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Que stions tMP)TM !:!!/ 807 IN! integrate significant material from earlier BID are of biological or medical interest. For homework assigned on MasteringPhysics, go to Problems labeled www.masteringphysics.com chapters; Problem difficulty is labeled as I (straightforward) to 11111 (challenging), 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.