You should know how to computethe electric fie1dofa collection of point charges.
Rememberthat the sum of the individual frelds is a vector sum.Add the x componentsto get the
x componentof the sum; add the y componentsto get the y componentof the sum.The
magnitudeof the electric field producedby a single point chargeq, at a point a distancer away,
is given by E: k lql/r'. This mustbe multipliedby the sineor cosineof an angleto obtaina
component.You must also determinethe sign ofthe component.
Someproblemsdealwith electricfield lines.You shouldknow that the electricfield at any
point is tangentto the line through that point, that the number oflines per unit areapassing
through an areaperpendicularto the lines is proportional to the magnitudeof the freld, and that
lines emanatefrom positive chargeand end at negative charge.
You will also needto know that the magnitudeof the force on a chargein an electric field is
given by the prodact of the ctarge andthe electric field: F = qE. For a positive charge,the force
is in the samedirection of the electric fie1d,while for a negativecharge,it is in the opposite
directionof the electricfie1d.
Questionsand Example Problemsfrom Chapter 20
QuestionI
The figure below showsfour situationsin which chargedparticles are fixed in place on an axis.
In which situation(s)is there a point to the left of the particle where an eiectronwill be in
equilibrium?
-3q
+q
r--...-.------1
@
lAcB -l|
L_
-3q
+3,1
\r/
Question2
The figure to the right showsfour situationsin
which particles of charge+q or -.4 are ltxed in
place. ln eac[ the particles on the x-axis are
equidistantfiom the y-axis. What is the direction
ofthe net force on the middle particle in each
case?
r)
-)
\-r--'-.:-,1
3)lN*'tl
.
F-i--.--'
'l) l)']^i
+q
(d,)
Question3
Drawings I and II show two examplesof electric field lines. Decide which of the following
statementsaretrue and which are false, defendingyour choice in eachcase.(a) In both I and II
the electric field is ihe sameeverywhere.(b) As you move from left to right in eachcase,the
electric freld becomesshonger.(c) The electric field in I is the sameeverjrwherebut becomes
strongerin II as you move fiom 1eftto dght. (d) The electric fields in both I and II could be
createdby negativechargeslocatedsomewhereon the left and positive chargessomewhereon
the right. (e) Both I and II arisefrom a single positive point chargelocatedsomewhereon the
1eft.
(o)
._--.-...-...--.
-.-----..-...------.---.--....:
I'I
I
&%
$tw
----------.
ow
(r)w
(")B
Problem I
A platecarriesa chargeof-3.0 pc, while a rod carriesa chargeof+2.0 pc. How manyelectrons
m;st be transferredfrom the piate to the rod, so that both objectshave the samecharge?
-l.O,uC
J
-bel
)
At#.*' ^'.r,.ii A4 ^
- l.Sa^ c
lp b^r *"A
"B O* g. ""ir{*
.C[= ne ->
n=fi/e=
ad -D'5oAc?,
" "9^
4rd
tar\.Vl, p.o"fu)" V\r
- ).$OrlD-6C
- 1,6r lor>
l,6oa^lo-)qc
It,
r.l3
l,t"" )D''!ufi'^" m*d .Ix
II
Problen2
The nucleusofthe helium atom containstwo protonsthat are separaledby about 3.0 x 10-" m.
Find the magnitudeofthe elecfrostaticforce that eachproton exertson the other. (The protons
remain togetherin the nucleusbecausethe repulsive electrostaticforce is balancedby an
attractiveforce called the skong nuclearforce.)
$?
= *l'6oA*lD-'oc
----_-_--__-_.j_.-,
nr-
t^:3.1o*10-'em
tr=7
F. KI t,ll$,1
/\ %P
n
l'
I
F . (1.99- {ooN ,'/Kz')( t.t,oA"1o-'rc)o
(3.o*16..'5ro)*
f - a_:.atr
F= QoN
= + l)',,.c
-a'iaC
Qa=
Sr
= t3to'tC
S+
Problem 3
:
Given that 4 +12 p'C andd = 16 cq find the direction and magnitudeofthe net electrostatic
force exertedon chargeq1 in the figure below.
<----*_l{ .lo "c
A= f]g:!_Ul: (r.1q-rotN"'%i)(
l A " ld t c
[e]u = Cl,qq'164N"'r(3.
t3,
=
)ol.lNl
r]
rLm /
r.\
F.
E,
-- 3?.1\l
,. (0.3t*)\
\11- : L * /2)fx'
ra,* /nt = lol.lN- 3?.c N =
63.r N fc"fr"^',A!n
Problem 4
'A chargeof-3.00 pC is fixed at the centerof a compass.Two additionai chargesare fixed on the
circle ofa compass(radius:0.100 m). The chargeson the circle are-4.00 pC at the position
due north and +5.00 pC at the position due east.What is the magnitudeand direction of the net
electrostaticforce acting on the chargeat the center?Specirythe direction relative to due east.
tr
' -jre
6c\
= ( 8s4"lor N */c+)(r/'oo xtd6c)(:'oo*to
-=
(o-toa'n)I
'+ S,ue
( ? . r q * l o q N ^ / c . ) ( E - o o ^ 1 o6 c ) ( : . o o * 1 o t c )
(o-taa*;r
F*= *13'5N
'-Ft = -ld'sN
10,8N rrbr*l
13.55J 1",
E\[,. ---t f = \a-zrl
-----'
0. )ar,\'iT"/a)
I":t-r'*l
Problem 5'
Threepoint chargeshave equal magnitudes, to being positive and one negative.Thesecharges
are fixed to the cornersofan equi1u1ffqlt'iangle, asthe drawing shows.The magnitudeof each
of the chargesis 5.0 pC, and the lengths ofthe sidesofthe triangie are 3.0 cm. Calculatethe
magnitudeof the net force that eachchargedexperiences.
)-fu lar+"J.xj.e ftA &^^e o"1J a q C i
tr
(oo"
6oo
/AC
Go'
F
toe
tr
= Klq*)l$"l =
/ Ac
( 8 " 9 9 " l d ? N m % ) ) ( s . o " l o - b c f , 9 . D x r d 6 c )= !,50"to!N
----=:'
1l
(o,oaa-)\
\-'l
r
.50*lD'Ni
Nry.')(ro"tco.)!s-lo9 = 5--'--=-(.|%ulJJrl= (3.??16o
tf
^1.
I -^
/
t1v
^
,^\?n
\(,'\2Jv
<'l
t-
lAt
\
tu.
h
"
l
t
,"-"6o'- F*" = (^.sorlo^r) c-ctbo"- A"5o"looN
-la5N
-4=:
= - t-o. ))'.too" = -(e'5oxlo'N)'a; bDo= -g
A f,,
g- =f,n-\(F"/v.)=b.-'(-i#,) =66";:^
F^o*^ft -
?:oN ,}g =to"
F"-r ^ B
aSDN of &=-lto'
A
\./
= 4ct' e r, nr'2 "
Problem'6
tin):b1[. (ma1: 0.012kg) carriesa chargeof _18prC.Whatelecfic
field (rnapitude and
+
direction)is needed.to
causetheball to floai abovetheglound?
F =qtr
1
itu E= pU
)
I
^"Jr,r*er^*
n o"l4
?f . _
L
s-l r-
l-y:N)oy=O
/)
tl)=r,r+
3F
- *g
=O ---)
E- (::,^_rDEp:11
I-q€
A=
%
E = 6-5* l\u*L A^-,*84
l9^ lo-"6
Problem7
Two ch.ar.
ges,-16 and+4.0Fg, ge fxeg in placeandsepamted
by 3.0m. et *hat spot
ryC
alonga line throughthe chargesis ttrenet elegtricfreld zero?Locatethis spot[aj
i"tative to tli
positivecharge.(b) Whatwouldbethe_.foroeon
a chargeof+14 pC placei at this spot?
,d
3.o r.t
L
Z- nlX
L-t
'rM\,
-
l_ l Qr r c -
'=
\1,
c!
('t.o* 16-tq
-
Q! tdt)(do:.o.)
4(d-a)*:
ItJl-
-___+--:-u = J6
lr
.L
( d+3)
l6At ---+ 4( d..{,j+9) -_16t \
aqd
d'- aJ - >-O
,\-'-->
A
=o
( d+ 3'o'; I
(t) F= qd-Iolrl
( d -:.a"1(d" t.o^) = a
d=-),o*
t^
d = 3.o ro
zr,u^<.ea=o
n
d=3.orr,
Problem 8
What arethe saengthond direction of the eiectric freld at the position indicated by the dot in the
Figure below? Specifr the direction as an angle aboveor below horizontal.
,'r
-( E-o.',1a
f
/ ( 5.o "'.,)
I
t- -- J.oJ c^
"::-
5.D.-q
E= (Iee" ) ---)
:
-&"L.p"^,"* "" E:= ry
"!-,"1"
E.
E-
lel
N^%)(@
tz.rq"i""
=
--==-
(o-o?o7,", )'
E_ = (f, .le'tor NIZ{!:o
1.f,*lo3N/c
!o''")
--
( D. o?o?rD) A
XP^
= A* <-'yilsoE-r,,o.lso=O
XF,
= -€t-or^1g.-4-_aiog5"-= -f (l.t"rotr'r7)-a,ir,45"
= -).5*
Problem 9
A neuhal conducting sphereis betweentwo parallel chargedplates,as shown in the Figure
below. Sketchthe electric field lines in the region betweenthe plates.Be sureto include the
effect of the conductingsphere.
E = A-5,tou11
-qo"
"t o=
-*\J