Chapter 12 Notes

7/21/2019 Chapter 12 Notes

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CHAPTER 12

ELECTROSTATICS



12.1 COULOMB’SLAW

What is Electric Charge?

• - An intrinsic property o protons !n"e#ectrons$ %&ic& '!(e )p !## '!tter$is e#ectric c&!r*e.

• - A proton &!s ! positi+e c&!r*e$ !n"!n e#ectron &!s ! ne*!ti+e c&!r*e.



- T&e SI )nit or 'e!s)rin* t&e '!*nit)"e

o e#ectric c&!r*e is t&e coulomb (C).- T&e e#ectric c&!r*e is s!i" to ,e

quantized. The smallest amount offree charge is e=1.61!"1# C. $n%

electric charge& q& occurs as integermulti'les of the elementar% chargee& = ne

- T%o e#ectric!##y c&!r*e" o,ects eert !

orce on one !not&er$ c!##e" !selectrostatic force li*e chargesre'el and unli*e charges attracteach other.



The strength of electrical forcede'ends on

- T&e distance bet+een charges

- T&e !'o)nt o charge on eachob,ect



• T&e electrostatic force ,et%eent%o c&!r*e" o,ects is proportion!# tot&e quantit% of each charge !n"in+erse#y proportion!# to t&e squareof the distance ,et%een c&!r*es.

W&ere

(/ Co)#o',s const!nt

(/





0ierence !n" Si'i#!rities ,et%eenE#ectricity !n" r!+ity

• M!t&e'!tic!# or' o t&e Co)#o',#!% !n" #!% o *r!+it!tion +erysi'i#!r



E3AMPLE 1

W&!t is t&e e#ectrost!tic orce ,et%eent%o positi+e c&!r*es4 5q1 = 4 μC, q2= 8 μC, r = 10 cm]



A6SWER

/ (8.99 x 10^9) (4 x 10^-6) (8 x 10^-6) / (0.1)^2

= 28.8 N



• The force on a 'oint charge due to t+o or more

other 'oint charges• - T&ere !re t&ree c&!r*es q1, q2 and q3. Wha !"#$d

%& h& n& '"rc& "n q1 d#& " %"h q2 and q3

• - 7irst$ 8n" t&e '!*nit)"e !n" "irection o t&e orceeerte" on q1 % q2 (*+n"r*n+ q3).

• - T&en$ "eter'ine t&e orce eerte" on q1 % q3(*+n"r*n+ q2).

• - T&e n& '"rc& "n q1 * h& &c"r #m "' h&& '"rc&.

• - I %e &!+e n char+&d ar*c$&, h& *n&rac

*nd&&nd&n$ *n a*r, and h& '"rc& "n an "n& "'h&m, $& # a ar*c$& 1, * +*&n % h& &c"r #m

• 71$net / 712 9 71: 9 71; etc.



E3AMPLE 2

7orces 71 !n" 72 !ct in"epen"ent#y ontest c&!r*e <=>?. 7in" n&

5=1 / 2 @C$ =2 / @C$ => / ; @C



1 = qq/r2 = .2 N (" r*+h)

2 = qq/r2 = 2.9 N (" $&')

", n& = 1 2 = .2 2.9 = 4.3 N(" r*+h)

• N"&, h& $ar+&r &&c "' 1 (&&nh"#+h h& char+& !a ma$$&r) *

d#& " * closer proximity to q0.



E3AMPLE :

T&ree point c&!r*es !re !rr!n*e" !s s&o%n in t&e8*)re ,e#o%. <T!(e =1 / .; nC$ =2 / ;.D nC$ !n"=: / -2.D nC.?

!? 7in" t&e '!*nit)"e o t&e e#ectric orce on t&ep!rtic#e !t t&e ori*in.

,? 7in" t&e "irection o t&e e#ectric orce on t&e p!rtic#e!t t&e ori*in.



A6SWER

a) =q1q2 / r^2 (=9 x 10^9, q=char+& "' ar*c$&, r=d*anc&%&!&&n ar*c$&)

"rc& d#& " q15

1=(9 x 10^9)(.46 x 10^-9)(4.9 x 10^-9) / (0.3)^2

1 = 2.02 x 10^-6 N " h& $&' *nc& r&#$*& '"rc&

"rc& d#& " q35

2=(9 x 10^9)(4.9 x 10^-9)(2.9 x 10^-9) / (0.1)^2

2 = 1.323 x 10^- N d"!n!ard *nc& arac*& '"rc&

•) 7" nd ma+n*#d&, #& ha+"r&an h&"r&m

^2 = (2.02 x 10-6)^2 (1.323 x 10-)^2

= 1.3 x 10- N



,? 7" nd d*r&c*"n, #& r*+"n"m&r

an := 1.323 x 10^- / 2.02 x 10^-

6= 8.44; 'r"m h& n&+a*& x-ax*

=180 8.44 = 28.44 ; 'r"m "**& x-ax*



E3AMPLE ;

Ass)'e t&!t ! &y"ro*en !to' consistso !n e#ectron o c&!r*e e- or,itin* !proton o c&!r*e e9. C!#c)#!te t&e

r!tio o t&e e#ectrost!tics orce,et%een t&e e#ectron !n" proton tot&e *r!+it!tion!# orce ,et%een

t&e'. <M!ss o e#ectron$'/D.11>F-:1 (*$ '!ss o proton$'/1.1>F-2 (*?





1-.- Electric ields

ield Theor%

• T&e e#ectric orce is not G!ction !t ! "ist!nce ,)t is t&e!ction o ! feld.

• A 8e#" is ! p&ysic!# entity t&!t eten"s t&ro)*&o)t !+o#)'e o sp!ce !n" eerts orces.

• E#ectric 8e#" / E(/&t) and 0agnetic eld = 2(/&t)

• E#ectric 8e#"s s)rro)n" e+ery e#ectric c&!r*e !n" eerts !orce t&!t c!)ses e#ectric c&!r*es to ,e !ttr!cte" or

repe##e".



- W&!t %o)#" &!ppen to ! c&!r*e in e!c& 8e#"4

• A c&!r*e cre!tes !n e#ectric 8e#" !ro)n" itse# !n" t&e ot&er

c&!r*e ee#s t&!t 8e#".• Test charge 'oint ob,ect +ith a 3er% small 'ositi3e

charge so that it does not modif% the original eld

• E#ectric 8e#" !t ! *i+en point in sp!ce p#!ce ! 'ositi3e testcharge q at the 'oint and measure the electrostatic

force that acts on the test charge4 then

• A 8e#" is not )st !n !,str!ct concept t&!t %e )se to "escri,eorces. T&e 8e#" is real.

• I %e p#!ce ! positi+e point c&!r*e in !n e#ectric 8e#"$ t&ere%i## ,e ! +ector orce on t&!t c&!r*e in t&e "irection o t&ee#ectric 8e#"

• T&e '!*nit)"e o t&e orce "epen"s on t&e stren*t& o t&e



5enition of Electric ield

• We "e8ne t&e e#ectric 8e#" in ter's o theforce it e/erts on a 'ositi3e 'oint charge

• Unit o t&e e#ectric 8e#" 6JC <ne%tons perco)#o',?

• We c!n t&en %rite 7/=JE

• 6ote t&!t t&e e#ectric orce is p!r!##e# to t&e

e#ectric 8e#" !n" is proportion!# to t&e c&!r*e

• T&e orce on ! ne*!ti+e c&!r*e %i## ,e in t&eopposite "irection



Electric ield ines

• - We c!n re'resent the electric eldgra'hicall% b% electric eld lines 7 i.e.&cur3es that re'resent the 3ector forcee/erted on a 'ositi3e test charge.

• E#ectric 8e#" #ines %i## originate on 'ositi3echarges and

• terminate on negati3e charges.

• E#ectric 8e#" #ines do not cross. (Wh%?)

• T&e e#ectric orce !t ! *i+en point in sp!ce istangent to the electric eld line throughthat 'oint.





8ro'erties of ield ines

• T&e stren*t& o t&e e#ectric 8e#" isrepresente" ,y t&e "ensity o e#ectric8e#" #ines



• T&e "irection o t&e e#ectric 8e#" ist!n*ent to t&e e#ectric 8e#" #ines

• - T&e e#ectric 8e#" #ines ro' ! pointc&!r*e eten" o)t r!"i!##y.



MOTIO6 O7 A POI6T CHARE I6 AU6I7ORM ELECTRIC 7IEL0

• 7i*)re <!? s&o%s ! p!rtic#e o c&!r*e 9= 'o+in* %it& ! +e#ocity + int&e "irection o t&e e#ectric 8e#" E. T&e orce 7/=E %&ic& is in t&e"irection o + c!)ses t&e p!rtic#e o c&!r*e 9= to !cce#er!te !#on*t&e "irection o t&e e#ectric 8e#" E.

• Acce#er!tion $ ! / 7J' / =EJ'

<'/'!ss o c&!r*e" p!rtic#e?

• A ne*!ti+e point c&!r*e s)c& !s !n e#ectron 'o+in* %it& ! +e#ocity+ in t&e "irection o E eperiences ! orce 7/eE in t&e "irectionopposite to t&!t o E. T&is orce c!)ses t&e e#ectron to "ece#er!te.



• 7i*)re <,? s&o%s ! p!rtic#e o c&!r*e 9= enterin*! )nior' e#ectric 8e#" E %it& ! +e#ocity + %&ic&is perpen"ic)#!r to E. T&e orce 7/=E on t&e

p!rtic#e is const!nt!n" t&e "irection o E. T&is isi"entic!# to t&e 'otion o proecti#e )n"er *r!+ity. T&e &oriKont!# co'ponenet o +e#ocity o t&e p!rtic#e

re'!ins const!nt$ +

T&e +ertic!# co'ponent o +e#ocity incre!ses %it& !n!cce#er!tion

!/7J' /=EJ'

.



E3AMPLE 1

T&e 8*)re s&o%s t&ree in( "rops in ! ,),,#e-et printert&!t &!+e t&e s!'e '!ss ,)t "ierent c&!r*e enterin* !)nior' e#ectric 8e#" E %it& t&e s!'e +e#ocity +perpen"ic)#!r to t&e e#ectric 8e#". S(etc& t&e p!t&s o

t&e p!rtic#es in t&e e#ectric 8e#". Ep#!in or t&e"ierences in t&e p!t&s.

$



A6SWER

1- 9 : ; l



1-.9 :auss; la+

Electric lu/

• T&e e#ectric ) is "e8ne" to ,e

"r

Wh&r& < * h& &$&cr*c &$d and * h& ar&a

• .



•I s)r!ce !re! is not perpen"ic)#!r to t&e e#ectric 8e#" %e&!+e to s#i*&t#y c&!n*e o)r "e8nition o t&e )

Wh&r& * h& an+$& %&!&&n h& &$d and h& #n*&c"r ha * &r&nd*c#$ar " h& #r'ac&

.



• 7or ! c#ose" s)r!ce$ t&e )nit +ector is t!(en !s,ein* pointe" o)t%!r"

• W&ere ) #ines enter t&e s)r!ce$ t&e s)r!cenor'!# !n" t&e e#ectric 8e#" #ines !re !nti-p!r!##e#



• Is t&ere ! "ierence in t&e net ) t&ro)*& t&e c),e ,et%een t&et%o sit)!tions4

• 6o It is i'port!nt to re'e',er to proper#y t!(e into !cco)nt t&e

+!rio)s "ot pro")cts

• T&e e=)!tion %e &!+e or ) is 8ne or si'p#e sit)!tions

- t&e e#ectric 8e#" is )nior' !n"

- t&e s)r!ce !re! is p#!ne



• I t&e !re! is not p#!n!r$ t&en t&e

e+!#)!tion o t&e ) *ener!##yre=)ires !n !re! inte*r!# since t&e!n*#e %i## ,e continually changing.



• We st!rt ro'

• T&e e#ectric 8e#" is *i+en ,y

• T&e pro,#e' &!s sp&eric!# sy''etry$ t&ereore )se !sp&ere !s t&e !)ssi!n s)r!ce

• Since E is r!"i!#$ its "ot pro")ct %it& t&e "ierenti!# !re!+ector$ %&ic& is !#so r!"i!#$ is !#%!ys one

• A#so E is t&e s!'e !t e+ery point on t&e s)r!ce o t&esp&ere

• 7or t&ese re!sons$ E c!n ,e p)##e" o)t ro' t&e inte*r!#

!n" %&!t re'!ins is

• T&e inte*r!# o+er t&e s)r!ce !re! o t&e sp&ere yie#"s



• P)##in* !## t&is to*et&er t&en yie#"s



:aussian <urfaces

Electric ield of 8oint



Electric ield of 8ointCharge

• T&e e#ectric 8e#" o ! point c&!r*e N c!n ,e o,t!ine" ,y !

str!i*&tor%!r" !pp#ic!tion o !)ss #!%. Consi"erin* !!)ssi!n s)r!ce in t&e or' o ! sphere at radius r, theelectric feld has the same magnitude at every point othe sphere and is directed outward. The electric ux isthen just the electric feld times the area o the sphere.

.

Electric ield of



Electric ield ofConducting <'here





E3AMPLE 1



A6SWER

!? Use

/ <11>F-?J<; Q.Q1>F-12 <>.>1?F2?

/; 1>F 'F-1

,? E / >



E3AMPLE 2



A6SWER



E3AMPLE :



A6SWER

Usin* T cos :> / '*

T sin :> / =E / =<J2?

t!n :> / <=?J<2'*?

/ 1>F-D C 'F-2



12.; E#ectric potenti!#

T&e tot!# o t&e e#ectric ) o)t o !closed surace is equal to thecharge enclosed divided by the

permittivity.





E t f i hb i



Eect of a neighbouringconductor





E#ectric potenti!# ener*y



E3AMPLE 1



A6SWER

Chapter 12 Notes

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