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Physics48 (Fail 2All)
Chapter22: Electric Fields
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" Whether
you thinkyou canor thinkyou can't,you're usuallyright." - HenryFord
"It is our attitudeat the beginningof a dfficult taskwhich, more than anythingelse,will afect ir
outcone." -William James
successful
's
"Thefirst and mostimportantsteptowatd successis thefeeling thal we can succeed."
NelsonBoswell
Reading: pages580- 596
Outline:
,
S/
= electricfield
introduction
= electricfield of a point charge
= eiectricfield lines (PowerPoint)
= electricfield from a dipole
binomialexPansion
= electricfield calcuiations
continuouschargedistribution
line of chmge
chargeddisk
> point chmgein an electricfield
+ dipole in an electricfieid (Readon your own)
ProblemSolvingTechniques
You shouldknow how to computethe electric freld ofa collection of point charges.Rememberthat
the sum of the individual fields is a vector sum.Add the x componentsto get the x componentof the
sum;addthe y componentsto getthe y componentof the sum.The magaitudeof the electricfield
producedby a singlepoint chargeq, at a point a distancer away,is given by E = lql/4nesf. This
must be multiplied by the sineor cosineof an angleto obtaina component.You must alsodetermine
the sign of the component.
Someproblemsdeal with electricfield lines. You shouldknow that the electric fie1dat aay point is
tangert to the line throughthat poinl that the numberof lines per unit areapassingtt['ough al area
perpendicularto the lines is proportionalto the magritudeof the field, andthat iines emanatefrom
positivechargeandendat negativecharge.
r.\_-,
'=.'
You will alsoneedto know that the force on a chargein an eiectric fieid is given by the productof
the chargeandthe field. For a positivecharge,it is in the direction ofthe field while for a negative
chargeit is directedoppositeto the field.
You shouldknow how to calculatethe electric field ofa continuousdistribution of charge.Usethe
linear or areachargedensityto write an expressionfor the chargein an infinitesimal region,then
,^,
carry out an integrationover tlre entirechargedistribution.Don't forgetthat the field is a vectorand V.
\-//
you mustevaluatean integralfor eachcomponentor, in specialcases,usesymmetryto showa fie1d
vanishes.
component
Someproblemsdeal with the trajectoriesof chargesin electric frelds.If the field is uniform, the
accelerationofthe chargeis cohstantandyou may usethe kinematicequationsof constantmotion.
The problemsarequite similar to projectile motion problems;however,the accelerationis now due
to the forceof electric field ratherthanto gravity.
You shouldknow how to calculatethe torque ofa uniform electricfieid on an electric dipole andthe
potentialenergyofa dipole in an electricfield. ln somecases,you areaskedfor the work that is
doneby the field on a dipole whenthe dipole tums. This is the negativeof the changein the
potentialenergy.
Questions and Example Problems from Chapter 22
QuestionI
The figure below showstwo protonsand an electronthat areevenlyspacedon an axis. Whereon the
axis (otherthan at an infinite distance)is therea point at which their net electric field is zero:to the
left of the particles,to their righ! betweenthe lwo protons,or betweenthe electronandtle nearer
proton? ^
" <-
Y'ff
pe-------+
P'
T"PP
la.
Question2
In the figure below, two particlesof charge-q arearrangedsymmetricallyaboutthe y axis; each
producesan electric field at point P on that axis. (a) Arc the magnitudesof the fields at P equal?
(b) Is eachelectricfield directedtowardor awayfrom the chargeproducingit? (c) Is the magnitude
of the net electricfield at P equalto the suurof the magnitudesE of the two field vectors(is it equal
to 2E)? (d) Do the x componentsof thosetwo field vectorsadd or cancel?(e) Do their y components
addor cancel?(f) Is the directionof the net field at P that of the cancelingcomponentsor the adding
components?(g) What is the directionof ttre net field?
(")
A)))
( b ) -'=.t.n;.z.'J\t
/c\
1}4
rJ)
tt,c.nn!
(")
44
(f )
WW
t?)
-1
olA,o-&"1
I
7
d'
Question3
The figure bplow showsthreenonconductingrods,onecircular andtwo straight.Eachhas a uniform
chargeof magnitudeQ alolg i151ephalf and anotheralongits bottom half. For eachrod, what ig the
direction ofthe net electric field at point P?
-t . - 1
(a)
\
\
t-,O\.tal,Ottz,l
(r)
-
(.)
-/\|LO'J ta^tzh
)
Question4
The figure below showstwo disksand a flat ring, eachwith the samer:niform chargeQ. Rank the
objectsaccordingto the magnitudeof the electric field they createat points P, geatest first.
d,D^a"..
M"**4
E =h. fa..;,;'.
v
o, b,c
(b)
{d)
Problem 1
In the figwe below,the four particlesarefixed in placeandhavechargesqr = !tr2= +5e, q3: +ls,
md q+: -12e.Distanced: 5.0 pm. Whatis the magnitudeof the netelectricfield at point P dueto
theparticles?
-) -$-c-.
a &r".f <9,o-o* "" E =iA"'+"
- l2,e
+seqqr
^ ,,,P,,,
-o'Fr,
Y)(.,
,,\,r
f^
o + ct\aL?a r-};,.,r^-,*l'a o{ -
, @ro'a k^t
Fp*;")
I'ar,"Xt
-)
Fr
-8-n
/:
v'
t#q
q, w".* n a <-a.n^a9**^>f1
*r;
+5e
\,
I
I
\-.,
4rit.L
*--.
A^;=c
/ t-ra"l- iJal )
(aa)'
,-*" (31,
J'/
- 3\t)
- o
Problem 2
In the figure below, the three particles are fixed in place and have chargesql = q2-; +e and qz: +2e.
Distancea: 6.00 pm. What arethe (a) magnitudeand (b) direction of the net electricfield at point P i.*
dueto the particles?g__i
_-_,
/_
,)
\\
T+.t
\
,l L .;oi
-)
)
A"tt
4""
o',
-b.i/io?t'4'ta-'';t"*'
-l
1Ii\
*'A E
At' *"A
A,
E^'ton"'"Lq"o"s
^ t''n"'Q)^"\ fue' ^J
xru a,wvq
)^*"#.g-2'^,-.
_
1-= a' c-oai56
t #"4'a-h^q^-*#€;
E = l.60,.goaNr/.
/r
\
n
I
(5)
' )?@^ln.o\l.o."M/\) y}ec;4nAte
Problem 3
-
4-;,a
Zr.t
O=?5"
;t
The figure below showsan electricdipole. What arethe (a) magnitudeand @) direction(relativeto
the positive directionof the x axis) of the dipole's electricfieid at point P, locateda distancer >> d?
F
\4
2
l-
t
-,t3'
X -tau'"y"n
E+
G 4\r.a-
@v^+a^Yd! UM.,
Ne"fur! K^"I^"'Ji "AA
E c.oeO
'll
----J
\o
"* (t/t)"
j'v"g
--
c/.)
5ld"r"
1-
-->'
E+
Etno
AL JJxn O
lr\2
^'.' f
| =L,,.'r]
J
L+fied Lca("a/
E^rx
I
4'rt"
&r, F>>J
(^)
(b)
ffi21,1'./>'
f r\ (16;'1:7'
.--
t%d
rr€.
f .j1 J t/a:
LI
?,
rI -
I
14
4rt.
c'*(d/)"
Problem4
In the figwe below, two'curvedplasticrods,one of charge+q andthe other of charge-q, form a
circle ofradius R = 8.50 cm in an xy plane.The x axis passest}rough both of the connectingpoints,
andthe chargeis distributeduniformly on both rods.Ifq = i 5.9 Oa, what arethe (a) magnitudeand
(b) direction (relativeto the positive directionof the x axis) of the electric field producedat P, the
center of the circle?
r-
)l-
-
=
-..P-
r-"
lTQ-
lr-
d.E--_----
\= %/t = 4/s
Jq
r
r
---)dg= aos
3= )s
--:'
l\l
)ds
qfie-
+ lo)"
4^"f b"ot "t -q'pa
:
t t3:@
4 X ,<nAtarrv'ta r.'dnz.La
o.td.
'=:
)' -,1,v-'eJ S
)^ rcvi*^blta
r\
) &-m'0'^^
rr^Ar*"") S =AErT
li
F
= -'t"t l<.
"7 tt ?o
q Tre" A
4^
\
---
4lrL"
E' 4;t!) +.a,1 rt^-.)
'E
n"l-
A=
t:^rde
=(
i;"(
!))
ltl
o
,^^,fP'"-y ,*,tutrA
( -3)
*g',ra /\4\y\eaa ufi,pnaaA
"A 4 cAa^4
/
-r f--JL {rrc." \
--\l
R).J
O,o?Sorr. _
\= %/r:+A=
\f -w"olu/ /
,/ L
a
= _r_- p- -[-r- (r)]=
+
\7 "r :2
l>;ry
\^-.D"OAJo
)
o
'.
-1
/ 5'o.ldra c rl(o"or5o r"r)--
5,6^/ 1i_" c/^
'...-...-'
( ra.r N/.)C3)
=
ts_*).t;'%l' [-J)
o.ogSofr)
Problem5
In the figure'below,positive chargeq: 7.81pC is spreaduniformly alonga thin nonconductingrod
of iengti L = 14.5cm. What arethe (a) magnitudeand(b) direction (relativeto the positive direction
ofthel axis)of the electricfield at poinl P, at distanceR: 6.00cm fiom the rod alongits
bisector?
perpendicular
r-- -Jdtr - 4rrt-
dI
r\
l,--.L
-
\,- l/t----:X=\L
dtr
\dx
qnt.
r\
JX='\J*
c'axuaA,
X -lraw'1.^luO c.-. +---&
Afiv.;!
F= tJ4 = ;il.
..
F=
t,a...,?-t tb d,Ad
\l
X dK-&MqO
F
J xaB-
_/A.l/n C, = ) - =
t-\
E
R
r
3N
4t€-
(
dx
i ("'*)
. X ^?.
x 16
t-+g1
XA
Lln €" '
(
\
)
- ,/r,
L/x
4x
=(^)*L
f ffi2"
Jx
dx
---.-.-
r*1st)%
E= !)j-
4t€.
\R
4-nt.
/
\, -3"r.^ )v'.,3-.*t*Jt.t
-,r^tltffith:a X=qtq\&
S: ?.f lx1c,?C
| = o' l'l5r"r
|
L 4^(r'tB
-l-J 4^d*,hfr,t
,'l/
L
i{Lz,6h)'^
4" = AtU
I
E,4: D.ot.orr
^^^!)-b": X){-)O
-->
4nt- A
L7,r,4^
E = lX."f N/c ^r"fu.rrd"d
(rr.rN7")
5'
7
Problem 6
A disk of radius2-5 cm hasa surfacechargedensityof 5.3 1tC/m2on its upperface.What is the
magnitudeofthe electric field producedby the disk at a point on its cenualaxis at distance
z: 12cm from the disk?
It
A= 2-5t, = o.ox 5r'r
Z=
l3.tcr'= O.lO.rn
E=*e,(,-ft")
f = 5,3* iu' cl*+
:
D,larq
s.3"lo "%n')
[ , -'[^= (,(*fic"%_,)
L' 6ffi
[ ^--:Y'rJ
J
-'1
,
Problem 7
At what distancealongthe centralperpendicularaxis ofa uniforrniy chargedplastic disk of radius
0.600m is the magnitudeofthe electricfield equalto one-halftle magrdtudeofthe field at the
centerof the surfaceof the disk.
r!l
d/4A I Z -o ao E -- /aL.
=) o* c-Jth at br^5"4'.6
fl
E= V^,-(r-/ra;)
-l:-z,,&.
L +& ", "l*^tqA
,,* *r"^i z zotrl,.l E= t/x(7'..) -'
r-3-I
r---a<
It
= '/x +
-
/l-J
Z
| 214'
----r1l
7ae-(t-A)
o.,z'--nEia-t -.
: '/r(Y^r)
a
4 z^= E\ R
z"= B7s---4 z= Ytrg -=}$lr
{z'rA"
Problem8
O.396r,
A chargedcloud systemp.roducesan electricfield in the air nearEarth'ssurface.A particle of charge
-2.0 x 10-eC is actedon by a downwardelectrostatic
forceof 3.0 x 10-6N whenplacedin this field.
(a) What is the magnitudeof the electricfield? What arethe (b) magrdtudeand (c) direction of the
electrostaticforceFelexertedon a protonplacedin this field? (d) What is the magnitudeofthe
gravitationalforce F, on the proton?(e) What is the ratio of F"1/F in this case?
/^\ /-.
= - ^F --. EF-P^=t3'"ij9't)3
- ,/\'
(aJ
%b
_a'Oio* c
--)
tc/
v
'".)
( l.uoa'.'to (Z.so.'PtN/.) i
\ J'
(a"q,.to 'nn)
i
I^\
( J) h " = Y ) q --/||
r-r. r^-)^7 v.\tr.b'l"
(
'to
lO--'fh)11.8o-ls'):
t") Fy'Fu =
E-Q.5o " tD9nr,/ef
4
6.
LI i' u r n - l b r . r
lv
l\
l.6q *l.5toN
/,5 * lo'o
|,rr1* ld"N
),^tt ^,"4
\
\ ,\
Problem9
A 10.0g blockwith a chargeof +8.00x 10-5C is placedin electricfield E=(SOOOi-OO}hN/C . -^
What arethe (a) magnitudeard (b) direction (relativeto the positive directionof the x axis) of the
\J.
=
(d)
y
(c)
are
its
x
and
the
origin
at
t
0,
what
is
released
from
rest
at
Ifthe
block
force on the block?
coordinates
at t = 3.00s?
f]
-OF.^
_
0rvv,lL)
L_
: f? "oox i n / N
E
1.; I (u)
{.'tt- ('-oo.lo'rVt)1
io}rr/c)i;l
%E = ( 7.oo*ldEc] f( z.oo*tolub)e- {c.oo,.
E-
(o.avo1.r)
? - (c.o+:,x;i
=
&= r'& \ o.a,roN/
= -,l1"3"I
la-----;6-D
tr=m=@
=
c:)J".=*u o#,fi'
?:;fr=
-o'T:;8;+
( d)
=-'1!&'
at =
i
LLlo
t:;3J"1,
P"obl"mi6
E/n=
t-
-, / - D'o'r6N \
'
X = X"* Vo*f *'lactyi,"'
a = l^(ll"t1)'(3.oo')a
{ = lD8ro
3"oos
=J:e1.6. j
\/ l _=t/a.aot^
-4
An electronwith a speedof 5.00x 108cmlsentersan electricfieid of magnitude1.00x 103N/C,
-t
traveling alongthe fieid lines in the directionthat retardsits motion. (a) How far will flre electron
travel in the field beforestoppingmomentarilyand(b) how muchtime will haveelapsed?(c) If the
region with the elec.tricfreld is only 8.00mm long (too shortfor the electronto stopwithin it), rn'hat
fraction of the electron'sinitial kinetic energywill be lost in that region?
V : 5"oo^lobh/s
Vj* ),a (x-x") ---
E -- l" ooi loaN//
X - Xo:
-u]/^o
o
/"
tr/^:
l4l=
( i . r l xt o - q K
' t)
lql= l.?6*lo'q'e/s*--,
y-Xo=
- (5.oo"tou.1s)'
(- t' ?{, t o'e"/s9
"
712'* lo-ettt
- 5 . o o { l o Lo f 5
\ DJ
(c)
e = - 1 " ? 6 rl o ' e r / s r
- 1.11n16't*7r'
"
-DIL-z
KF.
AfgC = 7a'n(av)"
.= 4-'
'/a
7e'"'1|
V'.-voa
= e.e(nx)
AV._.
?.4(nx)
\t-
tVo'
'
tU
,
-\
.
A ( - l.tr"" I o'l"r/s ") ( t.oo^ toa^)
'
f - x.gs*lo-es
( E.oox loo
"/s")
-
rr
f az
| lb Q r/6