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QUESTIONS
Conceptual Questions
I. T he nonh pole of a bar magnet is broug ht near the center o f
another bar magnet, as shown in Fi gure Q24. 1. Will the force
between the magnets be attractive, repulsive. or zero? Why?
9. Two wires carry currents in oppos ite directi o ns, as in Figure
Q24.9. The rield is 2.0 mT at a po int be low the lower wire. What
are the streng th and d irection o f the fi eld at po int 1 (mi dway
betwee n the two wires) and at point 2 (the same d istance above
the upper wire as the 2.0 mT po in t is below the lower wire)?
·2
.,
Is
FIGURE 024 .9
- 2.0 mT out of page
FIGURE Q24 .1
2. You have a bar mag net whose po les are not marked. How can
you fi nd whi ch pole is north and whi ch is south by using only a
pi ece of strin g?
3. Whe n YO LI are in the southern hemi sphere, does a compass po int
north or south ?
4. Green turtles use the earth 's mag netic fi eld to navigate. Th ey
BIO see m to use the ri e ld to te U them the ir lat it ude-how far north
or south of the equator they are. Ex pl ain how kn ow in g the
direction o f the eillth's fi eld could give thi s in formati on.
5. Ahorsesfloe magnet consists of a bill magnet ben t into aU-shape,
as show n in Figure Q24.5. Sketc h the magneti c fi el d li nes fo r a
horseshoe magnet.
10. As show n in Figure Q24. 10, a uniform magnet ic fiel d po ints
upward, in the plane of the paper. A long wire perpend icular to
the paper ini tiall y carri es no current. Wh en a c urren t is tu rned
o n in the wire in the direct ion shown, the magnetic fi e ld at point
I is fo und to be zero . Draw the magneti c fi eld vector at po int 2
whe n tbe current is on.
•
2·
ii
,.
FIGURE 024 .5
6. What is the current d irecti on in the wire of Figure Q24.6?
Expl ain .
,
,
®
0
,
,
FIGURE 024.6
,
FIGURE 024 .7
7. What is the c urren t d irectio n in the wire of Figure Q24.7?
8. S ince the wires in the wall s of your house carry current, you
might expect that you could use a compass to detect the positions
of the wires . In fact, a compass will experi ence no de nec ti on
when brought near a c urrent-carry in g wire because the curre nt
is AC (mean in g "alternat ing current" -the current sw itc hes
direction 120 times each second). Explain why a compass doesn '(
react to an AC current.
FIGURE 024 .11
FIGURE 024 .10
II. Two lo ng wires carry curre nts in the d irections shown in Figure
Q24. 11 . O ne wire is 10 cm above the other. In w hi ch d irecti on
is the mag netic fie ld at a po in t halfway between them?
12. If an electron is not mov ing, is it poss ible to set it in moti on
using a mag neti c fiel d ? Expl ain .
13. Fig ure Q24 .1 3 shows a so lenoid as seen in cross sect ion. Compasses are pl aced at po in ts I and 2. In which directi on will each
compass po int when the re is a large curre nt in the directi o n
shown? Exp lain.
2·
.............•.
,.
FIGURE 024 .13
808
CHAPTER
24
Magnetic Field s and Fo rces
14. One long so leno id is placed in side
anothe r sole no id with twice the dia·
meter but Lhe same length. Each soleno id
carries the same current but in opposite
direclions, as shown in Figme Q24. 14. If
they also have the same number of
turns, in which direction does the mag·
netic fi eld in the cen ter point ? Expl ain.
IS. What is the inilia/ direction o f deflec. FIGURE 024 .14
tion for the charged particles e nterin g the magnet ic fi elds
shown in Figure Q24. IS?
20. Two posit ive charges are moving in a uniform magneti c fi eld
with veloc ities , as shown in Figure Q24.20. The magnetic force
on each charge is also shown. In which d irect ion does the mag·
netic fi eld point?
f
--t-~f'--'-. -
x
FIGURE 024 .20
(,)
y
(b)
• Ii •
FIGURE 024 .15
2 1. An electron is moving in a circu lar orbit in the earth' s magnetic
field directly above the north magneti c po le. Viewed from
above, is the rotati on clockwi se or counterclockw ise?
22. A proton moves in a region of uniform magnetic fi e ld, as shown
in Figure Q24.22. The ve locity at one in stant is shown. Will the
subsequent motion be a clockwise or counterclockwise orbit?
16. What is the il/ilia/ direct ion of defl ect ion for the charged parti·
c1es enteri ng the magnetic fie ld s shown in Figure Q24. 16?
(a)
- j
j
e-!-j
j
j
j
Ions
measured
. -,; .
- --1-- --
(b )
FIGURE 024 .16
17. Determ ine the magneti c fi el d direction that causes the charged
partic les shown in Figu re Q24. 17 to ex peri ence the indicated
magneti c forces.
(,)
FIGURE 024 .17
+---'---~---L-~ B (T)
o
FIGURE 024 .22
(b)
r
,,
~
0.15
0.30
FIGURE 024 .23
23 . The detector in a mass spectrometer records the number of ions
measured at a fixed position as the fi e ld is varied. For a sample
consist in g of a sin gle atomic species, two peaks were found
where one was expected, as show n in Fi gure Q24.23. The most
like ly ex planati o n is that the atoms received d ifferent charges
when ioni zed. If the two peaks correspond to ion s wi th charges
+e and +2e. which peak is whi ch? Explain.
24. A proton is moving near a long, current·canying wire. When the
proton is at the point shown in Figu re Q24.24, in which direc·
tion is the force o n it?
f. into page
F
18. Determine the mag net ic field di rection that causes the charged
parti c les s hown in Fi gure Q24. IS to ex perie nce the indi cated
magnet ic force s.
I'
@
Wire
@
(b)
(a)
Fout of page
Ii inlo page
19. An e lectron is moving near a long, curre nt·c arry ing wire, as
shown in Fi gure Q24. 19. What is the directio n of the mag net ic
force on the electron ?
--
I'
Wire
Proton
Proton
FIGURE 024 .25
FIGURE 024 .24
FIGURE 024 .18
B
A
2S. A proton is moving near a long, curren t·carryin g wire . Whe n
the proton is at the point shown in Fi gure Q24.2S, in wh ic h
d irectio n is the force o n it?
26. A long wire and a square loop lie
y
in the plane of the paper. Both
carry a current in the d irect ion
shown in Fi gure Q24.26. In
wh ich d irection is Lhe net force
on the loop? Exp lain .
FIGURE 024 .26
L
fIl
L
,
FIGURE 024 . 19
27. The computers that contro l MRI machines can not have CRT
monitors. Explain why this is so.
Problems
c
28. A Slinky is a child's lOy thal is a lon g coil sprin g.
Suppose yo u take a Slinky and let it hang down
and stretch out so that the coils do nOllo Lich each
other, as in Fi gure Q24.28. Now you con nect the
Slinky to a power supply and pass a large DC cur~
rent through il. Think about the current in the
coils. Will the Slinky ex pand or contract?
FIGURE Q24 .28
29. A soleno id carries a c urrent that produces a fi e ld in s ide il. A
wire carryil,1g a c urrent lies in side the soleno id , at th e cente r,
carrying a current along the so le noid 's axis. Is there a force o n
this wire due to the fi e ld ofthe solenoid? Explain.
30. You want to make an electromagnet by wrapping wire around a
nail. Should you use bare copper wire or wire coaled with in slIlating pl asti c? Explain.
3 1. The moo n does not have a molten iron core like the earth , but
the moon does have a small magnetic fi eld. What might be the
source of thi s fi eld?
32. Arc haeolog ists can use in struments that measure small variation s in magnet ic field to locate buri ed
walls made of fired bri ck, as shown in
Figure Q24.32. When fired , th e ma gneti c mome nt s in the clay become rand o ml y aligned; as the clay coo ls, the
magnet ic mo ments line up with the
earth ' s fi eld and retain thi s alignment
even if the bri cks are subsequen tly
moved. Explain how thi s leads to a measurable mag neti c fi e ld variation over a
buried wall.
FIGURE 024 .32
809
34. II If a compass is placed above a A. ~
current-carry in g wi.re , as in Fi gure
B. ~
Q24.34, the needle will lin e up
c. ~
with the field o f the wire. Which o f
the views shows the correct ori e n- D. ~
tati o n of the need le for the noted FIGURE 024 .34
current direction ?
35 . I Two wires carry equal and oppo- 0
•
®
s ite curre nts, as show n in Fi gure
FIGURE 024 .35
Q24.35. At a point directly between
the two wires, the field is
A. Directed up. toward the top of the page .
S. Directed down , toward the bottom of the page.
C. Directed to the lefl.
D. Directed to the right.
E. Zero.
36. I Figure Q24.36 shows four particle s
moving to the ri ght as they enter a
reg io n of uniform magneti c field ,
directed into the paper as noted . All particles move at the same speed and ha ve
the same charge. Which parti cle has the
largest mass?
FIGURE 024 .36
37 . I Four parti cles of identi cal charge an d mass enter a region o f
uniform magnet ic field and fo ll ow the trajectori es show n in
Fi gure Q24.37. Whi ch parti cle has the highest veloc ity ?
FIGURE 024.37
A.
B.
C.
D.
Multiple-Choice Questions
33. 11 An unmag neti zed metal sphere hangs by a thread. When the
north pole of a bar magnet is
brought near, the sphere is
strong ly attracted to the m agnet, as shown in Fi gure Q24.33.
S
Then the magnet is re versed
and its south pole is bro ught FIGURE 024 .33
near the sphere. Ho w does the
sphere respond?
A. It is strongly attracted to the magnet.
B. It is wcakJy attracted to the magnet.
C. Il does not respo nd .
D. It is weak.ly repelled by the magnet.
E. It is strongly re pelled by the magnet.
38. I If aU of the partic les s how n in Figure Q24. 37 are electrons,
what is the direction of the magnet ic fi eld that produced the
indi cated deflection?
A. Up (toward the top of the page).
B. Down (toward the bottom o f the page) .
C. Out of the plane of the paper.
D. Into the plane of the paper.
39. I If two compasses are brought near enough
A.@@
to each other, the mag net ic fi el ds of the comB @@
passes the mselves will be larger than the field
o f the earth, and the needles will line up with
e @@
eac h other. Which o f the arrangements of two
D.@ @
compasses shown in Fi gure Q24.39 is a possiFIGURE Q24.39
ble stable arrangement?
PROBLEMS
Section 24.1 Magnetism
Section 24.2 The Magnetic Field
Section 24.3 Electric Currents Also Create Magnetic Fields
Section 24.4 Calculating the Magnetic Field Due to a Current
I. I What c urrents are needed to generate the magnetic fi eld
strengt hs of Ta bl e 24 .1 at a point 1.0 em from a long, strai g ht
wire?
2. I At what di stances from a very thin , strai ght wire carrying a
lOA curre nt wo uld the magnetic ficld strengths of Table 24 . 1 be
generated?
3. II The magnetic fi eld at the center of a I .G-cm-di ameter loop is
2.5 mT.
a. What is the current in the loop ?
b. A long , straight wire carries the sa me c urrent you found in
part a. At what distance from the wire is the magnet ic field
2.5 mT?
810
CHAPTER
24 Magnetic Fields and Forces
4.
111 For a particular sc ientific experimen t, it is important to be
complc tely iso lated from any magneti c fi e ld, including the
earth 's fie ld . A I.OO-m-diametercurren t loop with 200 turns of
wire is set up so that the fi eld at the center is exact ly equ al to the
earth's field in magnitude but opposite in d irection. What is the
current in the c urrent loop?
5. I Wh at are the magneti c field
I·
2.0cm
strength and direc tio n at
lOA
points 1 to 3 in Fi gure P24.5?
4.0cm
2·
lOA
FIGURE P24.S
3·
14. II A researcher would like to perform an experime nt in zero
magnetic fi e ld, which means th at the fi el d of the earth must be
cancelled. Suppose the experiment is done in side a so le no id of
di ameter 1.0 m, length 4.0 m, with a total of 5000 turns of wire.
The sole noi d is oriented to produce a fi e ld th at opposes and
exac tly cancels the fi e ld of the earth . Wh at current is needed in
the solenoid 's wire?
5.DA
15. III Wh at is the magneti c fi e ld
at the center of the loop in
Fi gure P24.15?
a
2.0 Clll
6. 1 Although the ev ide nce is weak, there has been conce rn in
BID recent yea rs over poss ibl e health effects from the magneti c:
fi e lds ge nerated by transmi ss ion lines. A typical hi gh-vo ltage
tran smi ssion line is 20 m off the ground and carries a current of
200 A. Estimate the magnetic field st ren gth o n the ground
underneath such a line. What percentage of the earth's magneti c
fi eld does this represent ?
7. 1 Some consumer groups urge preg nant women not to usee lecBK) tri c blankets, in case there is a health risk from the magnet ic
fields from the approxim ately I A current in the heater wires.
a. Estimate, stat in g any assumption s yo u make, the mag nct ic
fi eld strength a fetu s mi ght experience. What percentage of
the earth 's magnetic field is thi s?
b. It is becoming standard practice to make elec tri c blankets
with minimal ex ternal magnetic field. Eac h wire is paired
with ano ther wire that carr ies curre nt in the oppos ite direclion . How does thi s reduce the external magneti c fi e ld?
8. III A lo ng wire carryin g a 5.0 A current perpe ndi cular to the
.\')'-plane inte rsec ts the x-ax is at x = -2.0 cm. A seco nd , paral lel wire carryin g a 3.0 A current intersects the x-ax is at
x = +2.0 cm. At what point or points on the x-ax is is the magnet ic fi eld zero if (a) the two currents are in the same di recti on
and (b) the two curren ts are in opposite d irec ti ons?
9. II The ele ment niobium , whic h is a me tal, is a superconductor
(i.e. , no e lec trical res istance) at te mperatures below 9 K . However, the superconductivity is destroyed if the magnetic fi eld at
the surface of the wire of the me tal reac hes o r exceeds 0. 10 T.
Wh at is the max imum current in a stra ight, 3.0-mm-d iameter
superco nducting niob ium wire?
Hillt: You ca n assume that all the current nows in the center of
the wire.
10. I The small currents in axo ns correspondin g to nerve impulses
BID produce meas urable magnetic fi el ds. A typical axon carries a
peak current of 0.040 J.LA . What is the stre ngth of the fi e ld at a
di stance of 1.0 mm ?
II . II A solenoid used to produce magnetic fields fo r researc h pu!'poses is 2.0 m long, with an inner rad ius of 30 cm and 1000
turns of wire. When running, the solenoid produces a field of
1.0 T in the ce nter. Given thi s, how large a current does it carry?
12. I Two conce ntric eUITCnt loops lie in the same plane. The smal ler
loop has a radius of 3.0 cm and a current of 12 A. The bigger loop
has a current of20A. The magnetic field at the center of the loops
is found to be zero. What is the radius of the bigger loop?
13. I The magneti c fi eld of the brain has been measured to be
BID approx imate ly 3.0 X 10- 12 T . Although the current s that cause
thi s fi e ld are quite complicated, we ca n get a rou gh es timate of
their size by modelin g them as a single circular currcnt loop 16cm
(the width of a typica l head) in diameter. What current is needed
to produce such a fi eld at the center of the loop ?
FIGURE P24 .1S
16. I Experimen tal tests have shown that hammerhead sharks can
BIO detect mag neti c fi elds. In one such test, 100 turn s of wire were
wrapped around a 7.0- m-d iamete r cy lind rical shark tank. A
magnctic field was created inside the ta nk whe n thi s co il of wire
carri ed a c urrent of 1.5 A. Sharks trained by gelling a food
reward when the fi eld was prese nt wou ld late r unamb iguo usly
respond when the field was turned o n.
a. What was the magnet ic fi eld strength in the center of the
tank due to the current in the co il ?
b. Is the stren gth of the co il' s fi eld at the ce nter of the tank
larger or smaller th an thaI of the earth ?
17. I We have seen that the heart produ ces a mag netic field that
BID can be used to diagnose probl ems with the heart. The magnetic
field of the heart is a dipole field produced by a loop curre nt in
the outcr layers of the. heart. Suppose the fi e ld at the cen ter of
the heart is 90 pT (a pT is 10 .... 12 T) and that the heart has a diamete r of approximately 12 Col. What current circu lates around the
heart to produce this field?
18. 11111 You have a l.O-m-lo ng copper wire. Yo u wa nt LO ma ke an
N-turn current loop that ge ne rates a 1.0 mT mag netic fi eld at
the ce nte r when the c urrent is 1.0 A. Yo u must use the entire
wire. What wilJ be the diameter of your coil ?
19. lUll In the Bohr model of the hydroge n atom, the e lec u'on moves
in a c irc ular orbi t of radius 5.3 X 10- 11 m with speed 2.2 X
106 m/s. According to this mode l, what is the magnetic fi eld at
the center of a hydrogen atom due to the motio n of the electron?
Hint: Determine the avemge current of the o rbiting electron.
Sect ion 24.5 Magnetic Fields Exert Forces o n Moving Charges
20. I A proton moves with a speed of l.0 X 10 7 m/s in the directions shown in Figure P24.20. A 0.50 T magnetic fi eld points in
the pos itive x-direct ion. For eac h. what is mag neti c force on the
pro ton ? Give your answers as a mag nitude and a directio n.
(b)
(. )
y
li
FIGURE P24.20
x
,
!'
Ii
x
Problems
2 1. n An electron moves with a speed of 1.. 0 X 10 7 m/s in the di rections shown in Figure P24.2 1. A 0.50 T magnet ic field points in
the positive x-d irection. For each, what is magnetic fo rce
Fon
the electron? G ive your answers as a magn itude and a d irecti on.
(a)
(h)
-y~x
------,J..:F-/
ii
)'
811
b. What accelerati on do they experience due to the magne ti c
field, assuming that it is perpendicu lar to the ir path ? What is
thi s accelerat io n in units of g?
c. If the elec u'ons were to complete a full c irc ular orbit, w hat
would be the radius?
d. A m agne ti c fi e ld can be used to redirect the beam , but tbe
electrons are brought to hi g h speed by an e lectric field. Why
can ' t we use a magne tic fie ld for this tas k?
JiiF----~- x
jj
Section 24.6 Magnetic Fields Exert Forces on Currents
30. I What mag ne tic fi e ld strength a nd d irec ti on will lev it ate the
2.0 g wi re in Figure P24.30?
FIGURE P24 .21
2.0g
wire
8-field region
23. I The aurora is caused whe n electrons and protons, movi ng in
the earth 's m agnet ic field of ;::;:: 5.0 X 10- 5 T , colli de w ith mole-
c ul es of the at mosphere and cause them to glow. What is the
radius of the c ircu lar orbit for
24.
25.
26.
27.
28.
29.
lNT
a. An electron wit h speed 1.0 X 10 6 m/s?
b. A prOlo n with speed 5.0 X 10"" m/s?
III Problem 24.23 describes two particles that o rbit the earth's
mag netic fi e ld li nes. What is thejreqllellcy of the c ircul ar o rbit for
a. An electron w ith speed 1.0 X lOb Ill /s?
b. A proton with speed 5 .0 X 104 m/s?
1111 The microwaves in a microwave oven are produced in a spec ial
lube called a maglleflvll. The electrons orbit in a magnet ic fi e ld at
a frequency of2.4 GHz, and as they do so they e mit 2.4 GHz elec·
lromagnetic waves. W hat is the strength o f the magnetic field?
III A mass spectrometer sim ilar to the one in Fi g ure 24.36 is
des igned to separate protein fra gme nts. The fragmen ts are ion·
ized by the removal of a si ngle e lectron, then they ente r a 0.80 T
uni fo rm magnetic fie ld at a speed o f 2.3 X 10 5 m/s. If a fragme nt has a mass 85 times the m ass of the proton. what w ill be
the d is tance between the points where the ion e nters and exits
the magneti c field?
I In a certain mass spectrometer, particles with a charge of +e
are sen t into the spectrometer w ith a veloc ity of 2.5 X 105 m/s.
They a re fo und to move in a circ ul a r path w ith a radius of
0.2 1 m. If the mag netic fi e ld of the spec tro me te r is 0 .050 T,
what kind o f parti cles are these like ly to be?
III At I = 0 s, a proton is moving
y
with a speed of 5 .5 X 10 5 mls at
ii
an a ng le o f 30° from the x-ax is,
as shown in Fig ure P24.28.
A uniform magnetic fie ld of
- ---1.L-- L - - - - x
magnitude 1.50 T is pointing in
the pos itive y-d irection. W hat
FIGURE P24.28
will be the .v-coordi nate of the
proton 10 J..Ls later?
III Early black-and-white television sets used an e lectron beam
to draw a picture on the screen. The electrons in the beam were
acce leraled by a voltage of 3.0 kV; the beam was the n steered to
different points on the screen by co il s of wire that produced a
magne ti c fi eld of up to 0.65 T.
a. What is the speed of electrons in the beam?
I
1.5 A
22. I An electromagnetic flowmeter applies a magne tic field 0[0.20 T
BKJ to blood fl ow ing through a coronary anery at a speed o f 15 em/s.
What force is fell by a chlorine ion with a s ingle negative c harge?
tOem
FIGURE P24.30
3 1. I What is the ne t force (magnitude and direct ion) on each wire
in Fi g ure P24.31?
lOA
lOA
2
2.0em
3
2.0cm
lOA
FIGURE P24.31
50cm
32. I The unit of c urre nt, the ampere, is defin ed in terms of the
force betwee n curre nts. If two I.O·meter. long sect ion s of very
lo ng wires a d istance 1.0 m apart eac h carry a c urre nl of 1.0 A ,
what is the force between them? ( Ir the force between two actual
wires has thi s value, the c urrent is defi ned to be exactly I A .)
33. I A unifonn 2.5 T magnetic field points to the right. A 3.0-m.long
wire, carry ing 15 A , is placed a t an angle o f 30° to the fie ld, as
shown in Figure 24.33. What is the force (magnitude and di rection) on the w ire?
ii
FtGURE P24.33
34. I The four w ires in Figure P24 .34 are lilted at 20° w ith respect
to a uniform 0 .35 T fi e ld. If each ca rri es 4.5 A and is 0.35 m
long, what is the force (di rect ion and magn itude) o n each?
FIGURE P24 .34
812
CHAPTER 24
Magnetic Fields and Forces
35. II Magnetic informati on o n hard drives is accessed by a read
INT head that must move rapidl y back and forth across the disk. The
force to move the head is ge nerally created with a voice coil
actuator, a nat coil aI' fine wire that moves between the poles of
a strong magnet, as in Figure P24. 35. Assume that the co il is a
square 1.0 cm on a side made of 200 turn s of fin e wire with total
resistance 1.5 n. The field between the poles of the magnet is
0.30 1~ assume that the field does not extend beyond the edge of
the magn et. The co il and the mount that it rides on have a total
mass of 12 g.
a. If a voltage of 5.0 V is applied to the co il , what is the current?
b. If the current is clockwise viewed from above, what are the
magnitude and direction of the net force on the coil ?
c. What is the magnitude of the accelerat ion of the coil ?
s
FIGURE P24.35
Side view
Top view
7
40. II a.
What is the magn itude of the torque o n the c ircular current loop in Figure P24.40?
b. What is the loop 's eq uilibrium position?
2.0C1l1
®2.0A
FIGURE P24 .40
o[20""
Wirc
0.20 A
Section 24.8 Magnets and Magnetic Materials
41. II A computer di skette is a plasti c disk with a ferromagnetic coating. A singl e magnetic domain can have its mag net ic moment
o riented to point ei ther up or down, and these two orientations
can be interpreted as a binary 0 (up) or I (down). Each 0 or I is
called a bir of information. A diskeue stores roughJy 500,000
bytes of data on one side, and each byte contains e ight bits. Estimate the width of a magnetic domain, and com pare your answer
to the typi cal domain size given in the text. Li st any assumptions you use in your est imate.
42. I All ferromagneti c material s have a Curie remperalllre, a temperature above which they wiU cease to be magnetic. Ex plain in
some detail why you might expect this to be so.
General Problems
Section 24.7 Magnetic Fields Exert Torques on Dipoles
36. II A current loop in a molOr has an area of 0.85 cm2 . Il carrie s a
240 rnA current in a uniform fie ld of 0.62 T. What is the magnitude of the maximum torque on the current loop?
37. II A square current loop 5.0 cm o n each side carries a 500 rnA
current. The loop is in a 1.2 T uniform magnet ic field. The axis
of the loop, perpendicular to the plane of the loop, is 30° away
from the field direct ion. What is the magnitude of the torque on
the current loop?
38. I Figure P24.38 shows two sq uare current loops. The loops are
far apart and do not interact with each other.
a. Use force diagrams to show that both loops are in eq uilibrium , having a net force of zero and no torque.
b. One of the loop positions is stable. That is, the forces will
return it to equilibrium if it is rotated slightly. The other
position is unstable, like an upside-down pend ulum: If
rotated sli ghtly, it will not return to the positi o n shown .
Whi ch is which? Expla in.
Loop I
43 . II In Figure P24.43, a compass sits 1.0 cm above a wire in a cir[NT cuit con tainin g a 1.0 F capac itor charged to 5.0 V, a 1.0 n resisto r, and an open sw itch. The compass is lined up with the
earth's magneti c rield. The sw itc h is then closed, so there is a
current in the c ircuit, and the switc h re main s closed until the
capacitor has completely discharged.
a. At the position of the compass, what is the magn itude of the
magneti c field due to the current in the wire right after the
switch is closed? How does thi s com pare with the magnitude of the field orthe em'lh?
b. Describe how the compass ori en tati o n c hanges ri ght after
the sw itch is closed, and how the comp;:t<o;s orientation changes
as time goes on.
FIGURE P24.43
44. I The ri ght edge of the c irc uit in Fi gure P24.44 exte nds into a
[NT 50 mT uniform magnetic field. What are the magnitude and
direction of the net force on the c ircu il ?
Loop 2
3.0n
I5V=€;n
Ii
FIGURE P24.44
FIGURE P24.38
39. 1111 The eart h' s magnetic dipole moment of 8.0 X 1022 A· m2 is
generated by currents within the molten iron of the earth's outer
core . (The inner core is solid iron.) As a simple model, consider
the outer core to be a 3000-km-diam eter current loop. What is
the curren t in the curren t loop?
•
B = 50mT
45. II The IWO 10-em-long parallel wires in Figure P24.45 are sepaINT rated by 5.0 mm. For what val ue of the resistor R will the force
between the IWO wires be 5.4 X 10- 5 N?
R
2.0n
9.0V
FIGURE P24.4S
(?c,, [[
[ 3 : 90V
5.0 111m
Problem s
46. III The capac itor in Figure P24.46 is charged to 50 Y. The switch
INT closes at 1 = 0 s. Draw a graph showing the magnet ic fi eld
stre ngth as a fun ct io n of time at the pos iti o n of the dol. O n your
grap h in d icate the max imum field strength a nd prov ide an
appropriate numerical scale o n the horizontal ax is.
I.Oem
1++++++++++ 1
_ -_ ,
5.0n
1.0c",1
I
FIGURE P24 .46
FIGURE PZ4.47
47. II An elec tron trave ls with speed 1.0 X 10 7 mls between th e
INT two parallel charged pl ates show n in Figure P24.47. The pl ates
are se parated by 1.0 cm an d are charged by a 200 V battery.
What mag net ic fi eld strength and d irecti o n will all ow the elec·
tron to pass between the pl ates without being defl ec ted?
48. II The two spri ngs in Fig ure P24.48 eac h have a spring constant
INT of 10 N/m . They are stretched by 1.0 cm when a current passes
through the wire. How big is the curren t?
20cm
-=-- 1.2 V
!5em
x
"\"
B = O.SOT
8=O.SO T
FIGURE P24.48
FIGURE PZ4.49
49. II A dev ice called a rai/guf/ uses the mag netic force on currents
INT to launch projecti les at very high speeds. An ideali zed model of
a railgun is illustrated in Figure 24.49. A 1.2 V power suppl y is
connected to two cond ucting rails. A segmen t of copper wire, in
a reg ion of uni form magnetic fi eld, sl ides freely on the ra il s.
The wire has a 0.85 mn resistance and a mass of 5.0 g. Ignore
the res istance of the rails. When the power supply is switched on,
a. What is the current?
b. Wh at are the mag ni tude and d irect ion of the force on the
wire?
c. Wh at wiLl be the wire's speed after it has sli d a di stance of
6.0 em?
An antiproton (whic h has
50.
INT the same prope rti es as a proton except that it s charge is
-e) is moving in the combined electri c a nd magneti c
fields of Figure P24.50.
E = tOOOV/rn
a. What are the magn itude
and d irect io n of the FIGURE P24 .50
ant iproto n's accel erat ion
at thi s instant?
b. What would be the magnitude and d irection of the acceleratio n if V' we re reversed?
J£25T
;I I /,.~
813
5 1. I Typical blood veloc ities in the coronary arteries range from
INT 10 to 30 cm/s. An electromagnetic flow meter applies a magnet ic
BIO fi eld of 0.25 T to a coronary artery wi th a blood veloc ity of 15
cm/s. As we saw in Figure 24.38, thi s fi eld exerts a force on ions
in the blood, whi ch will separate. The ions will separate un til
they make an electric fi eld that exac tly ba lances the magnetic
force. Thi s electric tield produces a voltage that can be measured.
a. What force is fell by a sing ly ioni zed (pos itive) sod ium ion?
b. Charges in th e bl ood will separate unt il they produce an
electric field th at ca ncels this mag net ic force. What will be
the res ultin g electric fi e ld?
c. What vo ltage wi ll thi s elec tric field prod uce across an artery
with a d iameter of 3.0 mm ?
52. I A power line co nsists of two wires, each carry ing a current of
400 A in the same direc tio n. The lines are perpe ndi cular to the
earth's magneti c fi e ld, and are separated by a distance of 5.0 m.
Which is larger: the force of the earth' s magnetic fi el d on each
wi re or the magneti c fo rce between the wires?
53. III Bats are capable of nav igating usin g the earth 's fi eld-a plus
BID for an an imal th at may fl y great d istances fro m its roost at night.
If, whi le sleepi ng duri ng the day, bats are ex posed to a fi eld of a
similar mag nitude but d iffere nt d irec ti on than the earth 's fi eld,
they are more likely to lose their way during the ir nex t lengthy
night fli ght. Suppose YO ll are a researcher doing such an experi ment in a locat io n where the earth's fi el d is 50,u.T at a 60° angle
below horizonta l. You make a 50-e m-d iameter, 100-t urn co il
around a roosting box; the sleepi ng bats are at the center of the
coil. You wish to pass a curren t thro ugh the coil to produce a
field that, when combi ned with the eart h's fi eld, creates a net
fi el d with the same stre ngth and d ip angle (60° be low hori zo ntal) as the eart h's fi eld bu t with a horizontal compo nen t th at
po ints south rather th an north. W hat arc (he proper ori e ntati o n
of the coi I and the necessary current?
54. III At the equator, the earth 's fi eld is essen tially horizon tal; near
BID the north pole, it is nearly vertical In between, the angle varies.
As you move farther north, the d ip angle, the angle of the
earth 's field below horizontal , stead ily inc reases. G reen tu rtles
seem to use thi s d ip ang le to determi ne the ir lat itude. Suppose
you are a researcher wan ti ng to test thi s idea. Yo u have gathered
green turt le hatc hli ngs from a beac h where the mag ne tic fi e ld
strength is 50,u.T and the di p angle is 56°. You then put the turtl es in a 1.2-m -d iameter c ircul ar tan k and mon itor the direct ion
in which they swi m as you vary the magnetic fi el d in the tank.
You change the fi eld by passin g a current through a 100-turn
hori zontal co il wrapped around the tank. Thi s creates a fi eld th at
adds to that of the earth. What current sho uld you pass thro ugh
the coil, and in what direction, to produce a net fiel d in the center
of the tank that has a d ip angle of 62°?
55 . II Intern al co mpo nents of cath ode-ray-tube te lev isions and
computer monitors can become magnetized; the res ulting magneti c fi eld ca n de fl ect th e e lectro n beam an d d istort the colors
o n the screen. Demagneti zation can be accompli shed with a co il
of wire whose c urrent sw itc hes d irect ion rapi dly and gradua ll y
decreases in ampl itude. Ex pl ain what effect thi s will have on
the magnet ic momen ts of the magnet ic materi als in the dev ice,
and how thi s mi ght el iminate any magneti c ordering.
56. III A 1.0- m-long, 1.0-mm -di ameter copper wire carri es a current
INT of 50.0 A to the east. S uppose we crea te a magne tic fi eld th at
prod uces an upward force o n the wire ex act ly equ al in magn itude to the wire's weig ht, causing the wire to " lev itate." Wh at
are the fi eld's direct ion and magn itude?
814
CHAPTER 24
Magnetic Fields and Forces
57. 11 An in sulated coppe r wire is wrapped
around an iron nail. Th e resulting co il of
wire cons ists of 240 turns of wire that cover
1.8 e m of the nail, as shown in Figure
P24.57. A current of 0.60 A passes through
the wire. If the ferromagnetic propert ies of
the na il in cre ase the field by a factor of
100, what is the magnetic field stren g th
ins ide the nail?
a. Make a sketch showing the direction of the magnetic field
from the solenoid. On your sketch, label the induced north
magnetic pole and the induced south magnetic pole in the iron .
b. Will the force on the iron be attrac ti ve or repulsive?
c. Suppose thi s force moves the iron. Which way will the iron
move?
Passage Problems
FIGURE P24 .57
The Velocity Selector INT
58. 1111 Figure P24.58 is a cross sec tion through
INT three lo ng wires with linear mass density
50 g/m. Th ey eac h carry eq ual CUlTents in
the directions shown. The lower two wires
09
are 4.0 em apart and are attac hed to a table. 09
What current ! will allow the upper wire to
4.0Clll
'; fl oat" so as to form an equil ateral triangle
FIGURE P24 .S8
with the lower wires?
59. 111 A long, straig ht wire with a
INT linear mass density of 50 glm
is suspended by threads, as
shown in Figure P24.59. There
is a uniform magnetic field
10"
pointing veltically downward. F
A 10 A current in the wire
experi ences a horizontal magnetic force that deflects it to an
equilibrium angle of 100. 'What
is the strength of the magnetic FIGURE P24 .59
field B?
60. 11 A mass spectrometer is designed to sep<ll'<lte atoms of carbon
to determine the frac tion of different isotopes. (Isotopes of an
element, as we will see in Chapter 30. have the same ato mic
number but different atomic mass, due to different numbers of
neutrons.) There are three main isotopes of carbon . with the follow in g atomic masses:
qE= qvB
Solving for the ve loc ity, we get:
E
)'= -
B
A particle movi ng at this veloci ty will pass through the reg ion of
uniform fields with no deflection, as shown in Figure P24.62. For
hi gher or lower velocities than thi s, the particles will feel a net force
and will be deflected. A slit at the end of the region allows o nly the
particles with the correct velocity to pass.
if
Atomic masses
2.16 X 10-
26
kg
13.8
In experiments where all the charged particles in a beam are required
to have the same veloc ity (for example, whe n enterin g a mass spectrometer), sc ienti sts lise a velocity seleClOl: A vel ocity selector has a
region of uniform electric and magnetic fi elds that are perpendicular to
each other and perpendicular to the motion of the charged particles.
Both the electric and magnetic fields exert a force on the charged particles. If a particle has precisely the right velocity, the two forces exactly
cancel and the particle is not deflected. Equating the forces due to the
electri c field and the magnetic field gives the following equation:
"
1.99 X 10- 26 kg
Actj"V
physcs
,
~ ------~--+----r---1"
2.33 X 10- 26 kg
FIGURE P24.62
The atoms of carbon are si ngly ionized and enter a mass spectrometer with magneti c fi e ld strength B = 0.200 T at a speed of
1.50 X 10 5 m/s. The io ns move alo ng a semic ircular path and
exit through an exit sl iL How far from the en trance will the
beams of the different isotope ion s end up?
61. I A soleno id is near a piece of iron , as shown in Figure P24.61.
When a cu rren t is present in the soleno id, a magnetic field is
created. This magnetic field will mag netize the iron , and there
wili be a net force between the soleno id and the iron.
Curren! in solenoid
is clockwise :IS
viewed from the
right end.· .... .....
....
•
FtGURE P24 .61
Piece of iron is
lined up with the
ax is of the
solenoid .
62. I Assuming the particle in Figure P24.62 is positively charged,
what are the direct ions of the forces due to the electric field and
to the magnet ic field?
A. The force due to the e lectric field is directed up (toward the
top of the page); the force due to the magne ti c field is
directed down (toward the bottom of the page).
B. The force due to the el ec tri c field is directed down (toward
the bOllom of the page); the force due to the magnetic field
is directed up (toward the top of the page).
C. The force due to the electric field is directed out of the plane
of the paper; the force due to the magnet ic field is directed
into the plane of the paper.
D. The force due to the electric field is directed into the plane
of the paper; the force due to the magneti c field is directed
out of the plane of the paper.
Problems
63. I How does the kinetic energy of the part icle in Figure P24.62
chan ge as it traverses the velocity selector?
A. The kinetic e nergy increases.
B. The kineti c energy does not c hange.
C. The kinetic e nergy decreases.
64. I Suppose a panicl e with twice the velocity of th e particle in
Figure P24.62 enters the velocity selector. The path of thi s particle will curve
A. Upward (toward the top of the page).
B. Downward (toward the bOllom of the page).
C. Out of the pl ane of the paper.
D. Into the plane of the paper.
65. I Next, a particle with the same mass and veloc ity as the panicle in Fi gure P24.62 enters the velocity selec tor. This particle
has a charge of 2q-twice the charge of the particl e in Figure
P24.62. In thi s case, we can say that
A. The force of the electr ic field on the particle is greater than
the force of the magnetic field.
B. The force of the magnetic field on the parti cle is greater
than the force of the electric fi eld.
C. The forces of the electric and magnetic fields on the particle
are sti II equal.
Ocean Potentials INT
The ocean is salty because it contains many dissolved ions. As these
charged panicles mo ve with the water in strong ocean cUlTen ts, they
fee l a force from the earth' s magnetic field. Positive and negative
charges are separated unti I an e lectri c fi el d develops that balances
this magneti c force. Thi s field produces measurable potential differences that can be monitored by ocean researchers.
815
The Gulf Stream moves northward off the east coas t of the Un ited
States at a speed of up 1.0 3.5 m/s. Assume that the current fl ows at
this maximum speed and that the earth ' s field is SO J..LT tipped 60°
below hori zon tal.
66. I What is t.he direction of the magnetic force on a singly ionized
negati ve chlorine ion mov in g in this ocean current?
A East
8 . West
C. Up
D. Down
67. I What is the magn itude of the force on this ion?
A. 2.8 X 10- 23 N
B. 2.4 X 10- 23 N
C. 1.6 X 10- 23 N
D. 1.4 X 10
23
N
68. I What magn itude electric field is necessary to exactly balance
thi s magnet ic force?
A. 1.8 X 10-' N/C
B. 1.5 X 10-' NlC
C. 1.0 X 10-' N/C
D. 0.9 X 10- 4 NlC
69. I The electric field produ ces a potential difference. If YOLI
place one elec trode 10m below the surface of the water, you
will measure the greatest potential difference if you place the
seco nd electrode
A At the surface.
8. Aladepthof20m.
C. At the sa me depth 10m to the north.
D. At the same depth 10 m to the east.
Stop to Think 24.1: C. The com pass needl e will not rotate since
there is no force between the stationary charges on the rod and the
magnetic poles of the compass needle.
Stop to Think 24.5: C. The ri ght-hand rule for forces gives the
direction of the force. With the field into the paper, the force is to the
left if the current is toward the top of the paper.
Stop to Think 24.2: A. The co mpass needle will rotate to line up
with the field of the magnet, which goes from the north to the south
pole.
Stop to Think 24.6: B. Looking at the forces on the top and the bottom of the loop, we can see that the loop will rotate counterclockwise. Alternatively, we can look at the dipol e structure of the loop:
With a north pole on the left and a south pole on the ri ght, the loop
will rotate countercloc kwi se.
Stop to Think 24.3: D. The compass needle will rotate to line up
with the field cirding lhe wire. The ri ght-hand rule for fields shows
this to be toward the top of the paper in the fi gure.
Stop to Think 24.4: A, C. The forc e to prod uce these circular orbits
is directed toward the center of the circle. Using the ri ght-hand rule
for forces, we see that thi s will be true for the situati ons in A and C if
the particles are negati vely charged.
Stop to Think 24.7: B. All of the induced dipoles will be aligned
with the field of the bar magnet.