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Physics48 (FaII 2011)
Chapter21: Electric Charge
v
"Anyonewho has nevermadeo mistakehas nevertried anythingneu ,,- Albert Einstein
"Experienceis the namethat everyonegives to his mistake,s.
" - OscarWilde
"Theonlyreal mistakeis theonefrom whichwe learnnothing." * JohnPowell
"An expertis a person who hasmadeall the mistakesthat can be madein a very narrow field. "
NielsBohr
Reading: pages561* 573
Outline:
\"
+ eleckic charge
introduction
chargeis quantized
conservationof charge
* conductorsand insulators(PowerPoin0
= 3 waysof chargingan object(PowerPoint)
= Coulomb'sLaw
two shell theorems
principie of superposition
ProblemSolvingTechniques
The firndamentalproblemsof this chapterdealwith Coulomb'slaw. Giventwo chargesandtheir
separation,you shouldbe ableto calculatethe force (both magnitudeanddirection) eachexertson
the other.You shouldknow how to usevectoradditionto find the resultantforce whenmore than
onechargeinteractswith the chmgeof interest.Variationsincludeproblernsthat askyou to frnd one
ofthe chargesor the position ofa charge,giventhe force.
To find the value of one or mote of the chargesin someproblems,a preliminary calculationmustbe
performedprioi to using Coulomb'slaw. For exarnple,you may needto calculatethe total positive
chargein an object.The numbetof atomsin an object canbe found ftom the massofan atomand
the massof the object;the numberof protonsin an atom is given by the atomic number.Sometimes
the molar massis given (or canbe found in the periodic table of the ehemicalelements)andyou will
needto divide that quantity by th€ Avogadro constant(6.022 x 10r mol-r) to calculatethe massof
an atom.
.-v
to apply th9 shel.lthgorems-ln
Otherproblemsdealwith conductingspheresandyou will need
t*" identicaiconductingspherestouch eachother,the total
addition,you shouldknow ttrat ;;
chargeis sharedequallybetweenthem'
\-.
Finally,youshouldknowtherelationshipbetweenchargeandcurrent:cun€ntisthechargethat
*ou"i ittto or out of a region per unit time'
Chapter 21
Questionsand Example Problemsfrom
1
Question
"n'g.*1"h*
placeon an axis' ln
showsfour situationsin which ohargedparticlesarefixed in
iri"
wherean eleckon will be in equilibrium?
which situation(s)is there u polni io tlr" left of the particles
-tt
-q
-q
+i\q
-?,q
+)rJ
1.!
Question2
'q is,sunoundedby two circular rings of
ln the figure to the right, a centralparticie of charge
n r r. wh--atari tne magnitudeand direction of the net
oriaaii . *Jn,'*itir
Ji*gJ-p*u"s,
particles?
eleciostatic forceon the centralparticle dueto the other
F = Kir,llgrl
..r
t,
,;
v
7
l-
Question3
oftwo electriccharges.In eachfigure, a point labeledP is also
Givenbelovi are sevenarrangements
identified. All ofthe chargesarethe samesize,20 C, but they canbe eitherpositive or negative.The
chargesandpoint P all lie on a straightline. The distancesbetweenadjacentitems, eitherbetween
two chargesor betweena chargeandpoint P, areall 5 cm. Thereareno other chargesin this region'
For this problem,we aregoing to placea +5 c chargeat point P. Rankthesearrangementsfrom
greatestto leaston the basisofthe strengthofthe electric force on the +5 C chargewhen it is placed
at point P. That is, put first the arrangementthat will exert the shongestforce on the +5 C chargeat
point P, andput last the anangementthat will exertthe weakestforce on the +5 C chargewhen it is
F
placedat point P.
t-F
F
e-
J<-:_ F/u e.F
FI
F
|-
A -__+
g.OP
ooI
€.----t
+F/q
O O.
1-F
P
F
t---------)
-
oI6
OO.
-----.F
----)
F/q
P
F
?."F/q
ojo
P
o o.
Srrongesr,ErEr@^Mt
Weakest
Or, all ofthese arangementsexertthe sameshengthforce on the t5 C charge.
will exertzero force on the +5 C charge.
Or, all ofthese arrangements
Pleasecarefully explain your reasoning.
rT.
o
iX g^r,a #-\ Bw fuo 't!^h"c
'LA
oJfurl 7 n F/a
,t*n
zF/q
r^P\^e F=
K(roc)(qe)
( o.ororn)a
5 F/q
t r/4
F:
\f.
=F/,t
-'Problem 1'
it with a chargeof +1 '0 x 10-7c?
to
leave
a
coin
from
removed
be
to
have
How many electronswould
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to yourbrain'If thatcurrent
andaisnrffi thF;* "f ti";d (*d-th* oxvgen)
rhythmof heartbeat
passtbroug!yourchest?
electrons
for 2.00nin, nowmulyJonduction
oersists
LC= LA..s ( V^" t
-- l6/ax Ft A.7,)
U/
|qr=t Jt ----: , %= c"t
q = (p.loaA) ( t fo";
-- ' 3G,D C
t\
--4
oe
o.=
u:
f)= 4/u'=
399--,.
= a'as"loao
^: i
,'
'.'.) 'j
U-/
-r1,rr-l-(-P,i[?:,tr{ift ?tC
\,/
I
t i, 1r,r-,-r,.'tra,i
The initial chargeson the three identicaimetal spheresin the figure below arethe following: sphere
A, Q; sphereB, -Q/4; and sphereC, Q/2, where Q = 2.00 x 10-14C. SpheresA andB arefixed in
place,with a center-to-centerseparationof d : I .20 m, which is much largerthan the spheres.
SphereC is touchedfrst to sphereA and then to sphereB andthen it is removed.What then is the
magnitudeofthe electrostaticfolce betweenspheresA andB?
*
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ra
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l{"ar
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=l%s"l;:El:-fi
In thefigurebelow,fourparticlesfomra square.Thecharges
areqr JqA=Q-dfrd'Ei=iFq.
Whatis Q/qif thenetelectrostatic
&rce onpaiticles1 and4 is zero?
\Y
a-------1
T
I
I
I
I
I 3:;=a6.
9.,
a1
'-1,
tI
I
I
tr= gil+I
F.,
l-.
t
= -q'
Fr,=
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6,,= Ktt tt. E, [h,J-!g]
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4'
X F-: E, - E,-or'i 5o= KBlol
.
qa.
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''l
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4= Eq
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(r),/., = -4
.
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o
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=
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4
ld\
uoaqS
'Q IA'u
=D'om
Ke f q\- Kltilgi
aW
qr
APqv
-1"^t \' "'/
[i%=-ffi51
Problem5
C,
In the frgurbto the right,if Q: +3,20x 10-reC, q = t.6Ox 1O-re
particle
the
at
anda:2-00 cm, what is the electrostaticforce on the
origin dueto the otherchargedparticles?
X r=
Qs=
$3
$,
3.aoxlo-'qc
?.A0^lo-'1c
=6"to"16-'ag
= -3'to,.lD-rqc-
q : {.ox
lo-a r.,
Fru
tr
'11
t-
r
t--
I ra s---------.C
r
e-ll
vf,u bz\qo
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tI
II
.', v f A ,r-^
r,q -/&\45-
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v
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r't-t{
(9sl*to'x*V,1q
3 . A o^ 16 - r r s )( 3 . X o* t d ' q c )
( 3.o xro-arc,)\
l"ol" lo-)i51
Er= 2,,3or lD-'"N
! -r, = - E:- f,ncra:so-
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:-*
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( H..'- YaEB ;*
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) | - 1t.tt*ro€ear)3
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)d' (-?##Hj = a-8'6
aAA lto'
g = l.og"
7
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. %,=
.
t.odcro
r-4'oon
Q,
Problem 6
/:
In the frgurebelow, particle I of charge+q andparticle 2 of charge+4.00q are held at separation
L = 9.00 cm on an x axis. Ifparticle 3 of chargeq3is to be locatedsuchthat the threeparticles
remain in placewhen released,what must be (a) the ratio q:/q andthe (b) x and (c) y coordinatesof
particle32
$a non-a,Wfu
l*-/----l
=)
3 *.A
4.vw4 +",9"\ p6,,*ah,
a,""1
P.'-r X I
%. #
Z-X
X
o d-trif.a^zc-oX **n
\y
= F-rl
'
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t3
l,/
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l\l
il
a
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o
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+*".^ rh1r4i /.'^r. l a*
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= 71-.
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= 4q.,,)
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Kl%,llrrl - l<'lq,ll%".l
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----)
( Zbr,ru
: T-uu'=
Ty'+='4._'
q/q
932 =- %(q.q)
x^
L\
+ q^
L\
':---1
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Problem7
hang from
tn the figgd below, two tiny conductingballs of identicalmasszr and identicalchargeq
nonconJuctingthreadsof lengithL. Assumethat 6 is so small that tan 0 canbe replacedby its
approximateequat,sin 0.{a) Showthat
,u
( s'L
ij\^ts
l"
a'r*oo }'q^A A'"'U
W
\),/
)
\Lrcomg
ff)q
.-I
t--
gives&e equilibriurn sepatationx of the balls.
-
AY^AAp{\
,)r^fiuL $o"w
=
f- 11341e*t
co'
t%,fPr
E=a__nu
v
14-
x -+l
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Tr-erO
Z F.,=o
Tt-ta-t3
=o
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4Te.
{.x
z-
I
-bl
Jan"O=
F..=O+
.X
''( rtl'q
\
CAJE
-&trar*Uan'2fu4 Mn
(xh) =
->-t--
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af'
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x' m*
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sot+c**ToA
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