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668
CHAPTER 20
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;.:;./
Electric Fields and Forces
Fo r homewo~k assig~ed on MasteringPhysics, go t o
Problems labeled
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chapters;
INT
integrate sig nificant material from earlier
BID are of biological or medical interest.
Problem difficulty is labeled as I (straightforward) to 11111 (c halleng ing).
0,0
•
QUESTIONS
Conceptual Ouestions
I. What is alike abollt charges when we say "two like charges"?
Do they look, smell , or taste the same?
2. Four lightweight balls A, B, C, and Dare sllspended by threads.
Ball A has been touched by a plastic rod that was rubbed with
wool. When the balls are brought close together, withom·touching, the following observations are made:
• Balls B, C, and 0 are allracted to ball A.
• Balls Band 0 have no effect on each other.
• Ball B is attracted to ball C.
What are the charge states (posi tive, negative, or neutral) of
balls A, S, C, and D? Explain.
3. Plastic and glass rods that have been charged by rubbing with
wool and silk, respectively. hang by threads.
a. An object repels the plastic rod. Can you predict what it will
do to the glass rod? If so, what? If not, why not? Explain.
b. A different object attracts the plast ic rod. Can you predict
what it will do to the glass rod? If so, what ? If not, why not?
Explain.
4. a. Can an insulator be charged? If so, how would you charge an
insulator? If not. why not ?
b. Can a cond uctor be charged? if so, how would you charge a
conductor? If not, why not ?
5. When yo u take clothes out of the drier right after it stops, th e
clothes often stick to your hands a nd arms. Is your body
charged? If so, how did it acqu ire a c harge? If not, why does
thi s happen ?
6. A lightweight metal ball han gs by a thread. When a charged rod
is held near, the ball moves toward the rod , touches the rod,
then quickJy "fl ies away" from the rod. Ex plain this behavior.
7. As shown in Figure Q20.7, metal
A
B
sphere A has 4 unit s of negative
charge and metal sph ere B has 2
Touch
units of positi ve c harge. The two
spheres are brought into co ntact. FIGURE 020.7
What is the final charge state of
eac h sphere? Explain.
8. Figure Q20.8 shows a positively
charged rod held near, but not touching, a ne utral metal sphere.
a. Add plusses and minu ses to the
figure to show the charge di stribution on the sphere.
b. Does the sphere experience a net FIGURE 020 .8
force? If so, in which direction?
Explain.
10
9. A plastic balloon that has been rubbed with wool wiU stick to a
wall.
a. Can you conclude that the wall is charged? If not , why not?
IJ so, where does the charge come from?
b. Draw a charge diagram showi ng how the balloon is held to
the wall.
10. You are given two metal spheres on portable in sulatin g stand s, a
glass rod , and a piece of silk. Explain how to give the spheres
exactly eq ual but opposite charges.
II. A honeybee acquires a positive e lectric charge as it flies
BID through the air. Thi s charge causes pollen grain s to be attracted
to the bee. Explain, using words and diagrams, how a neutral ,
cond ucting pollen grain will be attracted to a positi ve ly charged
bee.
12. A metal rod A and a met al sphere B, on in sulatin g stand s,
touch each ot her as shown in Fi gure Q20.12. They are originally neutral. A positi ve ly charged rod is brought near (but not
touching) the far end of A. While the charged rod is st ill close,
A and B are separated. The charged rod is then withdrawn. Is
the sphere then positi ve ly charged, negatively charged, or neutral ? Exp lain.
~
FIGURE 020 .12
~
~A==::::J(s)
I
C = '
')(
y
13. Each part of Figure Q20.1 3 shows two points near two charges.
Compare the electric fi e ld strength s EI and £2 at the se two
points. Is EI > E2, E1 = E2, or EI < E2?
(, )
0
(h)
•,
0
•2
0
•2
,.
•2
0
(e)
0
•
•
(d)
(e)
•
0
•
0
(I)
•,
ED
FIGURE 020 .13
•2
e
•
•
2
Que s tions
14. Ion tophores is is a non invas ive
669
Multiple-Choice Questions
BID process that transports drugs
c
15.
16.
17.
BIO
18.
thro ugh the s kin without need les.
In the photo, the red elec trode is
pos iti ve and the b lac k e lec trode
is negati ve. Th e e lectri c ri eld
between th e electrodes w ill drive
the negati vely c harged mo lec ules
of an anest heti c through the
s kin . Sho uld the drug be placed
at the red OJ the black electrode?
Ex pl a in .
Rank in order, from largest 10
small est, not in g an y ti es, the d ec·
tr ic fi e ld strengths E I to £~ a l po in ts
1 to 4 in Fi gure Q20 . 1S.
A 10 nC charge sits at a poinl in
space whe re the mag ni tude of the
electr ic fi eld is 1200 N/C. Wh at
FIGURE Q20 .15
wiLl the magn itude of the fi e ld be if
the 10 nC charge is re placed by a 20 nC charge?
When DNA breaks in to fragment s in a cell , electrostatic forces
may actually inhi b it repair. Ex plai n why thi s happe ns.
A ho ll ow soda straw is uniformly c harged, as s how n in
Fi gu re Q20 . 18. Wh at is the elec tric field at the center (ins ide)
of the straw? Ex plain .
23. I Two lightweight. elec trica lly neutral co nd uctin g ba Us hang
from threads. Choose the d iagram in Fi gure Q20.23 that shows
how the baUs hang after:
a. Both are to uched by a negati vely charged rod.
b. Ball 1 is touched by a negat ive ly charged rod and ball 2 is
touched by a pos iti vely charged rod.
c. 8 0th are touched by a negati vely charged rod but ba ll 2
picks up more charge th an ball I.
d. O nl y ball 1 is touched by a negative ly charged rod.
Note that parts a through d are indepe ndent; these are not
actions taken in sequence.
c.
B.
A.
2
I
2
E.
D.
2
2
2
FIGURE 020 .23
24. I A U the charges in Fig ure Q 20.24 have th e same magn itude.
In whi ch case does the electr ic field at the dot have the largest
magni tude?
A.
~
•
B.
@
•
Inside straw
•
c.
++++++++
+
++++++++
+
•
D.
FIGURE 020 .24
+ + + + + + + +
25. I All the charges in Fig ure Q20.25 have the same magn itude.
FIGURE 020 .18
FIGURE 020 .19
19. A sm all pos iti ve charge q experi ences a force of mag nitude FI
when pl aced at po in t I in Figure Q20. l 9. In terms of F 1 :
a. What is the mag ni tude of the force on charge q at po int 3?
b. What is the magn itude o f the fo rce o n a charge 3q at point I ?
c. What is the magn itude of th e force on a charge 2q at point 2?
d. W hat is the magn itude of the force on a charge - 2q at
po int 2?
20. A ty pi ca l co mm erc ial a irplane is s truck by lig ht ni ng about
once pe r year. W hen thi s happe ns. the ex te rnal metal s ki n o f
the ai rpl ane mi g ht be bu rned, bu t the people and equipm e nt
ins ide the a ircraft ex per ie nce no ill e ffects. Ex pl a in why thi s
is so.
2 1. Microbes such as bac teria have small pos itive charges when in
BIO solu tion. Publ ic heal th agenc ies are ex plor in g a new way to
measure the presence o f small num bers o f microbes in dri nk ing
water by us in g electric forces to co nce ntrate the m icrobes.
Water is sent betwee n the two o ppos itely charged electrodes of
a parallel-plate capacitor. Any mi crobes in the water w iU collect
on o ne of the electrodes.
a . On whi ch e lectrode w ill the microbes collec t?
b. How coul d the mi crobes be eas il y removed fro m the electrodes fo r anaJ ys is?
22. a. Is there a poin t between a 10 nC charge and a 20 nC charge at
which the electr ic fi e ld is zero? If so, which charge is thi s
po int closer to? If not, why not?
b . Re peat part a for the case of a 10 nC charge and a - 20 nC
charge.
In whi ch case does the e lectric fi eld at the dot have the largest
magnitude ?
A.
@
c.
•
B.
•
D.
<!l
•
•
FIGURE 020 .25
26. I Al l the charges in Fi g ure Q20. 26 have the same magn itude.
In whi ch case does the electric fi eld at the dol have the largest
magni tude?
A.
•
@
c. @
•
B.
@
D.
•
•
FIGURE 020 .26
27. I A glass bead c harged to +3.5 nC exe rts an 8.0 X 10- 4 N
repu ls ive electri c force o n a plas ti c bead 2.9 cm away. W hat is
the charge on the pl asti c bead?
A. + 2. 1 nC
C. +2 1 "C
B. +7.4 nC
D. +740 "C
28. I A +7.5 nC point charge and a - 2.0 nC point charge are 3.0cm
apart. What is the elec tr ic fi eld strength at the mi dpo int between
the two charges?
A. 3.3 X 10] NrC
c. 2.2 x 10 5 Nrc
B. 5.7 x 10] Nrc
D. 3.8 x 10 5 Nrc
670
CHAPTER 20
Electric Fields and Forces
29. II Three point charges are arranged as shown in Figure Q20.29.
Which arrow best re presents the direction of the e lectric field
vector at the positio n of the dot?
~
.
- I nC
A.
30. II A rod has positive charge +q at one end and negati ve charge
-q at the ot her, forming a dipo le. The d ipo le is placed in a
nonuniform electric field represe nted by the field lines in
Figure Q20.30. Which arrow best indi cates the d irect io n of the
net electric forc e on the d ipole?
C.
D.
E.
G)
+3nC
FIGURE Q20 .29
- 12 nC
FIGURE 020 .30
PROBLEMS
Section 20.1 Charges and Forces
/
Section 20.2 Charges, Atoms, and Molecules
I . III A glass rod is c harged to +5 .0 nC by rubb ing.
a. Have electrons been removed from the rod or protons
added ? Explain.
b. How many electrons have been re moved or protons added?
2. III A plast ic rod is charged to - 20 nC by rubb ing.
a. Have e lec trons been added to the rod or proton s removed?
Explain.
b. How many electrons have been added or proton s removed?
3. III Suppose you have 1.0 mol of O2 gas. How many coul ombs o f
INT pos iti ve charge are con tained in the ato mi c nuclei of lhj s gas?
4. II A plastic rod that has been charged to - I 5.0 nC touches a
meta l sphere. A ft erward, the rod's charge is - 10.0 nCo
a. What kind of charged particle was transferred betwee n the rod
and the sphere, and in which direction? That is, did it move
from the rod to the sphere or from the sphere to the rod?
b. How many charged particles were tran sferred?
5.
A glass rod that has bee n c harged to + 12.0 nC to uc hes a
metal sphere. Afterward, the rod' s charge is +8.0 nC
a. What kind o f charged particle was transfel1-ed betwee n the rod
and the sphere, and in which direction ? That is, did it move
from the rod to the sphere or fro m the sphere to the rod?
b. How many charged part icles were tran sferred?
6. III Two identi ca l meta l spheres A and B are connected by a
metal rod. Both are ini tially neutral. 1.0 X 10 12 electrons are
added to sphere A. the n the connec tin g rod is removed. A fte r·
ward, what are the charge of A and the charge of B ?
7. II Two iden tical metal spheres A and B are connected by a plas·
tic rod. Both are initi aJly neutral. 1.0 X 10 12 e lectro ns are added
to sph ere A, then the con nect ing rod is removed. Afte rward,
what are the charge o f A and the charge of B?
8. II If two identical conducti ng spheres are in contact, any excess
charge w ill be evenly d istributed between the two. Three identi·
cal metal spheres are labeled A, S , and C Initi all y, A has c harge
q, B has charge -qI2, and C is uncharged .
a. What is the final c harge on each sphere if C is touched to 8 ,
removed, and then touched to A?
b. Starting again froll1the ini tial cond itions, what is the charge
on each sphere if C is touched to A, removed, and then
touched to 8?
Section 20.3 Coulomb's Law
9. II Two 1.0 kg masses are 1.0 m apart o n a fr ict ion less table.
Each has + 1.0 !,-C of charge.
a. Wh at is the magnitude of the electric force o n one of the
masses?
b. Wh al is th e ini tial acce lerati o n of eac h mass if th ey are
released and allowed to move?
10. III Two small plastic spheres each have a mass o f 2.0 g and a
charge of -5 0.0 nC They are placed 2.0 cm apart.
a. What is the magn itude o f the electric fo rce between the
spheres?
b. By what factor is the e lectric force on a sphere larger than
its we ight?
11. III A small plast ic sphe re wi th a charge of -5 .0 nC is near
anot her small plasti c sphere with a charge of - 12 nC If the
sphe res repel one another w ith a force of mag nitude
8.2 X .10--1 N, what is the di stance betwee n the spheres?
12. III A s mall meta l bead , labeled A, has a c harge of 25 nCo It is
touc hed to metal bead B, initi a ll y neut ra l, so that the two
beads share the 25 nC charge, but not necessaril y eq ually.
W hen the two beads are then placed 5.0 c m apart, the force
betwee n them is 5.4 X 10 -I N. Wh at are the c harges qA and qs
on the beads?
13. 1111 A s mall g lass bead has been charged to +20 nC A tiny ball
bearing 1.0 e m above the bead feels a 0.018 N dow nward elec·
tric force. What is the charge on the baJi bearing?
14. I What are the magni tude and d irection of the electric force on
charge A in Figure P20. 14?
IN!
- 1.OnC
I.One
AG)
FIGURE P20 .14
4.0nC
c0
B
1.0em
1.0em
15 . III in Fi gure P20. 15, charge Ch experiences no net e lectric force.
What is ql?
FIGURE P20 .1S
10cm
10 em
Problems
16. I Obj ec t A. which has been charged to + 10 nCo is at the
origin. Obj ect B, which has bee n charged to - 20 nC, is at
(x, y) = (0. 0 cm, 2.0 cm). What are the mag nitude and direction
of the electric force on each object?
17. I A small glass bead has been charged to +20 nCo What are the
INT mag nitude and direction of th e acceleration of (a) a proton and
(b) an elcctron that is 1.0 cm from the center of the bead?
Section 20.4 The Concept of the Electric Field
18. II What magnitude c harge crea tes a 1.0 N/C electric field at a
poin t 1.0 m away?
19. II What are the strength and direction of the electric field 2.0 cm
from a small glass bead that has been charged to +6.0 nC?
20. II A 30 nC charged particle an d a 50 nC charged parti cle are
near each other. There are no other charges nearby. The electri c
force on the 30 nC particle is 0.035 N. The 50 nC particle is
then moved very far away. Afterward , what is the magn itude of
the electric field at its original position?
2 1. J What are the strength and direction of the electric field 1.0 mm
from (a) a proton and (b) an e lectron?
22. j A + 10 nC charge is located at the origin.
a. What are the stre ngth s o f the e lectr ic fields at the
positions (x, y) = (5.0 cm, 0.0 c m), (- 5.0 cm, 5.0 cm), and
(- 5.0 em, - 5.0 cm)?
b. Dra w a fi eld di agram show in g the elec tri c field vectors at
these points.
23. I A - 10 nC charge is located at the origin.
a. What are the streng th s o f the electric fi e ld s at the posilion s (x, y) = (0.0 em, 5.0 em), (- 5.0 em, - 5.0 em), and
(- 5.0 cm, 5.0 c m)?
b. Draw a field diagram show in g the elec tri c fi e ld vectors at
these points.
24. III What are the stre ngth and direction of the electri c fi eld al the
position indi cated by the dot in Fi gure P20.24? Specify the
direct ion as an an gle above or below hori zon tal.
.
Section 20.6 Conductors and Electric Fields
32. III Storm clouds may build up large negative charges near their
bottom edges. The earth is a good con ductor, so the charge on
the cloud attracts an equ al a nd opposite charge on the earth
under the cloud. The electric field stre ngth near the earth
depends on the shape of the eart h's surface, as we can ex pl ain
with a simple model. Th e top metal plate in Fi gure 20.32 has
uniforml y distributed negative charge. The bollom metal plate,
which has a hi gh point, has an equal and opposite charge that is
fre e to move .
a. Sketch th e two pl ates an d the region between them , showin g the distributi on of positi ve charge on the bottom plate.
b. Complete yo ur diagram by sketc hin g electric field lines
between the two plates . .Be sure to note the direction of the
fi eld. Where is the field strongest?
c. Explain why it is more dangerous to be on lOp of a hill or
mountain during a lightning storm than on level grou nd.
5.0 e111
5.0em
5.0em
5.0 em
•
5.0 em
t
•
FIGURE P20 .32
o
+ + ++++++
FIGURE P20.33
5.0C111
. ,OoC
FIGURE P20 .24
25.
29. II A parallel-plate capac itor is co nstruc ted of two sq uare plates,
size L X L, separated by distance d. The plates are given charge
± Q. What is the ratio ErlE j of the final electri c fi eld strength Er
to the initi al e lectric fi el d strength Ej if:
a. Q is doubled?
b. L is doubled?
c. d is doubled?
30. II A parallel-plate capac itor is formed from two 4.0 cm X
4.0 cm electrodes spaced 2.0 mm apart. The e lectri c fi eld
strength in side the capac itor is 1.0 X lOb N/C. What is the
charge (in nC) on each electrode?
3 1. I Two identi cal close ly spaced c irc ular disks form a parallelplate capacitor. Transferring 1.5 X 109 electrons from one di sk
to the other causes the electric fi eld strength between them to be
1.0 X 105 N/C. What are the di ameters of the disks?
. ,ooC
1.0nC
671
-
- 1.0 nC
FIGURE P20 .25
What are the strength and direction of the electric fi eld at the
position indi catcd by th e dot in Fi gure P20.25? Spec ify the
direction as an angle above or below hori zo ntal.
33. III A neutral cond ucting sphere is between two parallel charged
plates, as shown in Figure P20.33. Sketch the electric field lines
in the region between the plates. Be sure to include the effe ct of
the conduct ing sphere.
Section 20.7 Forces and Torques in Electric Fields
Section 20.5 Applications of the Electric Field
26. II What are the strength and direction of an e lectri c fi eld that
INT will balance the weight of a 1.0 g plastic sphere that has been
charged to - 3.0 nC?
27. I What are the strength and direction of an electri c field that
INT will balance the weight of (a) a proton and (b) an electron?
28. II A 0.10 g pl astic bead is charged by the addition of 1.0 X 10 10
INT excess elec trons. What elec tri c fi eld E (stren gth and direction)
will cause the bead to hang suspended in the air?
34. III Two small plastic sphe res, one c harged to 17 nC and the
INT other to - 17 nC, are con nec ted by a 25-mm-Iong in sul ating
rod. Suppose thi s dipole is placed in a uniform e lectri c field
with strength 7.4 X \05 N/C. What is the maximum possible
torque on the dipole?
35. II A prote in molecul e in an electroph oresis gel has a negati ve
BID charge. The exact c harge depends on the pH of the solution, but
30 excess electro ns is lypical. Wh at is the magn itude of the
e lec tri c force on a protein with thi s charge in a 1500 N/C electric field?
672
CHAPTER 20
Electric Fields and Forces
36. II Large electric field s in cell membranes cause ion s to
BID move through the ce ll waH, as we will explore in C hapter 23.
The fi e ld st ren gth in a typical me mbrane is 1.0 X 107 N/C.
What is the magnitude of the forc e on a c alcium ion with
charge +e?
37. III Molecules of carbon mon- + 3.4 x 10- 21 C
- 3.4 X 10- 1 1 C
IN! ox ide are permanent electric
@-@
dipol es due to uneq ua l sharing
0.11 nm
of electrons betwee n the carbon
and oxygen atoms. Figure P20.37 FIGURE P20 .37
show s the di stance and charges. Suppose a carbon monoxide
mol ec ule with a hori zon tal axi s is in a vertical electric fi e ld o f
sU'ength 15,000 N/C.
a. What is the magnitude of the net force on the molecul e?
b. What is the magnitude of the torque on the molecule?
•
e
S.O cm
10cm
.
IOcm
-
1.0nC
FIGURE P20 .45
- I.OnC
FIGURE P20 .46
46. 11111 Whal are the stren gth and direction of the electric fi eld at the
positi o n indicated by the dot in Figure P20.46? Specify the
direct ion as an angle above or below hori zontal.
47. II What is the force on the 1.0 nC charge in Figure P20.47?
Gi ve your an swer as a magnitude and a direction.
1.0 nC
1.0nC
~
General Problems
~,
,
\ 1.0em
1.0 cm,"
38. 11111 A 2.0- mm-diameter copper ball is c harged to + 50 nC. What
INT fraction of its elec tro ns have bee n re moved? The dens ity of
copper is 8900 kg/m 3 .
39. I Pennies today are copper-covered zinc, but o lder pennies are
INT 3.1 g of so lid copper. What are the total positi ve charge and
total negative charge in a so lid copper penny that is electri cally
neutral ? The density of copper is 8900 kg/m 3.
40. II Two proton s are 2.0 fm apart. (I fm = I femtometer =
INT I X 10- 15 m.)
a . What is the magnitude of the electr ic force o n one proton
d ue to the other proton?
b. What is the mag nitude of the gravitational force on one proton due to the other proton?
c. What is the ratio of the elec tri c force to the gravitat ional
force?
41 . 1111 The nucleus of a 125 Xe atom (an isotope of the elemen t xenon
INT with mass 125 u) is 6.0 fm in diameter. It has 54 proto ns and
charge q = +54 e. ( I fm = 1 femtometer = 1 X 10- 15 m.)
a . What is the electr ic force o n a proton 2.0 fm fro m the s urface of the nucleus?
b. What is the proton 's acceleration?
Hint: Treat the spherical nucleus as a point charge.
42. III Two equall y charged, 1.00 g spheres are placed with 2.00 cm
INT bet ween the ir centers. When released, eac h beg in s to accelerate
at 225 m/s 2. What is the mag nitude of the c harge on eac h
sphere?
43. II Objects A and B are both positively charged. Both have a
mass of 100 g, but A has twice the charge o f B. When A and B
are placed with 10 cm between their ce nters, B ex periences an
electric force of 0.45 N.
a. How large is the force on A?
b. What are the charges qA and qA?
44. 11111 An electric dipo le is formed from ± 1.0 nC po int c harges
spaced 2.0 mm apart. The dipole is centered at the o ri g in,
ori e nted along th e y-axi s . What is the e lec tric field stre ngt h
at the points (a) (x, y) ~ ( 10 mm , mm) a nd (b) (.t, y) ~
(0 mm, 10 mm)?
45. III What are the strength and direction of the e lectr ic field at the
position indi cated by the dot in Fi gure P20.45? Spec ify the
directi o n as an ang le above or be low horizontal.
a
•
l.O,C
S.O c m
'''-(;)'
2.0 ,C
1.0cm,,'
,"-
60'/ '
@ --\ ---- f -- 0 2.O'c
1.0em
FIGURE P20 .47
\ ,1.Oem
,
,
(;)/'
(;).
2.0nc @ -_ L ___ f __ 'I.Ocm
- 2.0nC
FIGURE P20 .48
48. II What is the force on the 1.0 nC charge in Figure P20.48?
Gi ve your an swer as a magn itude and a direction.
49. I What is the magnitude of the force o n the 1.0 nC charge in
the middle of Figure P20.49 due to the four other charges?
- 2.0 nC
1.0em
- 2.0 nC
- 2.0 nC
1.0cm
2.0 nC
€I
,
,..
: 1.0 cm
: 1.0 em
1.0nC
1.0 nC
-(t)
- 2.0 nC
- 2.0 nC
- 2.0 nC
FIGURE P20 .49
2.0 nC
FIGURE P20 .50
50. III What are the magnitude and direction o f the force on the t .O
nC charge in the middle of Fi gure P20.50 due to the four other
charges?
5 1. II What are the mag nitude and direct io n of the force on the
1.0 nC c harge at the bottom o f Figure P20.51 ?
- 6.0 nC
2.0 nC
@
2.0nC
B
FIGURE P20 .51
52. 11111 A 5.0 nC point charge sits at x = O. At the same time, a
4500 N/C uniform elec tric field (created by di stan t source
charges) points in the positi ve x- direc tion . At what point along
the x-ax is, if any, would (a) a proton and (b) an electron ex peri ence no net force ?
Problems
53. II The net fo rce o n the 1.0 nC charge in Fi gure P20.53 is zero.
What isq?
q
o
1,0nC
(±)
4.0 em
[ 200m
(±} 2.0nC
FIGURE P20 .53
3.0el11
2.0nC @
3.0(:111
54. II Two parti cles have positive charges q and Q. A thi rd charged
parti cle is placed halfway betwee n the m. What mllstthi s parti cle's charge be so th at the net force on c harge Q is zero?
55. 11111 Fi gure P20.55 shows four charges at _Q
q
the corners of a sq uare of side L. Assume
q and Q are pos iti ve.
a. Draw a d iagram show in g the three
forces o n c harge q due to the ot her
charges. Gi ve your vectors the cor,
rect relati ve lengths.
L
b. Find an ex press ion for the mag ni tude
4Q
-Q
e
62.
1111
673
A 0.020 g plasti c bead hangs from a
INT li ghtwe ig ht thread. Anot her bead is
fi xed in pos iti on be neath the po int
where the thread is ti ed. If bot h beads
have charge q, the moveab le bead
sw in gs o ut to th e pos itio n shown in
Fi gure P20.62. What is q?
5.0el11
63. 11 11 You have a li ghtweig ht spring whose
FIGURE
P20.62
INT unstretched length is 4.0 cm . You' re
curio us [0 see if you can lise thi s spri ng to measure charge.
First, you attac h one end of the spri ng to the ce ili ng and hang a
1.0 g mass from it. This stretches the spring to a length of 5.0 cm.
You then attac h two small pl ast ic beads to the opposite e nds of
the spri ng, lay the spring on a fricti on less tab le, and give each
plasti c bead the sa me charge . T hi s stretches the sprin g to a
length of 4.5 c m. Wh at is the mag nitude of the charge (in nC)
on each bead?
64. 11111 Two 3.0 g spheres on 1.0- m-l o ng threads repel each other
INT after being equally charged, as show n in Fi gure P20.64. What is
the charge q?
®
56.
INT
57.
INT
58.
BIO
59.
60.
INT
61.
INT
of the net force on q.
FIGURE P20 .55
Suppose the magn itude of the proto n
charge differs from th at of the e lectron charge by a mere I part
in 109 .
a. What would be the force be tween two 2.0-mm-di ameter
coppe r spheres 1.0 cm apart? Assume that each copper atom
has an eq ual number of el ec trons and proto ns. The density
of copper is 8900 kg/m 3.
h. Wo ul d thi s amount of force be detectab le? What can YOll
concl ude from the fact that no such forces are observed?
III In a simpl e model of the hydroge n ato m, th e el ec tro n
moves in a c ircul ar orbit of rad iu s 0.053 nm aroun d a stati o nary proton . How man y revo lu tio ns per seco nd does the el ectron make?
Hint: Wh at mu st be true fo r a force that ca uses c irc ul ar
mo ti o n?
III A 0. 10 g honeybee acquires a charge of +23 pC whi le fl yin g.
a . The e leC lri c fi eld near the surface of the earth is typicall y
100 N/C, d irected downward. Wh at is (he rat io of the e lectric force on the bee to the bee 's we ight?
b. W hat e lectri c fi e ld stre ngth and directi o n would all ow th e
bee to hang suspended in the air?
11111 A + 10 nC charge is located at (x. y) = (0 c m, 10 cm) and a
-5.0 nC charge is located (x, y) = (5.0 cm, 0 cm). Where would
a - 10 nC charge need to be located in order th at the electri c
fi e ld at the origin be zero?
III Two 2.0-c m-di ameter d isks face each o ther, 1.0 mm apart.
They are charged to ± 10 nCo
a. What is the electri c fi eld strength between the d isks?
b. A proton is shot from the negati ve d isk toward the pos iti ve
d isk. What launch speed must the proton have to j ust barely
reac h the pos iti ve di sk?
1111 The electron gun in a telev isio n tube uses a uniform electri c
field to accelerate electrons fro m rest to 5.0 X 107 m/s in a d istance of 1.2 cm. Wh at is the electric fi el d stre ngth?
3.0 g
65.
11111
3.0 g
q
FIGURE P20 .64
An e lec tri c fi eld
q
if = ( 100,000 N/C. ri ght) cau ses the 5.0 g
INT ball in Fi gure P20.65 to hang al a 20 angle. Wh at is the charge
0
o n the bal.l ?
-E
,
,
q
5.0 g
T------ -
FIGURE P20 .65
66.
1111
An electric fie ld
o
-:25 nC
E
+
2.0g
,------+ -
FIGURE P20 .66
E=
(200,000 N/C, ri ght) causes the 2.0 g
INT ball in Fig ure P20.66 to hang at an angle. What is (J?
67. II A small charged bead has a mass of 1.0 g. It is held in a uniINT form electri c fi el d E = (200,000 N/C, up) .Whe n the bead is
re leased, it acce lerates upward with an acce lerali on of 20 m/s 2 •
What is the charge on the bead?
68. II A bead with a mass of 0.050 g and a charge of 15 nC is free 10
INT slide o n a ve rti ca l rod. At th e base of the rod is a fi xed 10 nC
charge. In equilibrium , at what he ight above the fi xed charge
does the bead rest?
69. II A small bead with a pos iti ve charge q is free 10 slide on a horINT izontal wire of length 4.0 cm. At the left end of th e wire is a
fi xed charge q, and at the right end is a fi xed charge 4q. How fa r
from the left e nd of the wire does the bead come to rest?
674
CHAPTER 20
Electric Fields and Forces
In Problems 70 and 7 1 you are given the equation used to so lve a
problem. For each of these,
a. Write a realistic problem for which this is the correct equat ion.
b. Finish the sol ution of the problem.
(9.0 X 10' N . m' /C' ) X N X ( 1.60 X 10- 19 C)
70. III ~---~c:---:-::--;c-=----~
( I.O X 10 6 m) 2
= 1.5 X 10' N/C
71. III
(9.0 X 10' N . m' /C' )q'
(0.0 15 m)'
0.020 N
72. I If the chargin g collar has a positive charge, the net charge on
a droplet separating from the stream will be
A. Positi ve. B. Negative. C. Neutral.
D. The charge will depend on the type of cell.
73. I Which of the followin g describes the charges on the droplets
that e nd up in the five tubes, moving from left to right?
A.
+2q. +q. O.-q, - 2q
B. +q, +2q,0,-2q, - q
Passage Problems
Flow Cytometry BID
Flow cytometry, illu strat ed In
Figure P20.72, is a technique used to
sort cell s by type. The ce ll s are
placed in a con ducting sal in e solution
which is then forced from a no zzle.
The st re am breaks up into smaLl
droplets, each con taining one cell. A
metal co llar su rrounds the stream
ri ght at the point where the droplets
separate from the st ream. Charging
the co ll ar polarizes the conduct in g
liquid , caus in g the droplels to be·
come c harged as they break off from
the st re am. A lase r beam probes the
solut ion just upslfeam from the
c hargin g co llar, looking for the pres·
ence of certa in types of cells. ALI
droplets co ntainin g one parti c ular
type of cell are give n the same charge
by the charging collar. Droplets with
other desired types of cells rece ive a
different charge, and droplets with no
desired cell receive no charge. The charged droplets then pass
between two parallel charged electrodes where they receive a hori·
zontal force that directs th em into different co llection tube s,
depending on their charge.
N
O
,J.Io - D
Uq9id ______
''',''
~
~~7
Lasc r ~
;,
probe
~
Charging
collar
C, II,
""
-©
~
C. - q,-2q, 0, +2q, +q
D. - 2q,-q, 0,+q,+2q
74. I Because th e drop lets are conductors, a droplet's positi ve
and negati ve charge s will separate while the droplet is in the
region between the deflection plates. Suppose a neutra l
droplet passes between the plates. The droplet ' s dipole
mom ent will point
A. Up.
B. Down.
C. Left.
D. Right.
75. I Another way to son the droplets would be to give eac h
droplet the same charge, then vary the electric field between the
deflection plates. For the apparatus as sketched, thi s technique
will not work because
A. Several droplets are between the plates at one time , and
they would all feel the same force.
B. The ce ll s in the soluti on have net charges that would affect
the droplet charge.
C. A droplet with a net c harge would alway s experience a net
force between the plates.
D. The droplets would all repel eac h other, and thi s force
would dominate the deflecting force.
FIGURE P20 .72
Stop to Think 20.1: A. The electroscope is originally given a posi·
tive charge. The charge spreads out, and the leaves repel eac h other.
When a rod Wilh a negative charge is brought near, some of the posi·
live charge is attracted to the top of the eleclroscope. away from the
leaves. There is less charge on the leaves, and so they move closer
together.
Stop to Think 20.2: q,,( + 3e) > qA( + Ie) > qo(O) > qll( -Ie)
> qd- 2e).
Stop to Think 20.3: B. The two forces are an actionireaclion pair,
opposite in direction but eqllal in magn itude.
Stop to Think 20.4: En > EA > ED > Eco The field is propor·
tional to the charge, and in verse ly proportional 10 the square of the
distance.
Stop to Think 20.5 : C. Electric field lines sfarl on positi ve charges.
Very near to each of the positive charges, the field lines should look
like the fi eld lines of a single positive charge.
Stop to Think 20.6: FA = F 8 = F c = F D = FE" The field in side a
capac itor is the same at all points. Because the field is uniform, the
force on the proton will be the sa me at all points. The electric field
ex ists at aU points whether or not a vec tor is shown at that point.