e le't "i#e $' E* i" a! i!#e'i!ite !(mer eca("e +e ca!#ra+ a" ma!y li!e" $' '$rce a" +e li-e* .(t t&e (a!tity $! t&e ri&t &a!# "i#e$' t&e e(ati$! &a" a #e'i!ite )al(e* It i" calle# electric 'l(6* Let (" #e!$te it

y * He!ce

NOUN 3/


31/342


E* S 3*2

E* 3*2 "&$+" t&at t&e electric 'l(6 i" a Scalar, ei! t&e "calar %r$#(ct $' t+$)ect$r"* Si!ce E i" mea"(re# i! NC51, t&e (!it $' 'la6 i" Nm2C51

E6&*>'( 1

#" E

E #" E S #" S1

S2

F#!r( 3.2

4i(re 3*2 "&$+" a cl$"e# "(r'ace S i! t&e '$rm $' a cyli!#er $' ra#i(" R"it(ate# i! a (!i'$rm electric 'iel# 4, t&e a6i" $' t&e cyli!#er ei! %arallel t$t&e 'iel#* F&at i" t&e 'l(6 $' t&e electric 'iel# t&r$(& t&i" cl$"e# "(r'ace

So'!t#on

Fe ca! +rite t&e t$tal electric 'l(6 t&r$(& t&e "(r'ace S a" t&e "(m $' t&reeterm", a! i!teral $)er t&e "(r'ace, S1i*e t&e le't cyli!#er ca%* S2, t&e cyli!#er"(r'ace, a!# S3, t&e ri&t ca%* T&(" 'r$m E* 3*2, +e &a)e

= E. ds S

= E. ds + E .ds + E. ds S1 S2 S3

4$r t&e le't ca%, a!le '$r all %$i!t" i" 1?///, E i" c$!"ta!t, a!# all t&e)ect$r" #" are %arallel*

T&ere'$re, E * #" E 0c$" 1?// #" 5E#" 5 ER

2

S1

Si!ce t&e area $' t&e ca% i" R2*Similarly, '$r t&e ri&t &a!# ca%

NOUN 31


32/342


E* #" ER2 S3

Si!ce t&e a!le / '$r all %$i!t" $! t&e ca%*4i!ally, '$r t&e "(r'ace S2*

E*#" /S2

Si!ce t&e a!le @//'$r all %$i!t" $! t&e cyli!#rical "(r'ace*

Fe ca! !$+ "(m (% t&e t$tal 'l(6 t&r$(& t&e cyli!#rical "(r'ace S a"

5 ER2 / ER2 /

T&ere'$re, t&e t$tal $(t+ar# 'l(6 $' t&e electric 'iel# t&r$(& t&e cl$"e#

"(r'ace $' 'i(re 3*2 i" 7er$*

3.2 G&!))) L&B

I! "ecti$! 3*1, +e '$(!# t&at8

0i T&e !(mer $' li!e" $' '$rce cr$""i! a!y cl$"e# "(r'ace i"%r$%$rti$!al t$ t&e !et c&are e!cl$"e# y t&e "(r'ace

0ii T&e electric 'l(6 t&r$(& a!y cl$"e# "(r'ace i" %r$%$rti$!al t$ t&e

t$tal c&are e!cl$"e# y t&e "(r'ace*Fe ca! 0ii Mat&ematically a" '$ll$+"

e!cl$"e# 3*3Or E* #" e!cl$"e#**3*

E

#"

R

F#!r( 3.3

NOUN 32


33/342


T$ e)al(ate t&e %r$%$rti$!ality c$!"ta!t i! e(ati$! 3*3 $r 3*, let (" c$!"i#era %$"iti)e %$i!t c&are i! 'ree "%ace a!# a "%&erical "(r'ace $' ra#i(" Rce!tre# $! a" "&$+! i! 'i* 3*3* T&e 'la6 t&r$(& a!y "(r'ace i" i)e! ye(ati$!, i*e

E *#" E *#" c$" *3*;

F&ere i" t&e a!le et+ee! t&e #irecti$! $' t&e electric 'iel# a!# t&e$(t+ar# !$rmal t$ t&e "(r'ace*

N$+, t&e ma!it(#e $' t&e electric 'iel# at a #i"ta!ce R #(e t$ %$i!t c&are i" i)e! y

E 1

$ R2

T&e 'iel# %$i!t ra#ially $(t+ar# "$ t&at t&e electric 'iel# i" e)ery+&ere%arallel t$ t&e $(t+ar# !$rmal t$ t&e "(r'ace*

T&e! / a!# c$" 1* P(tti! t&e )al(e" $' E a!# c$"i! e(ati$! 3*;,t&e 'l(6 t&r$(& t&e "%&erical "(r'ace $' ra#i(" R ec$me"

1 #" 1 #"

"%&ere $ R2 $ R2N$te t&at t&e e6%re""i$! '$r t&e ma!it(#e $' t&e electric 'iel# &a" ee! ta-e!

$(t"i#e t&e i!teral "i! eca("e it &a" t&e "ame )al(e 0it i" c$!"ta!te)ery+&ere $! t&e "%&erical "(r'ace* T&e remai!i! i!teral i" 9("t t&e area"$' all i!'i!ite"imal eleme!t", #", $! t&e "%&ere* I! $t&er +$r#, t&e remai!i!i!teral i" t&e "(r'ace area $' t&e "%&ere, t&at i"

#" R2

T&e! t&e 'la6 ec$me"

1 R2 E$ *3*= 4o R2

C$m%ari! e!" 3* a!# 3*=, +e $"er)e t&at t&e %r$%$rti$!ality c$!"ta!t i"1$* He!ce +e &a)e

E* #" e!cl$"e# 3*> o

NOUN 33


34/342


E(ati$! 3*> i" -!$+! a" Ga(""" la+* It tell" (" t&at t&e electric 'la6 t&r$(&t&e "%&ere i" %r$%$rti$!al t$ t&e c&are a!# i" i!#e%e!#e!t $' t&e ra#i(" $' t&e"(r'ace*

3.3 A>>'#"&t#on o= G&!))) L&B

Ga(""" la+ a%%lie" t$ a!y &y%$t&etical cl$"e# "(r'ace 0calle# a Ga(""ia!"(r'ace a!# e!cl$"i! a c&are #i"tri(ti$!* H$+e)er, t&e e)al(ati$! $' t&e"(r'ace i!teral ec$me" "im%le $!ly +&e! t&e c&are #i"tri(ti$! &a""(''icie!t "ymmetry* I! "(c& "it(ati$!, Ga(""" la+ all$+" (" t$ calc(late t&eelectric 'iel# 'ar m$re ea"ily t&a! +e c$(l# ("i! C$(l$m" la+* Si!cea(""" la+ i" )ali# '$r a! aritrary cl$"e# "(r'ace, +e +ill ("e t&i" 'ree#$mt$ c&$$"e a "(r'ace &a)i! t&e "ame "ymmetry a" t&at $' t&e c&are#i"tri(ti$! t$ e)al(ate t&e "(r'ace i!teral* Fe "&all !$+ ill("trate t&e ("e $'Ga(""" la+ '$r "$me im%$rta!t "ymmetrie"*

3.3.1 S>%(r#"&' S4**(tr4

A c&are #i"tri(ti$! i" "%&erically "ymmetric i' t&e c&are #e!"ity 0t&at i",t&e c&are %er (!it )$l(me at a!y %$i!t #e%e!#" $!ly $! t&e #i"ta!ce $' t&e

%$i!t 'r$m a ce!tral %$i!t 0calle# ce!tre $' "ymmetry a!# !$t $! t&e#irecti$!*

F#!r( 3.+

4i(re 3* re%re"e!t" a "%&erically "ymmetric #i"tri(ti$! $' c&are "(c& t&att&e c&are #e!"ity i" &i& at t&e ce!tre a!# 7er$ ey$!# r* S%&erical"ymmetry $' c&are #i"tri(ti$! im%lie" t&at t&e ma!it(#e $' electric 'iel#

NOUN 3


35/342


al"$ #e%e!#" $! t&e #i"ta!ce r 'r$m t&e ce!tre $' "ymmetry* I! "(c& a"it(ati$!, t&e $!ly %$""ile #irecti$! $' t&e 'iel# c$!"i"te!t +it& t&e "ymmetryi" t&e re#ial #irecti$! J $(t+ar# '$r a %$"iti)e c&are 0'i 3* a!# i!+ar# '$ra !eati)e c&are* E6am%le $' "%&erically "ymmetric c&are #i"tri(ti$!" are8

0i a %$i!t c&are

0ii a (!i'$rmly c&are# "%&ere, a!#

0iii a (!i'$rmly c&are# t&i! "%&erical "&ell

E6&*>'( 1. U"e Ga(""" la+ t$ #eri)e t&e e6%re""i$! '$r t&e electric 'iel#$' a %$i!t c&are*

So'!t#on

r #"

F#!r( 3./

4i(re 3*; "&$+" a %$"iti)e %$i!t c&are * U"i! Ga(""" la+, let (" 'i!# $(tt&e electric 'iel# at a #i"ta!ce r 'r$m t&e c&are *

Dra+ a c$!ce!tric "%&erical G(a""" "(r'ace $' ra#i(" r* +e -!$+ 'r$m"ymmetry t&at E %$i!t" ra#ially $(t+ar#* I' +e #i)i#e t&e Ga(""ia! "(r'acei!t$ #i''ere!tial area" #", t&e! $t& E a!# #" +ill e at ri&t a!le" t$ t&e"(r'ace, t&e a!le et+ee! t&em ei! 7er$* T&(" t&e (a!tity E*#"

ec$me" "im%ly E#" a!# Ga(""" la+ ec$me"

$ E *#" E$ E#"

Si!ce E &a" t&e "ame ma!it(#e '$r all %$i!t" $! t&e Ga(""ia! "(r'ace , +eca! +rite

$ E * #" $ E#" $ #" *3*?

H$+e)er, t&e i!teral i! e(ati$! 3*? i" "im%ly t&e area $' t&e "%&erical"(r'ace, i*e r2 He!ce

NOUN 3;


36/342


$ E 0r2

Or E $r2 3*@

E(ati$! 3*@ i" c$(l$m" la+ i! t&e '$rm +e #eri)e# it i! (!it 1*

Fe ca! !$+ "ee t&at Ga(""" la+ a!# C$(l$m" la+ are !$t t+$i!#e%e!#e!t %&y"ical la+" (t t&e "ame la+ e6%re""e# i! #i''ere!t +ay"*

3.3.2 T%( E'("tr#" F#(' o= & S>%(r#"&' C%&r( D#)tr#!t#on

E1P1

P2 E2

F#!r( 3.

Let (" c$!"i#er a t$tal c&are : +&ic& " "%rea# (!i'$rmly t&r$(&$(t a"%&ere $' ra#i(" R a" "&$+! i" 'i(re 3*=* Fe +a!t t$ 'i!# t&e electric 'iel# at"$me %$i!t "(c& a" P1$(t"i#e t&e #i"tri(ti$! a!# at %$i!t P2 i!"i#e it*

0a 4$r %$i!t" $(t"i#e t&e c&are #i"tri(ti$!, let (" #ra+ a Ga(""ia!"(r'ace S1$' ra#i(" r, t&r$(& t&e %$i!t P1*

HoB o B( noB t&( &&nt&( o= t%( )>%(r#"&' )4**(tr4

An)B(r:.eca("e $' t&e "%&erical "ymmetry, t&e electric 'iel#i" t&e "ame at all %$i!t" $! t&e Ga(""ia! "(r'ace

$%&t #) t%( #r("t#on o= t%( ('("tr#" =#('

An)B(r: At a!y %$i!t $! t&e Ga(""ia! "(r'ace, t&e 'iel# i" ra#ically#irecte#, i*e %er%e!#ic(lar t$ t&e "(r'ace, "$t&at t&e a!le et+ee! t&e !$rmal t$ t&e "(r'ace a!# t&eelectric 'iel# #irecti$! i" 7er$* T&at i" c$" c$" / 1 0Hereit i" a""(me# t&at t&e "%&ere &a" a %$"iti)e c&are, i' t&ere i" a!et !eati)e c&are, t&e 'iel# +ill %$i!t ra#ially 0i!+ar#+&erey 1?/a!# c$" 51*

NOUN 3=


37/342


T&e! t&e 'l(6 t&r$(& t&e Ga(""ia! "%&ere S, ec$me"

E1* #"1, E1c$" #"1,

E1#"1 0"i!ce c$" 1

r21 E1 *3*1/

Si!ce#", i" 9("t t&e "(r'ace area $' t&e "%&ere S1, i*e*r2

A>>'4#n G&!))) '&B

r12E1 :E$ Si!ce t&e c&are e!cl$"e# +it&i! t&e "%&ere S1 i" :

E1 1 :E$ r12 3*11

E(ati$! 3*11 "&$+" t&at t&e 'iel# at all %$i!t" $! "(r'ace S1i" t&e "ame a" i'all t&e c&are" +it&i! t&e "(r'ace S1+ere c$!ce!trate# at t&e ce!tre*

0 4$r %$i!t" i!"i#e t&e c&are #i"tri(ti$!, t&e electric 'iel# #e%e!#" $!&$+ t&e c&are i" #i"tri(te#* T&i" i" eca("e a!y Ga(""ia! "%&ere+it& r '$r t&e 'l(6 "till &$l#"* H$+e)er, t&e c&aree!cl$"e# i" "$me 'racti$! $' :* T&e )$l(me $' t&e c&are "%&ere i" R3a!#it 3

c$!tai!" a t$tal c&are :* Si!ce t&e c&are i" "%rea#i! (!i'$rmly t&r$(&$(tt&e "%&ere, t&e )$l(me c&are #e!"ity i" c$!"ta!t a!# i" i)e! y*

:R3

3

NOUN 3>


38/342


T&ere'$re, t&e c&are e!cl$"e# y t&e "%&ere S2+ill e 9("t t&e )$l(me $'t&at "%&ere m(lti%lie# y t&e )$l(me c&are #e!"ity, t&at i"

e!cl$"e# r23 6 : : r23

3 R3 R3

A%%lyi! t&e Ga(""" la+ 0e!* 3*>, +e &a)er22 E2 : r22R3

S$ t&at

E2 1 : r2E$ R3 3*12

I''!)tr&t( B#t% & )(t"% t%( &r#&t#on o= t%( ('("tr#" =#(') ot% #n)#( &n

o!t)#( & )>%(r#"&' "%&r( #)tr#!t#on.

An)B(r:

'i * 3*>

E

R / R P

T&e electric 'iel# i!"i#e t&e #i"tri(ti$! i!crea"e" e!erally +it& #i"ta!ce'r$m t&e ce!tre 0E r* O! t&e $t&er &a!#, $(t"i#e t&e c&are #i"tri(ti$!,t&e electric 'iel# 'all" $'' a" 1r2 'i(re 3*> i" a "-etc& $' t&e 'iel#" i!"i#e a!#$(t"i#e t&e "%&ere*

NOUN 3?


39/342


3.3.3 L#n( S4**(tr4

A c&are #i"tri(ti$! &a" cyli!#rical "ymmetry +&e! it i" i!'i!ity l$! a!#&a" a c&are #e!"ity t&at #e%e!#" $!ly $! t&e %er%e!#ic(lar #i"ta!ce 'r$m a

li!e calle# "ymmetry a6i" 0"ee 'i* 3*?

r

G(""ia! S(r'ace

E

F#!r( 3.5

.y "ymmetry, t&e electric 'iel# +ill %$i!t ra#ially $(t+ar# 'r$m t&e a6i" a!#it" ma!it(#e +ill #e%e!# $!ly $! t&e %er%e!#ic(lar #i"ta!ce 'r$m t&e a6i"*0Fe a""(me %$"iti)e c&are, '$r !eati)e c&are t&e 'iel# %$i!t" i!+ar#* Let

(" 'i!# e6%re""i$! '$r t&e electric 'iel#, E at a #i"ta!ce r 'r$m t&e li!e c&are0"ay a +ire*

Fe #ra+ a Ga(""ia! "(r'ace +&ic& i" a circ(lar cyli!#rical $' ra#i(" r a!#le!t& l cl$"e# at eac& e!# y %la!e ca%" !$rmal t$ t&e a6i" a" "&$+! i!'i(re 3*?

T$ calc(late t&e 'l(6, y$( "&$(l# !$te t&at t&e electric 'iel# al"$ &a"cyli!#rical "ymmetry, +&ic& im%lie" t&at it" ma!it(#e at a %$i!t #e%e!#"$!ly $! t&e %er%e!#ic(lar #i"ta!ce $' t&e %$i!t '$rm t&e "ymmetry a6i", a!#it" #irecti$! &a" t$ e ra#ially $(t+ar#"*

T&e 'la6 t&r$(& t&e cyli!#rical "(r'ace i"

E *#" E#" E #" 2rlE **3*13

F&ere 2ri" t&e area $' t&e c(r)e# "(r'ace*

NOUN 3@


40/342


T&e 'la6 t&r$(& t&e e!# $' t&e cyli!#er i" 7er$ eca("e t&e 'iel# li!e" are%arallel t$ t&e %la!e ca%" $' t&e Ga(""ia! "(r'ace* Mat&ematically, E a!# #"are %er%e!#ic(lar, "$ t&at c$" / i! t&e "calar 0#$t %r$#(ct E* #"*T&ere'$re, t&e $!ly 'la6 i" t&r$(& t&e c(r)e# %art $' t&e cyli!#er* Ga("""la+ tell" (" t&at t&e 'la6 i" %r$%$rti$!al t$ t&e c&are e!cl$"e# +it&i! t&e

cyli!#rical Ga(""ia! "(r'ace, i*e*

2r E e!cl$"e# $

S$ t&at E e!cl$"e# 3*1 2$rl

I' t&e li!e c&are #e!"ity i" , t&e! t&e c&are e!cl$"e# y t&e Ga(""ia!cyli!#er $' le!t& l* He!ce e! 3*1 ec$me"

E e!cl$"e# l **3*1; 2 $r 2$rl 2$r

Fit& rear# t$ t&e electric 'iel# i!"i#e t&e +ire, +e "&all c$!"i#er t+$ ca"e"8

0i S(%%$"e t&e c&are i" #i"tri(te# (!i'$rmly +it&i! t&e +ire +it&c&are #e!"ity *

P E r

R

F#!r( 3.7 An (n'&r( #(B o= t%( B#r(

Let t&e ra#i(" $' t&e +ire e r* t$ 'i!# E at t&e i!!er %$i!t P1a #i"ta!ce r a%art'r$m t&e a6i" $' t&e +ire, +e #ra+ a Ga(""ia! "(r'ace 0i*e a cyli!#er $'ra#i(" r a!# le!t& %a""i! t&r$(& P a" "&$+! i! 'i(re 3*@* A" +e "a+earlier, t&e 'l(6 i" #(e t$ t&e c(r)e# "(r'ace $!ly* He!ce 'r$m Ga(""" la+*

NOUN /


41/342


E* #" 2rE 1E$

T&e c&are 1i!"i#e t&i" Ga(""ia! "(r'ace % r2

E 2 r r2 $

Or E r *3*1=2$

T&(" t&e electric 'iel# at a %$i!t i!"i#e a! i!'i!ite (!i'$rmly c&are# +ire i"ra#ially #irecte# a!# )arie" a" t&e #i"ta!ce 'r$m it" a6i"*

0ii F&e! t&e c&are i" $! t&e "(r'ace $' t&e +ire $r cyli!#er $!ly, t&e

electric 'iel# at a!y %$i!t i!"i#e it i" 7er$ eca("e t&e !et c&are i! t&eGa(""ia! "(r'ace t&r$(& t&i" %$i!t i" 7er$*

HoB o() t%( ('("tr#" =#(' !( to & "%&r( B#r( or "4'#n(r

(>(n on #t) r!)

An)B(r: E(ati$!" 3*1; a!# 3*1= "&$+ t&at electric 'iel# #(e t$a c&are# +ire $r cyli!#er #$e" !$t #e%e!# (%$! it"ra#i("* I! e''ect, t&e 'iel# e&a)e" a" i' t&e c&are $!t&e +ire $r cyli!#er +ere c$!ce!trate# i! a li!e al$!it" a6i"*

3.3.+ P'&n( S4**(tr4

F&e! t&e c&are #e!"ity #e%e!#" $!ly $! t&e %er%e!#ic(lar #i"ta!ce 'r$m a%la!e, t&e c&are #i"tri(ti$! i" "ai# t$ &a)e %la!e "ymmetry* T&e electric'iel# i" e)ery+&ere !$rmal t$ t&e %la!e "&eet a" "&$+! i! 'i(re 3*1/,

%$i!ti! $(t+ar#, i' %$"iti)ely c&are# a!# i!+ar#, i' !eati)ely c&are#*

)

r

)

r

NOUN 1


42/342


F# 3.10 A "%&r( #)tr#!t#on B#t% >'&n( S4**(tr4 )%oB#n ('("tr#"

=#('

T$ 'i!# t&e electric 'iel# at a #i"ta!ce i! 'r$!t $' t&e %la!e "&eet, it i" re(ire#

t$ c$!"tr(ct a Ga(""ia! "(r'ace* A c$!)e!ie!t Ga(""ia! "(r'ace i" a cl$"e#cyli!#er $' cr$""5"ecti$!al area S a!# le!t& 2r* T&e "i#e" $' t&e Ga(""ia!"(r'ace are %er%e!#ic(lar t$ t&e "ymmetry %la!e a!# t&e e!#" $' t&e "(r'aceare %arallel t$ it* Si!ce !$ li!e" $' '$rce cr$"" t&e "i#e", t&e 'l(6 t&r$(& t&e"i#e" i" 7er$* .(t t&e li!e" $' '$rce cr$"" %er%e!#ic(lar t$ t&e e!#", "$ t&at Ea!# t&e area eleme!t )ect$r #" $! t&e e!#" are %arallel* T&e c$" i! t&e

%r$#(ct E*#" i" 1 $)er $t& e!#" 051 i' c&are i" !eati)e* Si!ce t&e 'l(6t&r$(& t&e "i#e" i" 7er$, t&e t$tal 'l(6 t&r$(& $(r Ga(""ia! "(r'ace t&e!

ec$me"

Z E#" 2ES$t& e!#"

T&e 'act$r, 2 ari"e" eca("e t&ere are t+$ e!#"* T&e Ga(""" la+ i)e"

2 ES e!cl$"e# E$

I' i" t&e "(r'ace c&are #e!"ity, t&e! t&e c&are e!cl$"e# i" "*He!ce E 3*1>

2$+.0 Con"'!)#on

T&i" (!it i" a '$ll$+5(% $' t&e %re)i$(" (!it* I! %artic(lar, y$( &a)e !$+lear!t t$ a%%ly t&e Ga(""" la+ '$r t&e "$l(ti$! $' %r$lem" i!)$l)i! electricc&are" +it& li!ear "%&erical a!# %la!e "ymmetry* Y$( a%%reciate t&at t&e"$l(ti$! $' %r$lem" +it& t&e Ga(""" la+ i" !$t a" te#i$(" a" t&e ("e $'c$(l$m" la+* Al+ay" rememer t&at Ga(""" la+ a%%lie" t$ a cl$"e#"(r'ace, ("(ally re'erre# t$ a" a Ga(""ia! "(r'ace a!# e!cl$"i! a!y c&are#i"tri(ti$!* 4$r %r$lem" i!)$l)i! t&e a%%licati$! $' Ga(""" la+, c&$$"e a

"(r'ace &a)i! t&e "ame "ymmetry a" t&at $' t&e c&are #i"tri(ti$! t$e)al(ate t&e "(r'ace i!teral* H$+e)er +e !$te t&at (!li-e C$(l$m" la+ it"!$t "(''icie!t t$ #etermi!e t&e electric 'iel#" i! all ca"e"*

/.0 S!**&r4

NOUN 2


43/342


t&e !(mer $' li!e" $' '$rce cr$""i! a cl$"e# "(r'ace i" %r$%$rti$!alt$ t&e t$tal c&are e!cl$"e# y t&e "(r'ace*

t&e c$!ce%t $' electric 'l(6 (a!ti'ie" t&e !$ti$! Q!(mer $' li!e" $''$rce cr$""i! a "(r'ace t&e electric 'l(6, i" #e'i!e# a" t&e "(r'ace

i!teral $' t&e electric 'iel# E $)er a "(r'ace a" '$ll$+"8

E *#"

+&ere #" i" a! i!'i!ite"imal )ect$r +&$"e #irecti$! at a!y %$i!t i"t$+ar#" t&e $(t+ar# #ra+! !$rmal t$ t&e "(r'ace at t&at %$i!t, it"ma!it(#e ei! t&e area $' t&e "(r'ace*

Ga(""" la+ i" E *#" $

I! +&ic& i" t&e !et c&are i!"i#e a! imai!ary cl$"e# "(r'ace 0calle#a Ga(""ia! "(r'ace a!# $ i" %ermitti)ity $' 'ree "%ace* Ga(""" la+e6%re""e" a! im%$rta!t %r$%erty $' t&e electric 'iel#*

T&e electric 'iel# $(t"i#e a "%&erically "ymmetrical "&ell +it& ra#i(" ra!# t$tal c&are i" #irecte# ra#ially a!# &a" ma!it(#e

E 1 0 r > R $ r2

T&e c&are e&a)e" a" i' it +ere all c$!ce!trate# at t&e ce!tre $' t&e"%&ere*

T&e electric 'iel# #(e t$ a! i!'i!ite li!e $' c&are +it& (!i'$rm c&are%er (!it le!t&, , i" a #irecti$! %er%e!#ic(lar t$ t&e li!e $' c&area!# &a" ma!it(#e

E 2 $r

T&e electric 'iel# #(e t$ a! i!'i!ite "&eet $' c&are i" %er%e!#ic(lar t$t&e %la!e $' t&e "&eet a!# &a" ma!it(#e*

E 2$F&ere i" t&e "(r'ace c&are #e!"ity*


NOUN 3


44/342


1* T&e electric 'iel# i! a certai! "%ace i" i)e! y E 2// r* H$+ m(c&'l(6 %a""e" t&r$(& a! area A i' it i" a %$rti$! $'

0a T&e 6y J %la!e

0 T&e 67 J %la!e

0c T&e y7 J %la!e

2* A 'lat "&eet $' area ;/cm2 carrie" a (!i'$rm "(r'ace c&are #e!"ity *A! electr$! 1*;cm a %$i!t !ear t&e ce!ter $' t&e "&eet e6%erie!ce a'$rce $' 1*?61/512N #irecte# a+ay 'r$m t&e "&eet* 4i!# t&e t$tal c&are$! t&e "&eet*

3* S(%%$"e t&at a %$"iti)e c&are i" (!i'$rmly #i"tri(te# t&r$(&$(t a

"%&erical )$l(me $' ra#i(" R, t&e c&are %er (!it )$l(me ei! e*0a U"e Ga(""" la+ t$ %r$)e t&at t&e electric 'iel# i!"i#e t&e

)$l(me a!# at a #i"ta!ce r 'r$m t&e ce!tre, i"E er

3$

0 F&at i" t&e electric 'iel# at a %$i!t $(t"i#e t&e "%&erical)$l(me at a #i"ta!ce r 'r$m t&e ce!tre E6%re"" y$(r a!"+eri! term" $' t&e t$tal c&are +it&i! t&e "%&erical )$l(me*

0c C$m%are y$(r a!"+er t$ 0a a!# 0 +&e! r R*

0# S-etc& a ra%& $' t&e ma!it(#e $' E a" a '(!cti$! $' r, 'r$m r $ t$ r 3R*

.0 R(=(r(n"( An Ot%(r R()o!r"()

C$llee P&y"ic"* Sear" 4*F, ema!"-y M*F a!# Y$(! H*D*A##i"$!5Fe"ley %(li"&i! C$m%a!y, L$!#$!* 1@>;

Electr$"tatic i! 4ree S%ace* I!#ira G&a!#i O%e! U!i)er"ity* PHE 5/>, 2//1

P&y"ic"* A te6t$$- '$r A#)a!ce# Le)el St(#e!t"* T$m D(!ca!B$&! M(rray 0P(li"&er" Lt#* L$!#$!* 1@?2

NOUN


45/342


ELECTRIC POTENTIAL

T&'( O= Cont(nt

NOUN ;

UNIT 3


46/342


1*/2*/3*13*23*3

3*3*;3*=*/;*/=*/>*/

I!tr$#(cti$!O9ecti)e"E(i%$te!tial S(r'aceP$te!tial #(e t$ a P$i!t C&areP$te!tial #(e t$ a Sy"tem $' C&are

P$te!tial Di''ere!ceRelati$! .et+ee! Electric 4iel# a!# Electric P$te!tialElectric 4iel# a!# P$te!tial $' a! Electric Di%$leC$!cl("i$!"S(mmaryT(t$r Mar-e# A""i!me!tRe'ere!ce" A!# Ot&er Re"$(rce"

1.0 Intro!"t#on

Y$( +ill recall 'r$m y$(r "t(#y $' PHY 1/1* Eleme!tary mec&a!ic" t&at+$r- i"I #$!e +&e! t&e %$i!t $' a%%licati$! $' a '$rce (!#er$e" a#i"%laceme!t i! it" $+! #irecti$!* I' a $#y A e6ert" a '$rce $! a!$t&er $#y. a!# +$r- i" #$!e, a tra!"'er $' e!ery $cc(r" +&ic& i" mea"(re# y t&e+$r- #$!e* 4$r e6am%le, i' +e li't a ma"", m t&r$(& a )ertical &ei&t, &, t&e+$r- #$!e, F y t&e '$rce +e a%%ly i" F m&* T&e e!ery tra!"'er i" m&a!# +e c$!"i#er t&at t&e "y"tem ai!" a!# "t$re t&at am$(!t $' ra)itati$!al

%$te!tial e!ery +&ic& i" $tai!e# 'r$m t&e c$!)er"i$! $' c&emical e!eryy $(r m("c(lar acti)ity* F&e! t&e ma"" 'all", t&e "y"tem l$"e" ra)itati$!al%$te!tial e!ery, a!#, !electi! air re"i"ta!ce, t&ere i" a tra!"'er $' -i!etic

e!ery t$ t&e ma"" e(al t$ t&e +$r- #$!e y ra)ity*T&e mea!i! $' electric %$te!tial ca! e ill("trate# y t&e a$)e a!al$y'r$m a"ic mec&a!ic"* A $#y +&e! rai"e# a$)e t&e eart&" "(r'ace i" "ai#t$ ac(ire %$te!tial e!ery eca("e it ca! #$ +$r- i! 'alli!* I' it i" 'ree t$m$)e i! a ra)itati$!al 'iel# it +ill 'all t$ t&e %$"iti$! i! +&ic& it" %$te!tiale!ery i" 7er$* Similarly, a c&are# $#y i! a! electric 'iel# &a" %$te!tiale!ery, a!# it +ill te!# t$ m$)e t$ t&$"e %art" $' t&e 'iel# +&ere it" %$te!tiale!ery i" "maller* F&e! a %$"iti)e c&are i" re%elle# y a!$t&er %$"iti)elyc&are# $#y a!# m$)e" a+ay, it" %$te!tial e!ery #ecrea"e"* It +ill e 7er$+&e! it i" c$m%letely a+ay 'r$m t&e i!'l(e!ce $' t&e c&are# $#y, t&at i" at

i!'i!ity* Fe "elect a" t&e 7er$ $' electric %$te!tial t&e %$te!tial at a! i!'i!ite#i"ta!ce 'r$m a!y electric c&are"*

D(=#n#t#on o= E'("tr#" Pot(nt#&'

NOUN =


47/342


T&e electric %$te!tial at a %$i!t i! a 'iel# ca! e #e'i!e# a" t&e +$r- #$!e %er(!it c&are m$)i! 'r$m i!'i!ity t$ t&e %$i!t*

Y$( "&$(l# !$te t&at +e are al+ay" a""(mi! t&at t&e c&are #$e" !$t a''ectt&e 'iel# i! a!y +ay*

T&e c&$ice $' t&e 7er$ $' %$te!tial i" %(rely aritrary a!# +&il"t i!'i!ity maye a 'e+ &(!#re# metre" i! "$me ca"e", i! at$mic %&y"ic" +&ere #i"ta!ce" $'1/51/m are i!)$l)e#, it !ee# $!ly e a )ery "mall #i"ta!ce a+ay 'r$m t&ec&are re"%$!"ile '$r t&e 'iel#*

Electric %$te!tial i" a %r$%erty $' a %$i!t i! a 'iel# a!# i" a "calar "i!ce it#eal" +it& a (a!tity $' +$r- #$!e $r %$te!tial e!ery %er (!it c&are* T&e"ym$l '$r %$te!tial i" [ a!# t&e (!it a 9$(le %er c$(l$m 0BC51 $r )$lt" 0[*

2.0 O-("t#()

A=t(r )t!4#n t%#) !n#t, 4o! B#'' ( &'( to:

C$m%(te t&e +$r- #$!e i! ta-i! a c&are 'r$m $!e %$i!t t$a!$t&er i! a! electric 'iel#*

C$m%(te t&e electric %$te!tial at a %$i!t #(e t$ a "i!le c&are

Relate t&e electric %$te!tial a!# electric 'iel#, a!# t&erey c$m%(tet&e electric 'iel# at a %$i!t -!$+i! t&e electric %$te!tial*

C$m%(te t&e electric %$te!tial at a %$i!t #(e t$ a #i%$le a!# a(a#r(%$le

3.1 E!#>ot(nt#&' S!r=&"()

All %$i!t i! a 'iel# +&ic& &a)e t&e "ame %$te!tial ca! e imai!e# a" lyi! $!a "(r'ace, calle# a! e(i%$te!tial "(r'ace* F&e! a c&are m$)e" $! "(c& a"(r'ace !$ e!ery c&a!e $cc(r" a!# !$ +$r- i" #$!e* T&e '$rce #(e t&e 'iel#m("t t&ere'$re act at ri&t a!le" t$ t&e e(i%$te!tial "(r'ace at a!y %$i!t*T&ere'$re, e(i%$te!tial "(r'ace" a!# 'iel# li!e" al+ay" i!ter"t at ri&t a!le"*

NOUN >


48/342


4iel# li!e E(i%eteateal S(r'ace

F#!r( 3.1 E!#>ot(nt#&' )!r=&"( =or & >o#nt "%&r(

Fe ca! !$+ "ee t&at a" electric 'iel# ca! t&ere'$re e re%re"e!te# %ict$riallyy 'iel# li!e" a!# y e(i%$te!tial "(r'ace 0$r li!e" i! t+$ #ime!"i$!al#iaram"*

4i(re 3*1 "&$+" t&e e(i%$te!tial "(r'ace" '$r a %$i!t c&are* T&e"e arec$!ce!tric "%&ere" 0circle" i! t+$ #ime!"i$!"*

I' e(i%$te!tial are #ra+! "$ t&at t&e c&a!e $' %$te!tial 'r$m $!e t$ t&e !e6ti" c$!"ta!t, t&e! t&e "%aci! +ill e cl$"er +&ere t&e 'iel# i" "tr$!er* T&i"'$ll$+" 'r$m t&e 'act t&at i! $r#er t$ %er'$rm a certai! am$(!t $' +$r- i!"(c& rei$!" a "&$rter #i"ta!ce !ee# e tra)elle#*

3.2 Pot(nt#&' !( to & >o#nt "%&r(

:$: A . C r

\6

6

'i* 3*2

Fe +i"& t$ 'i!# t&e %$te!tial at %$i!t A i! t&e 'iel# $' a! i"$late# %$i!tc&are : "it(ate# at %$i!t /, "(c& t&at / A r a" "&$+! i! 'i* 3*2*

Let (" imai!e a )ery "mall %$i!t c&are :$i" m$)e# y a! e6ter!al ae!t'r$m C #i"ta!ce 6 'r$m A, t&r$(& a )ery "mall #i"ta!ce 6 t$ . +it&$(ta''ecti! t&e 'iel# #(e t$ :*

A""(mi! t&e '$rce 4 $! :$ #(e t$ t&e 'iel# remai!" c$!"ta!t $)er, 6, t&e+$r- F y t&e e6ter!al ae!t $)er 6 aai!"t t&e '$rce $' t&e 'iel# i"

NOUN ?


49/342


F 4 056 *3*1

D$ y$( -!$+ +&y +e &a)e t$ i!"ert t&e !eati)e "i! '$r 6 T&i" i" t$ ta-eacc$(!t $' t&e 'act t&at t&e #i"%laceme!t 6 i" i! t&e $%%$"ite #irecti$! t$ t&ati! +&ic& 4 act"*

A%%lyi! c$(l$m" la+*

4 : :$ ] 1$ 62

F : :$ ] 056$ 62

T&e t$tal +$r- #$!e, F i! ri!i! :$ 'r$m i!'i!ite :$ 'r$m i!'i!ity t$ A i"

F 5: :$ r #6 5 : :$ 516r $ 62 $

: :$ 3*2

3.3 Pot(nt#&' !( to & )4)t(* o= "%&r()

Let (" !$+ c$!"i#er a "y"tem $' c&are"* Li-e i! t&e %re)i$(" ca"e $' electric'iel# +e "&all 'i!# t&e "(%er%$"iti$! %ri!ci%le )ery ("e'(l* T&at i", t&e t$tal

%$te!tial, [%at a %$i!t P #(e t$ a "y"tem $' c&are" 1, 2, **,Ni" e(alt$ t&e "(m $' t&e %$te!tial" #(e t$ t&e i!#i)i#(al c&are" at t&at %$i!t*

I' 1, 2, *N are t&e #i"ta!ce" $' t&e c&are" 1, 2, * Nre"%ecti)ely 'r$m t&e %$i!t P, t&e %$te!tial at t&at %$i!t i"

% 1 2 * N 3* $1 $2 $NY$( +ill !$te i! e* 3* t&at eac& c&are i" acti! a" i' !$ $t&er c&are i"

%re"e!t*

T&e %$te!tial at %$i!t P* may e +ritte! i! a "(mmati$! '$rm a"

% 1 N iri 3*;$

i 1

E6&*>'( 1

NOUN @


50/342


T&e '$ll$+i! %$i!t c&are" are %lace# $! t&e 6 5 a6i"8 2 c at 6 2/cm,53c at 6 3/cm, 5c at 6 /cm* 4i!# t&e %$te!tial $! t&e 6 J a6i" at t&e$rii!*

So'!t#on

Fe -!$+ t&at %$te!tial i" a "calar (a!tity* U"i! t&e "(%er%$"iti$! %ri!ci%le,t&e %$te!tial at t&e $rii! 06 / i" i)e! y

$ 1 3 iri$

I 1O! "("tit(ti! t&e !(merical )al(e" $' ia!#i, +e $tai!

[$ @ 6 1/@Nm2C52 2 6 1/5= C 5 3 6 1/ 5= C 5 6 1/5= C/*2/m /*3/m /*/m

@ 6 1/@Nm2C52 1/;Cm51J 1/5;Cm 51J 1/5; Cm51

5@ 6 1/Nm C51

5@ 6 1/[

3.+ Pot(nt#&' D#==(r(n"(

Let (" +rite #$+! t&e am$(!t $' +$r- #$!e i! ri!i! a (!it %$"iti)e c&are'r$m i!'i!ity, 'ir"t t$ %$i!t A a!# t&e! t$ %$i!t ., "&$+! i! 'i(re 3*3*Rememer t&at %$i!t A a!# . are +it&i! t&e 'iel# $' c&are *

YA A

Y. .

NOUN ;/


51/342


F#. 3.3

U"i! e(ati$! 3*3, t&e %$te!tial" at %$i!t A a!# . are

[A $A

A!# [. $.

T&e #i''ere!ce $' t&e"e t+$ %$te!tial" 0i*e [.J [A i" t&e +$r- #$!e i! ta-i!a (!it c&are 'r$m A t$ ., a!# it i" calle# t&e %$te!tial #i''ere!ce t&e t+$

%$i!t" . a!# A* it i" +ritte! a"

[.A [.J[A 1 5 1 **3*= . A

Fe $"er)e t&at t&e +$r- #$!e i" carryi! t&e c&are i! a! electric 'iel# i"i!#e%e!#e!t $' %at&* It i" 9("t t&i" %at& i!#e%e!#e!ce t&at e!ale" (" t$ #e'i!et&e c$!ce%t $' %$te!tial*

.y t&e +ay, y$( "&$(l# !$te t&at i', i!"tea# $' t&e (!it %$"iti)e c&are, +etra!"%$rt a c&are 1et+ee! A a!# ., t&e! t&e +$r- F #$!e i" i)e! y8

F 1

[.A 1

0 [.J [A *3*>

O! a 'i!al !$te, I +a!t y$( t$ ear i! mi!# t&at t&e %$te!tial #i''ere!ce 0%*#*'$r "&$rt i" a )ery im%$rta!ce c$!ce%t i! t&e 'iel# $' electr$"tatic" a!#c(rre!t electricity* It" -!$+le#e &el%" (" t$ #etermi!e t&e e6act )al(e $' t&ec(rre!t +&ic& 'l$+" et+ee! a!y t+$ %$i!t" i! a! electric circ(it, %r$)i#e#t&e re"i"ta!ce et+ee! t&e t+$ %$i!t" i" -!$+! * Fe "&all "ee t&i" later i! t&i"c$(r"e 0m$#(le 3

3./ R('&t#on (tB((n E'("tr#" F#(' &n E'("tr#" Pot(nt#&'

A . E E

/ c&are :6 6

4i 3*

NOUN ;1


52/342


Let (" c$!"i#er a c&are : at a %$i!t A i! a! electric 'iel# +&ere t&e 'iel#"tre!t& i" E* T&i" c$!'i(rati$! i" ill("trate# i! 'i(re 3*

T&e '$rce, 4 $! : i" i)e! y

4 E:

I' : m$)e" a )ery "&$rt #i"ta!ce 6 'r$m A t$ . i! t&e #irecti$! $' E, t&e!t&e +$r- #$!e F y t&e electric '$rce $! i"

F '$rce 6 #i"ta!ce 46 E:6 0a""(mi! E i" c$!"ta!t $)er A.

I' t&e %*# et+ee! . a!# A i" [, +e &a)e y t&e #e'i!iti$! $' %*#*

[ +$r- #$!e %er (!it c&are F 5 E: 6

: :T&at i" [ 5E6

T&e !eati)e "i! i" i!"erte# t$ "&$+ t&at i' #i"%laceme!t" i! t&e #irecti$! $'E are ta-e! t$ e %$"iti)e, t&e! +&e! 6 i" %$"iti)e, [ i" !eati)e, i*e t&e

%$te!tial #ecrea"e"*

I! t&e limit, a" 6 5555/1E ec$me" t&e 'iel# "tre!t& at a %$i!t 0A* I!calc(l(" !$tati$!

E Lim [ #)6555/ 6 #6

#)#6 i" calle# t&e %$te!tial ra#ie!t i! t&e #irecti$! a!# "$ t&e 'iel# "tre!t&at a %$i!t e(al" t&e !eati)e $' t&e %$te!tial ra#ie!t t&ere*

?!()t#on: I" %$te!tial ra#ie!t a )ect$r $r a "calar

An)B(r: Y$( !$tice t&at %$te!tial ra#ie!t i!)$l)e" #i"%laceme!t *T&ere'$re, it i" a )ect$r*

It i" mea"(re# i! )$lt" %er metre 0[m51* T&e [m51a!# NC51are $t& (!it" $'E, (t t&e [m51i" t&e $!e t&at i" c$mm$!ly ("e#*

NOUN ;2


53/342


I' t&e electric 'iel# E i" (!i'$rm, t&at i" it i" c$!"ta!t i! ma!it(#e a!##irecti$! at all %$i!t", it '$ll$+" t&at

#) i" c$!"ta!t i*e #) 5E *3*?#6 #6

[ E6 E 5) *3*@ 6

i! $t&er +$r#", t&e %$te!tial c&a!e" "tea#ily +it& #i"ta!ce 0Recall t&e ca"e$' #"#t c$!"ta!t, '$r (!i'$rm )el$city

E6&*>'( 2

?!()t#on: T+$ lare &$ri7$!tal, %arallel metal %late" are 2*/cm a%art i!air a!# t&e (%%er i" mai!tai!e# at a %$"iti)e %$te!tial relati)et$ t&e l$+er "$ t&at 'iel# "tre!t& et+ee! t&em i" 2*; 6 1/ ;

[m51*

0a F&at i" t&e %*#* et+ee! t&e %late"

0 I' a! electr$! $' c&are 1*= 6 1/51@C a!# ma"" @*1 61/531- i" lierate# 'r$m re"t at t&e l$+er %late", +&at i" it" "%ee# $!reac&i! t&e (%%er %late

So'!t#on

0a I' E i" t&e 'iel# "tre!t& 0a""(me# (!i'$rm a!# [ i" t&e %*#* et+ee!t&e %late" +&ic& are at a #i"ta!ce # a%art, +e &a)e 0'r$m e(ati$! 3*@

[ E# 02*; 6 1/; [m51 6 02*/ 6 1/52m ;*/ 6 1/3)$lt"

0 T&e e!ery c&a!e 0i*e +$r- #$!e F +&ic& $cc(r" +&e! a c&are: m$)e" t&r$(& a %*# $' [ )$lt" i! a! electric 'iel# i" i)e! y

F :[

T&ere i" a tra!"'er $' electrical %$te!tial e!ery 'r$m t&e 'iel# t$ -*e* $' t&eelectr$!, He!ce +e &a)e

:[ ^ m)2

+&ere ) i" t&e re(ire# "%ee# a!# m i" t&e ma"" $' t&e electr$!

NOUN ;3


54/342


T&ere'$re, ^ m)2 :[

[ 2) m

i*e ) 261=61/51@ C 6 0;*/ 6 1/3 [0@*1 6 1/531-

2 6 1*= 6 1/51@ 6 ;*/ 6 1/3 C BC51

@*1 6 1/531 -

0I[ 1 BC51

1= 6 1/1;m2;52

@*1

0I B INm 1 -m S52m

*2 6 1/1m"51

3. E'("tr#" F#(' &n Pot(nt#&' o= &n E'("tr#" D#>o'(

A %air $' e(al a!# $%%$"ite c&are, , "e%arate# y a )ect$r #i"ta!ce a i"calle# a #i%$le* 0"ee 'i(re 3*;* T&e )ect$r a, +&ic& i" al"$ al$! t&e a6i" $'t&e #i%$le, i" #ra+! 'r$m t&e !eati)e t$ t&e %$"iti)e c&are*

A m$lec(le c$!"i"ti! $' a %$"iti)e a!# !eati)e i$! i" a! e6am%le $' a!

electric #i%$le i! !at(re* A! at$m c$!"i"t" $' e(al am$(!t $' %$"iti)e a!#!eati)e c&are" +&$"e ce!tre c$i!ci#e, &e!ce a! at$m i" !e(tral '$r all%$i!t" $(t"i#e it* H$+e)er, i! t&e %re"e!ce $' a! e6ter!al electric 'iel#, t&ece!tre" $' %$"iti)e a!# !eati)e c&are" et "e%arate#* T&e at$m t&e!

ec$me" a #i%$le*

A" +e "&all "ee i! m$#(le 2, t&e electric 'iel# a!# %$te!tial i! t&e )ici!ity $'a #i%$le '$rm" t&e 'ir"t "te% i! (!#er"ta!#i! t&e e&a)i$(r $' #ielectric"(!#er t&e i!'l(e!ce $' a! e6ter!al electric 'iel#*

3..1 E'("tr#" F#(' &t & >o#nt P &'on t%( &6#) o= t%( #>o'(

5 a

c PA .

Y

'i(re 3*;8 Electric #i%$le A. +it& ce!tre C a!# a6i" a *

NOUN ;


55/342


T&e %$i!t P i" al$! t&e a6i"*

Let t&e #i"ta!ce et+ee! t&e mi#5%$i!t $' t&e #i%$le a!# t&e %$i!t +&ic& i"al$! a6i" e e(al t$ r* Fe "&all e)al(ate t&e electric 'iel# at P*

T&e electric 'iel# at P #(e t$ * i" i)e! y

r $ 0r5a22

i" a (!it )ect$r i! t&e #irecti$! C%*

A!# t&at #(e t$ J i"

E 5 r

$ 0r

a

2

2

T&e re"(lta!t 'iel# at P i"

E E E5 r 1 5 1

rJa 2 ra 2

2 2

02a r r $ r25a2 2

E 2 P r '$r r __ a 3*1/

$r3

F&ere % a r **3*11

Y$( +ill !$tice t&at, i! t&e #e!$mi!at$r, +e &a)e !electe# a2 a" c$m%are#t$ r2, "i!ce a ``r i" act(al %&y"ical %r$lem"* I! e(ati$! 3*1/, ar &a" ee!re%lace# y t&e )ect$r (a!tity P, +&ic& i" -!$+! a" t&e #i%$le m$me!t* It+ill e $' i!tere"t '$r y$( t$ -!$+ t&at i! at$mic a!# m$lec(lar #i%$le, a

1/51/

m a!# r __a*

3..2 Pot(nt#&' !( to & #>o'(

Let (" e)al(ate t&e %$te!tial [% at P, a #i"ta!ce r 'r$m t&e mi#5%$i!t C $' t&e#i%$le* 0"ee 'i(re 3*=* t&e li!e 9$i!i! P t$ C ma-e" a! a!le +it& t&e#i%$le a6i", a *

NOUN ;;


56/342


T&e #i"ta!ce" $' P 'r$m J a!# are AP a!# .P re"%ecti)ely* 4r$m t&ee$metry, y$( +ill !$tice t&at

.P SP PC J CS r J a 2 c$"

A!# AP TP TC CP r a 2 c$"R

r

"

5 a A C .

T

He!ce t&e %$te!tial at P i" e(al t$

[% 1 1 E$ 0 r J a2c$" 0r a2 c$"

a c$" E$ 0r2J a2 c$"2

F&e! P i" 'ar a+ay, r2i" lare c$m%are# t$ a2 c$"2a!# !electi! a2c$"2i! t&e #e!$mi!at$r, +e ca! +rite

[% % * r Pc$" **3*12$r2 $r2

/ +&e! 2 0 P lie" $! t&e %er%e!#ic(lar i"ect$r

NOUN ;=


57/342


#i%$le a6i"

$( "&n "on"'!( =ro* (!&t#on 3.10 &n 3.12 t%&t:

0i T&e #i%$le %$te!tial )arie" a" 1r2a!# t&e 'iel# a" 1r3 a" c$m%are# t$ a

%$i!t c&are '$r +&ic& t&e %$te!tial )arie" a" 1ra!# t&e 'iel# a" 1r2*T&(" t&e %$te!tial a!# 'iel# #ecrea"e m$re ra%i#ly +it& r a #i%$le t&a!'$r a %$i!t c&are*

0ii T&e #i%$le %$te!tial )a!i"&e" $! %$i!t" +&ic& lie $! t&e %er%e!#ic(lari"ect$r $' t&e #i%$le a6i"* He!ce !$ +$r- i" #$!e i! m$)i! a te"tc&are al$! t&e %er%e!#ic(lar i"ect$r*

+.0 Con"'!)#on

I! t&i" (!it, y$( &a)e lear!t t$ c$m%(te t&e electr$"tatic %$te!tial $' a c&are#i"tri(ti$!* Y$( &a)e "ee! t&at i' y$( 'ir"t #eri)e t&e e6%re""i$! '$r t&e

%$te!tial, ei! a "calar (a!tity, it 'acilitate" t&e #eri)ati$! $' t&e e6%re""i$!'$r t&e electric 'iel# at a %$i!t* T&e c$!ce%t $' %$te!tial i" al"$ im%$rta!t

eca("e electric %$te!tial i" l$$"ely li!-e# t$ t&e +$r- #$!e y t&e electricc&are* 4$r t&e c$m%(tati$! $' t&e t$tal %$te!tial #(e t$ a "y"tem $' c&are",+e &a)e aai! '$(!# t&e "(%er%$"iti$! %ri!ci%le )ery &a!#y* Fe &a)ec$m%(te# t&e electric 'iel# a!# %$te!tial $' a #i%$le a!# y$( &a)e ee!a#)i"e# t&at t&i" i!tr$#(cti$! t$ t&e electric 'iel# $' a #i%$le +ill 'acilitatey$(r (!#er"ta!#i! $' t&e e&a)i$(r $' #ielectric" (!#er t&e i!'l(e!ce $' a!e6ter!al electric 'iel#* Y$( +ill "ee t&i" i! m$#(le 2*

/.0 S!**&r4

T&e +$r- #$!e i! ta-i! a (!it %$"iti)e c&are 'r$m $!e %$i!t t$a!$t&er i! electric 'iel# i" i!#e%e!#e!t $' t&e %at& c&$"e! et+ee! t&et+$ %$i!t"

T&e %$te!tial at a %$i!t i" t&e +$r- #$!e i! carryi! a (!it %$"iti)ec&are 'r$m i!'i!ity t$ t&e %$i!t aai!"t t&e electric 'iel#*

T&e %$te!tial rat a #i"ta!ce r 'r$m a %$i!t c&are i" i)e! y

r $r

T&e %$te!tial #i''ere!ce .Aet+ee! t+$ %$i!t . a!# A i" e(al t$t&e +$r- #$!e i! ta-i! a (!it %$"iti)e c&are 'r$m A t$ .* i' a c&are i" ta-e! 'r$m A t$ ., t&e! t&e +$r- #$!e i" *

F .A 0.J A

NOUN ;>


58/342


T&e (!it $' %$te!tial #i''ere!ce i" t&e )$lt* T&e %$te!tial #i''ere!ceet+ee! %$i!t A a!# . i" 1 )$lt +&e! t&e +$r- #$!e i! carryi! (!it%$"iti)e c&are et+ee! t&e t+$ %$i!t" i" e(al t$ 1 9$(le*

T&e electric 'iel# $' a #i%$le at a %$i!t al$! t&e a6i" $' t&e #i%$le i"

i)e! y

E 2P E$r3 '$r r __a

At a %$i!t $! t&e %er%e!#ic(lar i"ect$r $' t&e #i%$le a6i", t&e electric'iel# i"

E 5% $r3 '$r r __a

F&ere r i" t&e #i"ta!ce $' t&e %$i!t 'r$m t&e ce!tre $' t&e #i%$le a!# Pi" t&e #i%$le m$me!t


1* 4i!# t&e electric %$te!tial at %$i!t A a!# ., #(e t$ t+$ "mall "%&ere Ka!# Y, 1*/m a%art i! air a!# carryi! c&are" $' 2*/ 6 1/5?C a!# 52*/ 61/5? C re"%ecti)ely* A""(me t&e %ermitti)ity $' air $ a!# 1$ @*/6 1/@Nm2C52* 0"ee 'i(re 3*>

.

1*/m 1*/m

A 1*/m K 1*/m Y

2* 4i!# t&e %$te!tial at t+$ %$i!t" A a!# . at #i"ta!ce" 1/cm a!# ;/cm'r$m a c&are $' 2c $! "&$+! i! 'i(re 3*?* Al"$ 'i!# t&e +$r-!ee#e# t$ e #$!e i! ri!i! a c&are $' /*/;c 'r$m . t$ A*

2c A /*/;c .

4i* 3*?1/cm

;/ cm

NOUN ;?


59/342


3* C$m%(te t&e %$te!tial #i''ere!ce et+ee! %$i!t" A a!# . a""(mi!t&at a te"t c&are $(" m$)e# +it&$(t accelerati$! 'r$m A t$ . al$!t&e %at& "&$+! i! 'i(re 3*@

. C

# ;

A E

.0 R(=(r(n"() &n ot%(r R()o!r"()

A! I!tr$#(cti$! t$ Hi&er Sec$!#ary * P&y"ic"* B* M* Da" SarmaM$#er! .$$- Ae!cy Pri)ate Lt#* Calc(tta 1@>?

Electr$"tatic" i! 4ree S%ace* I!#ira Ga!#&i O%e! U!i)er"ity* PHE5/>2//1

A Sec$!# C$(r"e $' Electricity* A* E* E* Mce!7ie

T&e U!i)er"ity Pre""* Camri#e 1@>3

POTENTIAL FOR CONTINOUS CHARGE DISTRIUTION

AND ENERGY

T&'( o= Cont(nt)

NOUN ;@

UNIT +


60/342


1*/2*/3*13*1*1

3*23*33*3*;*/;*/=*/>*/

I!tr$#(cti$!O9ecti)e"Li!e c&areT&e E(i%me!t S(r'ace $' a U!i'$rm Li!e C&are

C&are# Circ(lar Di"cElectr$"tatic P$te!tial e!ery

Nat(re $' Electr$"tatic 4$rceMet&$# $' Imae"C$!cl("i$!S(mmaryT(t$r Mar-e# A""i!me!tRe'ere!ce" a!# Ot&er Re"$(rce"

1.0 Intro!"t#on

I! t&e %re)i$(" (!it", +e &a)e #i"c(""e# t&e electric 'iel#, E a!# t&e %$te!tial,#(e t$ #i"crete c&are #i"tri(ti$!"* I! t&e %r$ce"", y$( &a# t$ e)al(ate ali!e i!teral* O! t&e $t&er &a!#, y$( ca! al"$ calc(late E 'r$m y a "im%le#i''ere!tiati$!* I! t&i" (!it, +e "&all e6te!# t&e"e i#ea" t$ e)al(ate '$r "$mec$!ti!($(" c&are #i"tri(ti$!"*

I! t&i" (!it, y$( +ill al"$ lear! a$(t t&e c$!ce%t $' electr$"tatic e!ery a!#t&e !at(re $' t&e electr$"tatic '$rce* T&e"e are a"ic c$!ce%t" +&ic& +ill&el%i! y$( i! (!#er"ta!#i! !$t $!ly t&e remai!i! %art $' t&i" c$(r"e (t

al"$ ma!y $t&er c$(r"e i! P&y"ic" a!# C&emi"try*

2.0 O-("t#()

A'ter "t(#yi! t&i" (!it, y$( +ill e ale t$8

Otai! e6%re""i$!" '$r %$te!tial #(e t$ c$!ti!($(" a!# "ymmetricc&are #i"tri(ti$!"*

Calc(late t&e electr$"tatic %$te!tial e!ery '$r a i)e! c&are#i"tri(ti$!

S&$+ t&at t&e electr$"tatic '$rce i" c$!"er)ati)e*

3.1 T%( Pot(nt#&' !( to &n In=#n#t( L#n( C%&r(

I! (!it 2 $' t&i" m$#(le, +e #eri)e# a! e6%re""i$! '$r t&e electric 'iel# at a%$i!t !ear a! i!'i!itely l$! c&are# +ire 0$r a li!e c&are a" a! a%%licati$!

NOUN =/


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ELECTRIC, MAGNETISM AND MODERN PHYSICS.pdf