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you should know how to computethe electric field of a collection ofpoint charges.
Remembertfal the sum of the individual fields is a vector sum.Add the x componenlsto get t}le
x componeni ofthe sum; add the y oomponentsto get the y component of the sum. The
maenitude of the electric field produced by a single poinl charge q, at a point a distance r away,
is glven by E =klqlf. This must be multiplied by the sine or cosineof an angle to obtain a
component. You must also determine the sign of the componentSomeproblemsdeal with electric field lines. You should know that the electric field at an;
point ii tangentto the iine through that point, that the numberoflines per unil alea passing
ihrough an Lea perpendicularto the iines is proportional to the magnitudeofthe field, and that
lines emanatefrom positive charge and end at negative charge'
You will also need to know that the magnitude ofthe force on a charge in an electric fie1d is
given by the product of the chargeand the electric field: F: qE.For a positive charge,the force
is in the samedirection ofthe electric field, while for a negativecharge,it is in the opposite
direction of the elecnic field.
Questions and Example Problems from Chapter L8
QuestionI
_
Th. ftgut. below showsfour situationsin which chargedparticlesarefixed in piaceon ar ax1s.
in which situation(s)is therea point to the left of the particlewherean eiectronwill be in
equiiibrium?
-q
+q
A*B
-1
+3q
('r)
Question2
The figure to the right showsfour situationsin
which particlesof charge+q or -A arefixed in
place.In each,thepadcleson thex-axisare
equidistantfrom the y-axis. What is the direction
of the netforceonthemiddleparticlein each
case?
t)
w
"t\
.)
@
w
Iry
f---_-l
4l
-rq
+(l
(/)
\'''/
Question 3
Drawings I and I1 show two examplesof electric field lines. Decide which of the followin,r
statementsare true and which are false, defending your choice in each case. (a) ln both I ;d II
the electric field is the sameeverywhere.(b) As you move from left to right in eachcase,the
electric field becomes stronger. (c) The eiectric field in I is tlre same
but becomes
strongerin II as you move from left to right. (d) The electric fields in"r,"ry.h"."
both l and II could be
createdby negativechargeslocatedsomewhereon the left and positive chargessomewhereon
the right. (e) Both i and II arise flom a single positive point chargelocatedsimewhere on
the
left.
lFta" i
(q)
-<
tri
(b)
__=-+'
=?:-a
( ",1
l}'.,-t
w
lw':
(,d)
II
(e/
Problem I
A platecarriesa chargeof-3.0 pc, while a rod carriesa chargeof +2.0pc. How manyelectrons
must be transferredfi'om the plateto the rod, sothat both objectshavethe samecharee?
NaJl
O,a^a/. --
-3"OJ-^C+
).^HL
)
-J."5D.r,ta ,(, J-".X.^\ill
Q"Osg
o@*a
:
"
_l"o_qC
q cg\d,\,ql dg - o"so 4c
.rr;f-r^-,'*
)x )t^,^$t"")
4",.,\^9v pr-t t"fru^ol
cc
- )'
"50* lo-
=
- I . 6oAr
lo-rqC
ra
l"(?xlO'-
Problem 2
lnenucreusol 1nehetrumalom containstwo protonsthat are separated
by about3,0 x 10.r5m.
Find the magnitude of the elechostatic force that each proton exerts on the other. (ihe protons
remaintogetherin the nucleusbecause
therepulsiveelictrostaticforceis balanceiby aa
afiractiveforce calledtle strongnuclearforce.)
4p
'"c
= * l"(,.r1,,v
if
15iq j;t, t
f i = 3 . l o " l D - i er r r
=
v ,-a
-JnP
__-f
nI
d-'-
( ' , . t " , . t l . , , ) . t : , ( t , * , ; " : o - ' " c/ r
1
-=,
Cb' ',t)-'in
, "
e6
|\l
-=F-'
Problem3
- Two very srpallspheresareinitiallyneutralandseparated
by a distanceof 0.50m. supposethat
3.0 x 1013electronsareremovedfrom onesphereandplacedon theother.(a) Whatis the
magnitr.rdeofthe electrostaticforcethat actson eachsphele?(b) Is the force attractiveoI
repulsive?Why?
J.fuLi"j^'t'. t-;* rcrhJa{l
rc)*u"gr o'1 3. a\ ,1I o\7
r'va- )ipN,-*'r 9"o* o ^b',v,,'r6" lri
)
(2.o, 1o'3) (-t, aoax l o (
t+A
- 4 . ? ' 1 2 ,D
1 *bC
-- - 4 't lt lo-e t
d ,
*fi elb,= 4'
cr.rd :tiv c}- er -r4,0*-, 9',p't::i 2?'tu"'aro
Zit\D-LC
(q.z t*
/ /'\
I
16-b C)^
\?.
)
Eh
( b)
,ir' A 1**,t'fu,
Problem 4
cJ"atuono.n.
Two additionalchargesarefixed on the
A chargeof-3.00 pC is fixed at thecenterofa compass.
(radius:0.100 m). The chargesonthecircleare-4.00 p1Cat the position
circle ola compass
due north and+5.00 pC at the positiondueeast.What is the magnitudeand direction of the net
electrostaticforceacting on the chargeat the center?Specirythe directionrelative to dueeast.
_.l.oo .a
?I
o"roo. i
j
o. roor.l
I
------1
i
- 3.oDAc
'F+ 5 J g
I
,
+ s.Ooue
r
+
6
4<\,o1\
ett
F
la
^
,--
\-a4'Y^ea1\t'
a
A
)aALut
.
-- Klt,lllr-l
i
Eru.
= ( 8 . 9 1 * l o aN m ' ' : ) ( q , o o , t o - ' " c ) ( 3 . o o i l d n c )
=
( o, too. )'
Eu^r
=
I 0.8 N J,^;rfrI
/====
.= 13.s r\ Q^dt(o.too.)I
tr*\F
=
---)
,/ (13. 5N)a+(*ro.:r.r)'
F= l?.sN
Problem 5
Given that 4= +12 ttC andd : 16 cm, find the direction and magnitudeof the net electrostatic
force exertedon charger7rin the figure below.
4z=-2-Oq
It= +cl
- - - - o- - - - - - -- -- -- - -e- -- - --- -----
lr.l
\l
(t.?q"i07W ) (at*rs'c) (irtlq'c.i
i
c\ a ,
|
l\
/b/.tN
^
(o"tt"n')
2,1
\/
E, +*---;0.,
--Ci---
,-)
l< Iq,-llq, t
F| : ' l
93= +3.0q
- 3 ?, ? \l
/\ < qa. rr\orr..;
m.t.,t/39:tgl3x-ErI{,c)
I
= l( l1.zll7"l LI 3l
"'L__-11---J'*
r- ;-
( o"72'r't)a
-t", -u:
- J . * t':u
{ . , :, ,vJ2r'r'
t r - - E = ,t1,
/ r t t . t . \ Jt
,'^a+
l-^, l-,,
3,'a l'.1
il
Problem6
A chargeof +3.00x 10-5C is locatedat a placewherethereis an electricfield thatpointsdue
eastandhasa magnitudeof 15000N/C. What arethe magnitudeanddirection of the force acting
on the charse?
--)
&
\--,
lffc
$: 1l'oo*
L
* n".cfo:-+-]ry $"a o., a +
= lb,oool,r/.
r
}.4.,
);\r
"ii
Cyl'-a{
F**'n;"
;1o^zcE-r, o" E
)
,J*qy pt-,*:
d"w,e-t
,,|rl
o'4
|
*,
it{
"t
-
+We
E
"Problem7
and
(mass:
0.012kg) carriesa chmgeof -1B pC. Whatelectricfield (magrritude
A tiny ball
direction) is neededto causethe ball to float abovethe ground?
r=r6tr
1I
t
Irq+
r-^'A ^ t*
An'-^'n
t Jr, E +^aa ru^dff",f
+cruca a,'! at
- ca,bJ\/XLE
p-rrt
4^ 'tr"
qutw"^1
Fv : mAy -- o
qtr- n2=o
F = 6.S*to3N/c
,tr--
tct 4
q
.'-.9
C3o,3rz>a?r""/O
l8x lo-bc
Problem8
Fourpoirrt clarges that havethe samemagnitudeof 2.4 x 10-t2C arefixed to the comersof a
sqo*" tttut is 4.-0cm on a side.Threeof the chargesarepositive andoneis negative.Determine
the masnitudeofthe net electricfieid that existsat the centerof the square'
+%r --l%e
r-.,'""9-a,,,eo.'aae
+ A+fl
?^
->
69
F, u {i
,
a
t*
a'no6"fi
,
q rcM^LdJ''tta
+%t
+%,
#s le*a
Y^'"
/a
c,
p=fl,,Dcrn)+
-- O" OA33r.)
1l
,tr - E^= Klt/ =
u6.1 N/e
-t)--
fa
rrric) ----;
E ^a' x (b,01*1or
Problem 9
Two charges,-16 pC and+4.0 pC, arefixed in piagea1d separatedby 3'0 m' (a) At whatspot
alonga ]ilie tlrough the chargesis the net electricfield zero?l,ocatethis spot relative to the
porit-ivecharge.(b) what would be the force on a chargeof +14 pC placedat this spot?
'
d
3"o rr
K ltl
F-'ca
|--.'
- lbuL
J I,D[c
<----------------
-E
E-16ue
E^"L=
h
{Ae
( S.11* tor5l-{)(+.orro*c)
-L.
_l{p,re
-(l
. l b* l o - ' c
(d*3.o")'
4 (a'.6d*q) = loJe
I !.J\- AL/d-3a --o
l?.
d
- A zr
d - 5I
.-\
+ l''{ c-
-- ( J!.\
=o
l\
u
tl
ct
|
.-
=
--:-'
#rl^
|
\/
( d-:.o./Ld"
r
d=-l.orn,,.r
d = 3"or")
q(d'+3)":lbd\
\
,..
l.on,) = u:
d=3.o,n