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706
Electric Potential
CHAPTER 21
Questions 23 through 27
refer to Figure Q21.23,
which s hows equ ipotential lines in a region of
space. The eq uipotent ial
lines are spaced by the
same difference in poten tial , and several of the
pOientials are give n.
23. I What
is
the
potential at point c?
,
,
loqv" ..
,
o
,
,.,
ov
--b. - --
28. I A bug zapper co nsists o f two metal pl ates con nected to a
hi gh- vo ltage power supply. The vo ltage between the plates is
set to g ive an e lectric field sli ghtly less than I X 106 VIm.
When a bug ni es between the two plates, it increases the field
enough to initiate a spark that inc inerates the bug. If a bug zapper has a 4000 V power supply, what is the approximate separation between the plates?
A. 0.05 em
B. 0.5 em
C. 5 em
A. - 400 V
B. -350 V
FI G URE 021 .23
C. - IOOV
D. 350 V
E. 400V
24. I At which point, a, b, or c, is the magnitude of the electric
field the greatest?
25. I What is the approximate magnitude of the eJectric field at
point c?
A. 100 Vim
B.300V/m
C. 800 Vim
D. 1500 Vim
E. 3000 Vim
26. I The direction of the e lectr ic field at point b is closest to
which direction?
A. Right
B. Up
C. Left
D. Down
27. II A + 10 nC c harge is moved from point c to point a. How
much work is req uired in order to do thi s?
A. 3.5 X 10- 6 J
B. 4.0 X lO- 6 J
C. 3.5 X 10- 3 J
3
D. 4.0 X 10- J
E. 3.5 J
D. 50cm
29. I An atom of helium and one of argon are sin gly ion ized-one
elec tron is removed from eac h. The two io ns are then accelerated from rest by the elecuic field between two plates with a
potential difference of ISO V. After accelerating from one plate
to the other,
A. The helium ion has more kinetic energy.
8. The argon ion has more kinetic energy.
C. Both ions have the same kinetic energy.
D. There is not e nough information to say which ion has more
kinetic energy.
30. II The dipole mome nt of the heart is shown
Bl0 at a particular in sta nt in Figure Q2 1.30.
Which of the foUowing potentiaJ differences
will have the largest positive val ue?
A. VI - V2
8 . VI - V3
C. V2
-
VI
D. V) - VI
FIGURE 021.30
PROBLEMS
Section 21.1 Electric Potential E nergy and E lectric Potential
Section 21.2 Sources of Electric Potential
I. III Moving a charge fro m po int A, where the potential is 300 V,
to po int B, where the potential is ISO V, takes 4.5 X 10-1 J o f
work. What is the value of the charge?
2. 1111 The graph in Figure P21.2 shows the electric potential energy
as a function of separation for two point charges. If one charge
is +0.44 nC, what is the other charge?
o 012
3 45678910
r (em)
-2
-4
- 6
FIGURE P21 .2
3. III It takes 3.0,uJ of work to move a 15 nC c harge from point A
to B. It takes -5.0,uJ of work to move the charge from C to B.
What is the potential difference Vc - VA?
4. I A 20 nC charge is moved from a point where V = 150 V to a
point where V = - 50 V. How much work is done by the force
that moves the c harge?
5. I At one point in space , the electric pote ntial energy of a 15 nC
charge is 45 ,uJ.
a. What is the electric potential at this point?
b. If a 25 nC charge were placed at this point, what would its
electric potential e nergy be?
Section 21.3 Electric Potential and Conservation of Energy
6. I An electron ha s been accelerated from rest through a potential difference of 1000 V.
a. What is its kinetic energy, in elec tron volts?
b. What is its kinetic energy, in joul es?
c. What is its speed?
7. I A proton has been accelerated from re st through a potential
difference of - 1000 V.
a. What is its kinetic energy, in electron volts?
b. What is its kinetic energy, in joules?
c. What is its speed?
8. 11111 What potential difference is needed to accelerate a I-Ie+ io n
(charge +e, mass 4 u) from rest to a speed of 1.0 X lOb m/s?
9. II An electron with an initial speed of 500,000 mls is brought to
rest by an electric fi eld.
a. Did the electron move inlO a region of hi gher po tentiaJ or
lower potential?
b. What was the potentiaJ difference that stopped the electron?
c. Wh at was the initial kinetic e nergy of the electron, in electron volts?
Problems
10. III A pro to n with an initi al speed of 800,000 mls is brought to
rest by an electric field.
a. Did the proton move into a region of hi gher poten ti al or
lower po ten ti aJ?
b. What was the poten tial difference that stopped the proton?
c . What was the initi al kinetic energy o f the proton, in elecU"on
volts?
Section 21.4 Calculating the Electric Potential
707
19. II a. What is the potential difference betwee n the terminal s of
an ord inary AA or AAA battery? (If you'rc not surc, find
one and look at the labe l.)
b. An AA battery is con nected to a parallel-plate capac it or
hav in g 4.0-cm-diameter pl ates spaced 2 mill apart. How
much charge does the battery move from one pl ate to the
other?
Section 21.5 Connecting Potential and Field
11. II The electric potential at a po int that is halfway betwee n two
ident ical charged particl es is 300 V. What is the potential at a
point that is 25 % ofthc way from one particlc to the other?
12. II A 2.0 cm X 2.0 cm parallel-p late capac itor has a 2.0 mm
spac in g. The elcctric ficld stre ngth ins ide the capac itor is
1.0 X 10' Vim.
a. What is the potenti al difference across the capac itor?
b. How much charge is on eac h plate?
L3. III Two 2.00 cm X 2.00 cm plates that form a parallel-plate
capaci tor are charged to ± 0.708 nCo What are the electric fi eld
sU"ength inside and the potential difference across the capacitor if
the spacing betwcen the pl ates is (a) 1.00 mm and (b) 2.00 nun ?
14. J a. In Figure P2 1. 14, which capaci tor pl ate, le ft or right, is the
positive plate?
b. What is the electric field strength in side the capacitor?
c. What is the potential energy of a proton at the midpo int o f
the capacitor?
ov
300 v
20. II a. In Figure P21. 20, which po int, A o r S, has a hi g her electri c potential?
b. What is the potenti al difference between A and B?
E [ ~ ~ V/Ill
~ -.,...;
B.
-7.0
E = 1200 VIm
~h
/
(Ill
M '
FIGURE P21 .21
FIGURE P21.20
2 1. III In Fi gure P2 1.2 1, the elec tri c potential at po int A is - 300 V.
What is the potential at point B, w hi c h is 5.0 e m to the ri ght
o f A?
22. II What is the pote nti al diffe re nce between Xi = 10 cm and
X f= 30 cm in thc uniform e lectric fi e ld Ex = 1000 VIm?
23. I What are the magni tude and direction of the electri c field at
the dot in Fi gurc P21.23?
3.0mm
y
1.0 ern
I.Oem
1.0em
------
,
1.0 em
•
,,
200 V
,
,
looV 200V
FIGURE P21.14
IS.
A +25 nC charge is at the origin.
What are the radii of the 1000 V, 2000 V, 3000 V, and 4000 V
eq uipotential surfaces?
b. Draw an cquipotenti al map in the xy-plane show in g th c
charge and these four surfaces.
a. Wh at is the electric potential
16.
"
%
2 Ocm "" \
I
at point s A, B, and C in
" 10em
..,
FigureP21.16?
AI
B ;
,2.0nC "
b. What is the potent ial energy
,,
-.o f an electron at each of these
points?
c
c. What are the potent ial differFIGURE P21 .16
ences .6.VAB and .6.VBC ?
17. III A I.O- mm-di ameter ball bearing has 2.0 X 109 excess electron s. What is the ball bearin g's potential?
18. II What is the elec tri c poten tial at the po int indi cated with th e
dot in Figure P2 1.1 8?
a.
,,~
-
2.0 nC
2.0 nC
@- ------ (!)
I
,
3.0em
I
,
(!)--------.
FIGURE P21.18
ov
45'
2.0 nC
oV
100 V
FIGURE P21 .23
200
v
- 200 V
FIGURE P21 .24
24. I What are the magnitude and direction of th e electric field at
the dot in Figurc P21.24?
-
Section 2 t.6 The Electrocardiogram
~L
25 . I Onc standard location fo r a pair
BID o f el ectrodes during an EKG is
shown in Figure P21.25. The potenti al difference 6. V ) I = V) - V I is
recorded. For eac h of the three
instants a, b, and c during the heart's
cycle shown in Figure 2 1.29. will
a V31 be pos iti ve or negat ive? FIGURE P21 .25
Explain.
26. I Th rce e lccU"odes, 1- 3, are atBID tach ed to a patient as show n in
Figure P21 .26. During ventri cu lar
depolarization (see Fi gure 2 1.29),
across whi ch pair of elec trodes is
the magn itude of the potenti al difference likel y to be the small est?
Explain.
'\ ~·r
FIGURE P21 .26
708
CHAPTER 21
Electric Potential
Section 21.7 Capacitance and Capacitors
27. III Two 2.0 em X 2.0 em sq uare aluminum electrodes, spaced
0.50 mm apan , are connected to a 100 V battery.
a. What is the capac itance?
b. What is the charge on the pos iti ve elec trode?
28. III An unc harged capac ito r is co nnec ted to the termi nals of a
3.0 V battery, and 6.0 j.LC flows to the positive plate. The 3.0 V
battery is the n disconnected and re placed with a 5.0 V ballery,
with the positi ve and negat ive terminal s connected in the same
ma nner as before. How much addi tio nal c harge flows to the
positive plate?
29. III You need to con struct a 100 pF capac itor for a sc ience project. You plan to cut two L X L metal squares and place spacers
between them. The thinnest spacers you have are 0.20 mm
thick. What is the proper value of L?
30. I A sw itch th at con nec ts a battery to a 10 j.LF capaci tor is
closed. Seve ral secon ds later yo u find that the capac itor pl ates
are charged to ± 30 j.Lc. What is the battery voltage?
3 1. I What is the vo ltage of a battery that will charge a 2.0 j.LF
capacilor to ± 48 j.LC?
32. I Two elec trodes con nected to a 9 .0 V battery are charged to
± 45 nCo What is the capacit ance of the electrodes?
33. I Initiall y, the switch in Figure P21.33 is o pen and the capac itor is uncharged. How muc h charge now s through the sw itch
after the sw itch is closed?
40. II A pair of 10 j.LF capac itors in a hi gh-power laser are charged
to 1.7 kY.
a. What charge is stored in each capaci tor?
b. How much energy is stored in eac h capacitor?
4 1. I Capac ito r 2 has half the capac itance and twice the potenti al
difference as capac itor I. What is the ratio (Udl/(Uch?
42. 1111 Two uncharged metal spheres, spaced 15.0 cm apart, have a
capac itance of 24.0 pF. How Illuch work would it take to move
J 2.0 nC of charge from one sphere to the ot her?
43. 1111 50 pJ of energy is stored in a 2.0 cm X 2.0 cm X 2.0 cm region
of uniform electric field. What is the electric field strength?
General Problems
44. II A 2.0-cm-di ameter paraHel-plate capacitor with a spac in g of
0.50 mm is c harged to 200 V. Wh at are (a) the total e nergy
stored in the elec tric field and (b) the e nergy density?
45. III What is the c han ge in e lectric po te ntial energy o r a 3.0 nC
point charge when it is moved from point A to point B in
Figure P21.45?
oA
5.0 em
AVD = 50V
25.0 nC
®
oB
1.5 em
FIGURE P21 .33
Section 21.8 Dielectrics and Capacitors
34. II A 1.2 nF parallel-plate capac itor has an air gap between its
plate s. It s capac itance increases by 3.0 nF when the gap is fiJled
by a dielectri c. What is the dielectric constant of that dielectric ?
35. III A sc ience- fair radio uses a homemade capacitor made of
two 35 cm X 35 cm sheets of alumi num foil separated by a
0.2S-mm-thick sheet of pape r. What is its capac ita nce?
36. III A 25 pF parallel-plate capac it or with an air gap betwee n the
plates is con nec ted to a 100 V battery. A Teflon sl ab is then
in sefl ed between the plates and com pl ete ly fill s the gap. What
is the change in the charge on the positi ve plate when the Teflon
is in serled?
37. II Two 2.0-c m-d iameter electrodes with a O. IO-mm -thi ck sheet
of Tenon between them are all ached to a 9.0 V battery. Without
di sco nnect in g the battery, the Teflo n is removed. What are the
c harge, potential difference, and electric field (a) befo re a nd
(b) after the Tefl on is removed?
38. 11111A capac itor with its plates separated by paper stores 4.4 nC of
charge whe n it is connected to a paflicular baltery. An otherwise
identical capacitor, but with its plates separated by Pyrex glass,
is conn ected to the same battery. How much charge does that
capaci tor store?
FIGURE P21 .45
FIGURE P2 1.46
46. II What is the pote ntial differe nce !:J. V34 in Figure P2 1A6?
47. II A-50 nC charged pani cle is in a uniform e lec tric field
INT E = ( 10 V1m, cast). An external force moves the particle 1.0 m
nonh, then 5.0 m east, then 2.0 m south, and fin all y 3.0 m west.
The particle begins and ends its mot ion with zero veloc ity.
a. How much work is done on it by the ex ternal force?
b. What is the potential difference between the particle's fi na l
and initi al positions?
48. II At a di stance r from a po int c harge, the electr ic pote nti a l
INT is 3000 V and th e magni tude of the electric field is
2.0 X 10' Vim.
a. What is the di stance r?
b. What are the electric potent ial and the magn itude o r the
elec tric fie ld at di sta nce rl2 from the charge?
49.
What is the electric po ten tial e nergy of the electron 111
Figure P21A9 ? The protons are fixed and can' t move.
®
1
:O.50nm
/
Proto ns L - -- - - - - - - - -- - - -e
2.0nm
1
: 0.50 nrn
\
FIGURE P21 .49
Section 21.9 Energy and Capacitors
39. III To what potent ial sho uld you charge a 1.0 j.LF capaci tor to
store 1.0 J of energy?
Electron
\
(t)
50. 1111 Two point charges 2.0 cOl apart have an electri c potential
e nergy - 180 j.LJ. The total charge is 30 nC. What are the two
charges?
Problems
5 1. II Two positive point charges are 5.0 cm apart. If the electri c
INT potenti al energy is 72 pJ, what is the magn itude of th e force
between the two charges?
52. 11111 A +3.0 nC charge is at x = 0 cm and a - 1.0 nC charge is at
x = 4 cm. At what poi nt or points on the x·ax is is the electr ic
potent ial zero ?
53. 11111A -3.0 nC charge is on the x-axi s at x = - 9 cm and a
+4.0 nC charge is on the x·ax is at x = 16 cm. At what poi nt or
points on the y·ax is is the electric poten ti al zero?
54. II A -2.0 nC charge and a +2.0 nC charge are located on th e
INT x·ax is at x = - 1.0 cm andx = + 1.0 cm, respectively.
a. At what position or positi ons on the x·ax is is the electri c
rie ld zero?
b. At what position or posi tion s on the x-axis is the electric
potenti al zero ?
c. Draw graph s of the electri c field stre ngth a nd the electr ic
potential along the x-ax is.
55. III A - 10.0 nC point charge and a + 20.0 nC point charge are
INT 15.0 cm apart on the x-axis.
a. What is the electric pote ntial at the point on the x-ax is
where the electric rield is zero?
b. What are the magnitude and direct ion of the e lectri c field at
the point on the x·axis, between the charges, where the clee·
tric potential is zero?
56. 11111A 2.0- mm -diam eter glass bead is positi vely charged. Th e
potenti al difference between a point 2.0 mm from the bead and
a point 4.0 mm from the bead is 500 V. What is th e charge on
the bead?
57. I In a se miclass ical mode l of th e hydroge n atom, th e electron
orb its the proton at a di stance of 0.05 3 nm .
a. What is the e lectri c potential of the proton at the position of
the electron ?
b. What is the e lectro n's poten tial energy?
58.
What is the elec tric potential at the point indi cated with the
dot in Figure P21.58?
10nC
2.0 nC
~
,,
3.0 em
,,
,
,, , ,
I
\
•
,,
3.0 em
4.0em
,
I
,
,
I
,
G---------3.0 em
- l.OnC
- S.OnC
~ -2.0~n;--
.- - - - - -. A
S.OnC
- l.OnC
FIGURE P21 .S8
FIGURE P21 .S9
59. I a. What is the electric potenti al at point A in Fi gure P21 .59?
b. What is the potential energy of a proton at point A?
60. III A proton 's speed as it passes poin t A is 50,000 m/s. It foll ows
the trajectory shown in Figure P2 1.60. What is the proton's
speed at point B?
,
,,
,
,,
,,
,,
,,
~
, '
,
1
FIGURE P21.60
I
,
,'
30 Y
lOY
8 1
,,
- lOY
709
6 1. II Electric outlets have a vo ltage of approximate ly 120 V
between the two parallel slots. Est im ate the elec tri c fi e ld
strength betwee n these two slots.
62. I Est im ate the magnitude of the e lectric fi eld in a ce ll memBID brane with a thickness of 8 nm.
63. II A Na+ ion moves from ins ide a cell , where the electri c potenBID tial is -70 mV, to outside the ce ll , where the potenti al is 0 V.
What is the c hange in the ion 's elec tric potential energy as it
moves from in side to outside the ce ll ? Does its energy in crease
or decrease?
64. III Suppose that a mol ec ular ion with c harge - IOe is embedBID ded withi n the 5.0-n m-thi ck cell membrane of a cell with
membrane potenti al -70 mV. What is the e lectric force on the
molecule?
65 . III The e lectr ic fi e ld strength is 50,000 VIm in side a parallelplate capac itor with a 2.0 mm spac ing. A proton is released
from rest at the pos iti ve plate. What is the prolon's speed when
it reaches the negat ive plate?
66. 11111 An alpha particle (the nucleus of a helium atom, wi th charge
INT +2e and a mass four times that of a proton) and an ant iproton
(w hi ch has the sa me mass as a proton but charge -e) are
released frolll rest a great di stan ce apart. They are oppos ite ly
charged, so eac h acce lerates toward the other. What are the
speeds of the two parti cles when they are 2.5 nm apart?
Hint: You' ll need to use tlllO conservat ion laws. And what does
"a great di stance" suggest about the ini tial val ue of r?
67. III A proton is released from re st at th e pos iti ve plate of a
parallel:plate capac itor. It crosses the capac itor and reaches the
negati ve plate with a speed of 50,000 m/s . Wh at will be the proton 's fin al speed if the ex perime nt is repeated with do uble the
amou nt of charge on each capacitor plate?
68. II The e lectric fi e ld streng th is 20,000 VIm in side a parallelplate capac itor with a 1.0 mm spacin g. An electron is released
from rest at the negative plate. What is the e lectron 's speed
when it reaches the positi ve pl ate?
69. II In the early 1900s, Robert Mill ik an used small charged
INT droplets of oil , suspended in an elect ri c fi e ld, to make the first
quantitat ive measurements of the e lectron 's charge. A 0.70-pmdiameter droplet of oil, hav in g a charge of +e, is suspe nded in
mida ir between two horizontal plates of a parallel-p late capacitor. The upward electric Force on the droplet is exactly balanced
by the downward force of gravit y. Th e o il has a dens it y of
860 kg/m3, and th e capac itor plates are 5.0 mm apart. What
mu st the potential difference between the pl ates be to hold the
droplet in equilibrium ?
70. 1111 Two 2.0-cm-d iameter di sks spaced 2.0 mm apart form a parall el- plate capac itor. Tbe e lectric fi e ld between the disks is
5.0 X 10' Vim.
a. What is the voltage across the capac itor?
b. How much charge is on each di sk?
c. An electron is launched from the negati ve plate. It strikes
the positive plate at a speed of 2.0 X 107 m/s. What was the
electron's speed as it left the negative plate?
7 1. II In p rotorl-bea m therap)', a hi gh-ene rgy beam of protons is
BID fired at a tumor. The proton s come to rest in the tumor, depositing the ir kinet ic energy and breakin g apart the tumor 's DNA,
thus killin g its cell s. For one pat ient , it is desired that 0. 10 J of
proton energy be deposited in a tumor. To create the proton
beam, the proton s are acce lerated from rest th rough a 10 MV
potential difference. What is the total charge of the protons th at
must be fired at the tumor to deposit the required energy?
710
CHAPTER
21
Electric Potential
72. 1111 A 2.5-mm-diameter sphere is charged to - 4.5 nCo An e lectron fired directly at the sphere from far away comes to within
0.30 mm of the surface of the targe t before being reflected.
a. What was the electron's initial speed?
b. At what distance from the surface of the sphere is the electron 's speed half of its initial value?
c. What is the acceleration of the electro n at its nlrning point?
73.
A proton is fired from far away toward the nucleu s of an iron
ato m. Lron is e lement number 26, and the diameter of the
nucleus is 9.0 fm. (1 fm = 10- 15 m.) What initial speed does the
proton need to just reach the surface of the nucleus? Assume the
nucleus remains aL rest.
74. II Two 10.0-cm-diameter electrodes 0.50 cm apart fonn a parallel-plate capac itor. The electrodes are attached by metal wires to
the tenninals of a 15 V bauery. After a long time, the capac itor is
di scon nected from the battery but is not di scharged. What are
the charge on each electrode, the electric field strength in side the
capac itor, and the potential difference between the electrodes
a. Right after the battery is disconnected?
b. After in sulatin g handl es are used to pull the e lectrodes
away from each other until they are 1.0 cm apart?
75.
Two 10.0-c m-diameter electrodes 0.50 cm apart form a parallel -plate capaci tor. The electrodes are attached by metal wires
to the terminal s ofa IS V battery. What are the charge on eac h
electrode, the electric field strength inside the capacitor, and the
potential difference between the electrodes
a. While the capacitor is attached to the battery?
b. After in sulatin g handles are used to pull th e e lectrodes
away from each other until they are 1.0 cm apart? The electrodes remain connected to the battery during thi s process.
76. III Determine the magnitude and direction of the e lectric field at
points I and 2 in Figure P21. 76.
FtGURE P21 .76
77. I Figure P21. 77 shows a series of eq uipotential curves.
a. Is the electric field stren gth at point A larger than , smalJ er
than , or eq ual to the fi eld strength at point B? Exp lain.
b. Is the e lectric fi eld strength at point C larger than , small er
than , or equal to the field strength aI point D? Explain.
c. Determine the electric fi eld if at point D. Express yo ur
answer as a magnitude and direction.
25
50
50
50
78. II Figure P2U8 shows the
electri c potential on a grid whose
squares arc 5.0 em on a side.
50
75
1(>0
50
c
a. Reproduce this figure on
•
B
your paper, then draw the 50 A 75
100
100 • 50
•
50 Y, 75 Y, and 100 Y equ i0•
potent ial surfaces.
50
100
50
25
75
b. Estimate the electric field
I
(strength and direction) at
6
25
50
50
50
points A, B, C, and D.
Potential in V
c. Draw the electric field vcctors at points A. B. C, and D FIGURE P21 .78
o n your diagram.
79.
The plates of a 3.0 nF parallel-plate capac itor are each
0.271112 in area.
a. How far apart are the plates if there's air between them?
b. If the plates are separated by a Teflon sheet, how thi ck is the
sheet?
80. 1111 The dielectric in a capac itor serves two purposes. It in creases the capac itance, compared to an otherwise ident ica l
capac itor with an air gap, and it increases the maximum pote nti al difference the capac ilor can support. If the electri c fi eld in
a material is suffi ciently strong, the material will suddenl y
become ab le to conduct, creat in g a spa rk. The critica l field
strength.. at which breakdown occurs, is 3.0 MV/m for air, but
60 MY/Ill for Teflon.
a. A parallel-p late capac itor cons ists of two sq uare plates ,
15 cm o n a side, spaced 0.50 111m apart with only air
between them. What is the maximum energy that can be
stored by the capac itor?
b. What is the maximum energy that can be stored if the plates
are separated by a 0.50-t11m-thick Teflon sheet?
8 1. 11111 The flash unit in a camera uses a special circuit to "step up"
INT th e 3.0 V from the batteries to 300 V, which charges a capac itor. The capac itor is then discharged through a fJa shlamp.
The di sc harge takes 10 /-Ls, and th e average power dissipated
in the flash lamp is 105 W. What is the capac itan ce of the
capac itor?
I
"
In Problems 82 through 85 you are given the eq uati on(s) used to
solve a probl em. For each of these,
a. Write a real ist ic probl em for which thi s is the con'ect equation(s).
b. Fini sh the so luti on of the problem.
(9 .0 X 10' N . m' /C' )q ,q,
82. I
90 X 10-' J
0.030 m
q, +q,= 40nC
83. II !( 1.67 X 10- 27 kg)(2.5 X 10' mI, )' + 0 =
!( 1.67 X 10- 27 kg)",' +
(9.0 X 10' N • m' /C' )(2.0 X 10 ' C)(1.60 X 10 " c)
0.0010
y(cm)
2
84. II
~v
,,
, "A , . . _0 v
,, ,,, ,
_-- - 1 V
,
,' 8..{"
"'
e C_--- - 2V
I
, T 'f
I
I
'0 '
"
-
FIG URE P21. 77 oto~~0'C~-'--------C2 x (em)
In
(9 .0 X 10' N' m' /C' )(3.0 X 10- 9 C)
0.030 m
(9 .0 X 10' N· m' /C' )(3.0 X 10- 9 C)
(0.030 m) + d
+
1200Y
R5 . II 400nC = ( IOOY)C
(8.85 X 10- 12 F/m)(O.IO
In
X 0.10 m)
C = ~------~~------~
d