3. The magnetic field lines form clockwise circles centered on the wire.

Transcription

1 CHAPTER : Magnetis Answes t Questins. The Eath s agnetic field is nt always aallel t the suface f the Eath it ay have a cnent eendicula t the Eath s suface. The cass will tend t line u with the lcal diectin f the agnetic field, and s ne end f the cass will di dwnwad. The angle that the Eath s agnetic field akes with the hizntal is called the angle f di.. The agnetic field lines cicle aund the wie and get weake as yu get fathe away f the wie. T deteine the diectin, use the Right Hand Rule. Ntice, if the wie was laid hizntally n this iece f ae in a left-ight diectin and the cuent was ving t the left, the agnetic field lines wuld be inting int the ae abve the wie and cing ut f the ae belw the wie. f the wie was laced eendicula t this age with the cuent cing ut f the end f the wie facing us, the agnetic fields wuld int aund the wie in a cunteclckwise diectin. 3. The agnetic field lines f clckwise cicles centeed n the wie.. The ight-hand ule shws us that if a cuent in a wie is inting diectly away f yu while the wie is in a agnetic field that ints f left t ight, the fce n the wie is inted dwnwad. See Figue -(a).. A agnet will nt attact just any etallic bject. F exale, while a agnet will attact ae clis and nails, it will nt attact cins ieces f aluinu fil. This is because agnets will nly attact the feagnetic ateials (in, cbalt, nickel, gadliniu, and se f thei xides and allys). n and its allys ae the nly cn ateials. These feagnetic ateials cntain agnetic dains that can be ade t teaily align when a stng agnet is bught nea. The alignent ccus in such a way that the nth le f the dain ints twad the suth le f the stng agnet, and vice vesa, which ceates the attactin. 6. The bas cannt bth be agnets. f bth wee agnets, then if like les wee laced clse t each the, the bas wuld eel each the. Only ne f the bas can be a agnet.. Tyical cuent in a huse cicuit is 6 Hz AC. Due t the ass f the cass needle, its eactin t 6 Hz (changing diectin back and fth at 6 clete cycles e secnd) will bably nt be nticeable. A DC cuent in a single wie culd affect a cass, deending n the elative ientatin f the wie and the cass, the agnitude f the cuent, and the distance f the wie Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 9

2 Chate Magnetis t the cass. A DC cuent being caied by tw vey clse wies in site diectins wuld nt have uch f an effect n the cass needle, since the tw cuents wuld cause agnetic fields that tended t cancel each the. 8. The agnetic fce will be exactly eendicula t the velcity, and s als eendicula t the diectin f tin. Since thee is n cnent f fce in the diectin f tin, the wk dne by the agnetic fce will be ze, and the kinetic enegy f the aticle will nt change. The aticle will change diectin, but nt change seed. 9. Use the ight hand ule t deteine the diectin f the fce n each aticle. n the lane f the diaga, the agnetic field is cing ut f the ae f ints abve the wie, and is ging int the ae f ints belw the wie. Ue left hand aticle: fce dwn, twad the wie Ue ight hand aticle: fce t the left, site f the diectin f the cuent Lwe ight hand aticle: fce t the left, site f the diectin f the cuent Lwe left hand aticle: fce u, twad the wie. Chage a exeiences an initial uwad fce. y the ight hand ule, chage a ust be sitive. Chage b exeiences n fce, and s chage b ust be unchaged. Chage c exeiences an initial dwnwad fce. y the ight hand ule, chage c ust be negative.. The ight hand ule tell us that as the sitive aticle ves t the ight, if it is deflected uwad the agnetic field ust be int the ae and if it is deflected dwnwad the agnetic field ust be ut f the ae. Als, the stnge the agnetic field, the e tightly the chaged aticle will tun. The agnetic field at the fist bend ust be elatively sall and inted int the ae. The agnetic field at the secnd bend ust be ediu in size and inted ut f the ae. The agnetic field at the thid bend ust be elatively vey lage and inted int the ae.. A agnet can attact an in ba, s by Newtn s thid law, an in ba can attact a agnet. Anthe cnsideatin is that the in has dains that can be ade slightly agnetic by an extenal agnetic field, as sed t a substance like lastic wd. 3. Sectin - shws that a CRT televisin ictue is ceated by shting a bea f electns at a sceen, and wheeve the electns hit the sceen it lights u f us t see. When yu hld a stng agnet t clse t the sceen, the agnetic field uts a fce n the ving electns F qv sin, which causes the t bend away f whee they wee sused t hit the sceen. These eant electns then cause ats f the sceen t light u that aen t sused t be lit and cause the ats t be slightly dake than they ae sused t be. The ictue seties ges cletely black whee the field is stngest because at these ints all f the electns that wee sused t hit that aticula st have been deflected by the stng field.. Put ne end f ne d clse t ne end f anthe d. The ends will eithe attact eel. Cntinue tying all cbinatins f ds and ends until tw ends eel each the. Then the tw ds used in that case ae the agnets. Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 98

3 Giancli Physics: Pinciles with Alicatins, 6 th Editin. N, yu cannt set a esting electn int tin with a agnetic field (n atte hw big the field is). A agnetic field can nly ut a fce n a ving chage. Thus, with n fce (which eans n acceleatin), the velcity f the electn will nt change it will eain at est. Hweve, yu can set a esting electn int tin with an electic field. An electic field will ut a fce n any chaged aticle, ving nt. Thus, the electic fce can cause the electn t acceleate f est t a highe seed. 6. The chaged aticle will nw tavel in a helix. t will cntinue in its iginal cicula ath while it is taveling in the diectin f the agnetic and electic fields, which is eendicula t the lane f the iginal cicle. F as lng as the electic field stays n, the aticle will ve in a cnstantly elngating helix (the itch f the helix will cntinue t incease), since the electic field will cause the chaged aticle t acceleate alng the electic field lines.. Using the cnfiguatin shwn in Fig. -8, the electic field uts a fce n the chaged aticles and causes the t acceleate in a vetical diectin f est (the negative aticles ae acceleated uwad and the sitive aticles ae acceleated dwnwad). Once the chaged aticles ae ving, the agnetic field nw als uts a fce n the chaged aticles. Using the Right Hand Rule, bth the uwad-ving negative aticles and the dwnwad-ving sitive aticles exeience a fce ut f the age, which is alng the diectin f the vessel. Thus, yes, bth the sitive and negative aticles exeience a fce in the sae diectin. 8. The bea f electns is deflected t the ight. The agnetic field ceated by the cuent in the wie,, is diected int the age n the side f the wie whee the electn bea is lcated. The ight hand ule tells us that the negative electns will feel a fce t the ight as they ve twad the wie in a dwnwad agnetic field. 9. A ving electic chage ceates bth electic and agnetic fields aund it. The electic field is adial and it lks vey siila t the tyical electic field that suunds a statinay electic chage. The agnetic field cicles the chage in a lane that is eendicula t the diectin f tin and it lks vey siila t the tyical agnetic field that suunds a cuent-caying wie. th f these fields decease in stength as yu g fathe away f the ving chage in any diectin.. Yes, thee culd be a nn-ze agnetic field in this egin f sace, even thugh the chaged aticle tavels in a staight line. One ssible situatin is that the chaged aticle is taveling in a diectin aallel ( anti-aallel) t the agnetic field lines. n this situatin, n agnetic fce is exeted n the chaged aticle, since the sin te in F qv sin is ze. The the ssible situatin is that the chaged aticle is taveling thugh cssed electic and agnetic fields in such a way that the electic fce and the agnetic fce ae canceling each the ut. F exale, if a sitively chaged aticle wee ving east in a egin f sace whee the electic field was suth (which ceates a fce twad the suth) and the agnetic field was dwnwad (which ceates a agnetic field twad the nth), and the agnitudes f E and wee chsen cectly, then the electic and agnetic fces wuld cancel ut, allwing the chaged aticle t tavel in a staight line.. N, a ving chaged aticle can be deflected sideways with an electic field that ints eendicula t the diectin f the velcity, even when the agnetic field in the egin is ze.. N, althugh when an electn is injected eendiculaly int a egin f unif agnetic field, the electn is fced t tavel alng a cuve in the shae f a efect cicle, the electn wuld tavel in a ath that is nly half f a cicle and at that int it wuld ce back ut f the agnetic field and head back in the diectin it cae. Yes, if an electn wee injected int the iddle f a lage Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 99

4 Chate Magnetis egin f sace ccuied by a eendicula agnetic field, the electn culd tavel in a clsed cicula ath. 3. f the ving electns ae changing seed as they ae being deflected, then an electic field is esent. This will be the case whethe nt a agnetic field exists in the sae egin f sace. f the ving electns ae being deflected but they ae nt changing seed, then nly a agnetic field is esent.. Use a sall l f cuent-caying wie that is able t ivt feely alng a vetical axis (the faces f the l shuld be inting hizntally). Use the ight hand ule t deteine which face f the l has a agnetic nth le inting ut f it. The nth and agnetic suth les ceated by the l will attet t ivt t align with Eath s agnetic field. The nth face f the l will int twad the agnetic suth le f Eath (which is nea the gegahic Nth Ple).. Cnside that the tw wies ae bth hizntal, with the lwe ne caying a cuent inting east and with the ue ne caying a cuent inting nth. The agnetic field f the ue wie ints dwnwad n the east half f the lwe wie and ints uwad n the west half f the lwe wie. Using the ight hand ule n the east half f the lwe wie, whee the agnetic field is dwnwad, the fce ints t the nth. Using the ight hand ule n the west half f the lwe wie, whee the agnetic field is uwad, the fce ints t the suth. Thus, the lwe wie exeiences a cunteclckwise tque abut the vetical diectin due t the agnetic fces f the ue wie. This tque is atteting t tate the tw wies s thei cuents ae aallel. Likewise the ue wie wuld exeience a clckwise tque tending t align the cuents in the wies. 6. (a) The cuent in the lwe wie is inting in the site diectin f the cuent in the ue wie. f the cuent in the lwe wie is twad the nth, then it ceates a agnetic field inting east at the ue wie. Using the Right Hand Rule, the cuent f the ue wie ust be twad the suth s that the agnetic fce ceated n it is uwad. (b) Yes, the ue wie is vetically stable. f the ue wie falls twad the lwe wie slightly, then the agnetic fce inceases t ush it back u t its stable sitin. f the ue wie ises away f the lwe wie slightly, althugh the agnetic field deceases, gavity will ull it back int its stable sitin.. The agnetic dains in the unagnetized iece f in ae initially inting in and diectins (which is why it aeas t be unagnetized). When the suth le f a stng extenal agnet is bught clse t the and agnetic dains f the in, any f the dains will tate slightly s that thei nth les ae clse t the extenal suth le, which causes the unagnetized in t be attacted t the agnet. Of cuse, when the nth le f a stng extenal agnet is bught clse t the and agnetic dains f the in, any f the dains will tate slightly s that thei suth les ae clse t the extenal nth le, which causes the unagnetized in t nw be attacted t the agnet. Thus, eithe le f a agnet will attact an unagnetized iece f in. 8. nitially, bth the nail and the ae cli have all f thei agnetic dains inting in and diectins (which is why they aea t be unagnetized). Thus, when yu bing the clse t each the, they ae nt attacted t eelled f each the. Once the nail is in cntact with a agnet (let s say the nth le), thugh, any f the nail s dains will align in such a way that the end tuching the agnet beces a suth le, due t the stng attactin, and the site end f the nail then beces a nth le. Nw, when yu bing the nail clse t the ae cli, thee ae ainly nth les f nail dains clse t the ae cli, which causes se f the dains in the ae cli t align in such a way that the end nea the nail beces a suth le, which is exactly the sae cedue that the nail was agnetized. Since the nail s dains ae nly atially aligned, Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

5 Giancli Physics: Pinciles with Alicatins, 6 th Editin it will nt be a stng agnet and thus the alignent f the ae cli s dains will be even weake. The attactin f the ae cli t the nail will be weake than the attactin f the nail t the agnet. 9. The tw ins will ce ut f the velcity select tin f the ass sectete at the sae seed, since v E (whee the chage q has canceled ut). Once the chages each the aea f the ass sectete whee thee is nly a agnetic field, then the diffeence in the ins chages will have an effect. The equatin f the ass sectete is q E, which can be eaanged as E q. Since evey quantity in the equatin is cnstant excet q, the dubly inized in will hit the fil at a half f the adius as the singly inized in. 3. The equatin f the agnetic field inside f a slenid is N l. (a) Nthing wuld haen t if the l diaete was dubled. The equatin shws that the agnetic field is indeendent f the diaete f the slenid. (b) wuld decease by a fact f. When the sacing between the ls is dubled, the nube f ls e length, N l, is cut in half, which deceases by a fact f. (c) Nthing wuld haen t if bth the length and the nube f ls wee dubled. The agnetic field des deend n the nube f ls e length, N l, but if bth the nube f ls and the length f the slenid ae dubled, this ati eains cnstant and the agnetic field desn t change. 3. T design a elay, lace the in d inside f a slenid, then int ne end f the slenid/d cbinatin at the iece f in n a ivt. A sing nally hlds the iece f in away f a switch, aking an en cicuit whee cuent cannt flw. When the elay is activated with a sall cuent, a elatively stng agnetic field is ceated inside the slenid, which aligns st f the agnetic dains in the in d and duces a stng agnetic field at the end f the slenid/d cbinatin. This agnetic field attacts the iece f in n the singy ivt, which causes it t ve twad the switch, cnnecting it and allwing cuent t flw thugh the lage cuent cicuit. n Rd Slenid Singy Pivt Piece f n Ca battey Lage cuent cicuit Sall cuent cicuit f dashbad switch State Slutins t Pbles. (a) Use Eq. - t calculate the fce with an angle f 9 and a length f ete. F F l sin sin 8. A.9T sin 9.6 N l (b) F sin 8.A.9T sin..3n l Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

6 Chate Magnetis. Use Eq. - t calculate the fce. F l sin A 6. T sin 6.N 3. Use Eq. -. F l F. N ax ax l.8 8. T.9A. The di angle is the angle between the Eath s agnetic field and the cuent in the wie. Use Eq. - t calculate the fce. F lsin.a.. T sin 38.3 N. Use Eq. -. The length f wie in the -field is the sae as the diaete f the le faces. F.8 N ax F l.6 T ax l 8. A. 6. T have the axiu fce, the cuent ust be eendicula t the agnetic field, as shwn in the fist diaga. Use F.3 F ax t find the angle between the wie and the agnetic field, l l illustated in the secnd diaga. F Fax.3 sin.3 sin.3 l l wie wie. (a) y the ight hand ule, the agnetic field ust be inting u, and s the t le face ust be a Suth le. (b) Use Eq. - t elate the axiu fce t the cuent. The length f wie in the agnetic field is equal t the diaete f the le faces. 6. N Fax F l.63a.a ax l..6t (c) Multily the axiu fce by the sine f the angle between the wie and the agnetic field. F F ax sin 6. N sin8. 6. N 8. The agnetic fce ust be equal in agnitude t the fce f gavity n the wie. The axiu agnetic fce is alicable since the wie is eendicula t the agnetic field. The ass f the wie is the density f ce ties the vlue f the wie. d F g l l g d g kg. 9.8 s. T A Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

7 Giancli Physics: Pinciles with Alicatins, 6 th Editin This answe des nt see feasible. The cuent is vey lage, and the Jule heating in the thin ce wie wuld bably elt it. 9. n this scenai, the agnetic fce is causing centietal tin, and s ust have the f f a centietal fce. The agnetic fce is eendicula t the velcity at all ties f cicula tin. v F qv v 6.6 kg.6 s ax 9 q.6 C.. The axiu agnetic fce as given in Eq. - can be used since the velcity is eendicula t the agnetic field. F 9 3 qv.6 C 8. s.t. N ax y the ight hand ule, the fce ust be diected t the Nth.. Since the chage is negative, the answe is the OPPOSTE f the esult given f the ight hand ule alied t the velcity and agnetic field. (a) left (b) left (c) uwad (d) inwad int the ae (e) n fce (f) dwnwad. The ight hand ule alied t the velcity and agnetic field wuld give the diectin f the fce. Use this t deteine the diectin f the agnetic field given the velcity and the fce. (a) dwnwad (b) inwad int the ae (c) ight 3. The agnetic fce will cause centietal tin, and the electn will ve in a clckwise cicula ath if viewed in the diectin f the agnetic field. The adius f the tin can be deteined. 3 6 v v 9. kg. s F qv. ax 9 q.6 C.3 T. The kinetic enegy f the tn can be used t find its velcity. The agnetic fce duces centietal acceleatin, and f this the adius can be deteined. KE v KE KE v KE q q q qv v Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 3.3T 6 9. ev.6 J ev.6 kg 9.6 C. T. The agnetic field can be fund f Eq. -, and the diectin is fund f the ight hand ule. Reebe that the chage is negative. 3 F. N ax F qv.6t ax 9 6 qv.6 C.9 s.6

8 Chate Magnetis The diectin wuld have t be East f the ight hand ule, alied t the velcity and the agnetic field, t give the e diectin f fce. 6. The fce n the electn due t the electic fce ust be the sae agnitude as the fce n the electn due t the agnetic fce. 3 E 8.8 V 6 6 E 3. s. s F F qe qv v 3. T f the electic field is tuned ff, the agnetic fce will cause cicula tin. 3 6 v v 9. kg. s 3 F qv. ax 9 3 q.6 C 3. T. (a) The velcity f the in can be fund using enegy cnsevatin. The electical tential enegy f the in beces kinetic enegy as it is acceleated. Then, since the in is ving eendicula t the agnetic field, the agnetic fce will be a axiu. That fce will cause the in t ve in a cicula ath. E E qv v v initial final v F qv ax qv v V q q q qv 6.6 kg V 9.3T.6 C. (b) The eid can be fund f the seed and the adius. Use the exessins f the adius and the seed f abve. v V q T T v qv q 6.6 kg 9.6 C.3 T 3.8 s 8. The velcity f each chaged aticle can be fund using enegy cnsevatin. The electical tential enegy f the aticle beces kinetic enegy as it is acceleated. Then, since the aticle is ving eendiculaly t the agnetic field, the agnetic fce will be a axiu. That fce will cause the in t ve in a cicula ath, and the adius can be deteined in tes f the ass and chage f the aticle. E E qv v v initial final qv qv F qv ax q q q v v V Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

9 Giancli Physics: Pinciles with Alicatins, 6 th Editin d V q d d V q d q q V q V q q q d d 9. F Exale -, we have that unif cicula tin is given by T T v q v v q v. Then, f chate, the eid f an bject ving in q v. Cbine these tw elatinshis.. F Exale -, we have that Thus q. v. The quantity v is the entu,, and s q q.. F Exale -, we have that KE v q, and s v q q q v and s we see that. The kinetic enegy is given by KE.. The angula entu f a aticle ving in a cicula ath is given by L v. F Exale v q -, we have that, and s v. Cbining these elatinshis gives the fllwing. q q L v q 3. The agnetic fce duces an acceleatin that is eendicula t the iginal tin. f that eendicula acceleatin is sall, it will duce a sall deflectin, and the iginal velcity can be assued t always be eendicula t the agnetic field. This leads t a cnstant eendicula acceleatin. The tie that this (axiately) cnstant acceleatin acts can be fund f the iginal velcity v and the distance taveled L. The stating seed in the eendicula diectin will be ze. qv F a qv a Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

10 Chate Magnetis 9 3 qv L ql 3. C. T. 3 d v t a t v v 3. kg 6 s 6. This sall distance justifies the assutin f cnstant acceleatin.. The agnetic fce will duce centietal acceleatin. Use that elatinshi t calculate the 6 seed. The adius f the Eath is 6.38 k, and the altitude is added t that. v F qv v q C T kg Cae the size f the agnetic fce t the fce f gavity n the in. F F g qv g C. s. T kg 9.8 s s t is fine t igne gavity the agnetic fce is e than illin ties lage than gavity.. (a) n the agnetic field, the tn will ve alng an ac f a cicle. The distance x in the diaga is a chd f that cicle, and s the cente f the cicula ath lies n the eendicula bisect f the chd. That eendicula bisect bisects the cental angle f the cicle which subtends the chd. Als ecall that a adius is eendicula t a tangent. n the diaga, because they ae vetical angles. Then, because they ae bth cleents f 3, s. We have since the cental angle is bisected by the eendicula bisect f the chd. because they ae bth cleents f 6, and is 8 because they ae vetical angles. Thus, and s in the textbk diaga, the angle at which the tn leaves 8. (b) The adius f cuvatue is given by x v q, and the distance x is twice the value f cs. v.6 kg. s 3 cs cs cs 3. 9 q.6 C.8 T 6. We assue the jue cable is a lng staight wie, and use Eq. -6. T A 6A.6 T. T cable 6. Cae this t the Eath s field f.6 T cable Eath.33. T., s the field f the cable is abut ties that f the Eath.. T Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 6

11 Giancli Physics: Pinciles with Alicatins, 6 th Editin. We assue that the wie is lng and staight, and use Eq T wie wie T A 69A 8. T find the diectin, daw a adius line f the wie t the field int. Then at the field int, daw a eendicula t the adius line, diected s that the eendicula line wuld be at f a cunteclckwise cicle. C D E 9. Since the fce is attactive, the cuents ust be in the sae diectin, s the cuent in the secnd wie ust als be uwad. Use Eq. - t calculate the agnitude f the secnd cuent. F l d F d. l 8.8 N 3A uwad T A A 3. Since the cuents ae aallel, the fce n each wie will be attactive, twad the the wie. Use Eq. - t calculate the agnitude f the fce. T A A F l 3.3 N, attactive d F the exeient t be accuate t.%, the agnetic field due t the cuent in the cable ust be less than equal t.% f the Eath s agnetic field. Use Eq. -6 t calculate the agnetic field due t the cuent in the cable..... T Eath cable Eath.. A T A Thus the axiu allwable cuent is.a. 3. We assue that the we line is lng and staight, and use Eq. -6. line T A 9A 8. Cae this t the Eath s field f 6.3 T line Eath.. T.. T The field f the cable is abut % that f the Eath T. T Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

12 Chate Magnetis 33. The field f each wie akes cncentic cicles abut the suce wie. The individual fields at int P ae eendicula t the lines f the wies t int P. We define as the field f the clse int, and as the field f the futhe int. Use Eq. -6 t calculate each individual field. T A A. T. T A A. tan.6 net.6 T cs 9 cs. T cs 6..6 T cs.6 net x 8. T T sin 9 sin. T sin 6..6 T sin.6 net y. T 3.c.c.c 9 net At the lcatin f the cass, the agnetic field caused by the wie will int t the west, and the Eath s agnetic field ints due Nth. The cass needle will int in the diectin f the NET agnetic field. wie T A 3A.8 Eath 3.89 T wie 3.89 T. T tan tan 9 N f W 3. The agnetic field due t the lng hizntal wie ints staight u at the int in questin, and its agnitude is given by Eq. -6. The tw fields ae iented as shwn in the diaga. The net field is the vect su f the tw fields. wie Eath. T T A.A.. T cs 3. T sin 3.8 T net x Eath net y wie Eath net net x net y net y. T net x. T.8 T. T.8 T tan tan belw the hizntal wie net wie Eath Eath net Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 8

13 Giancli Physics: Pinciles with Alicatins, 6 th Editin 36. The stea f tns cnstitutes a cuent, whse agnitude is fund by ultilying the tn ate ties the chage f a tn. Then use Eq. -6 t calculate the agnetic field. stea 9 9 T A. tns s.6 C tn.. T 3. (a) f the cuents ae in the sae diectin, the agnetic fields at the idint between the tw cuents will se each the, and s thei agnitudes shuld be subtacted. T A net. A T A A (b) f the cuents ae in the site diectin, the agnetic fields at the idint between the tw cuents will einfce each the, and s thei agnitudes shuld be added. T A A T A A net. 38. The fields ceated by the tw wies will se each the, s the net field is the diffeence f the agnitudes f the tw fields. The sitive diectin f the fields is taken t be int the ae, and s the clse wie ceates a field in the sitive diectin, and the fathe wie ceates a field in the negative diectin. net clse fathe clse clse T A.A 6 6. T. T Cae this t the Eath s field f 6. T net Eath T.. T The field f the wies is abut 3% that f the Eath. 39. The cente f the thid wie is.6 f the left wie, and.8 f the ight wie. The fce n the nea (ight) wie will attact the nea wie, since the cuents ae in the sae diectin. The fce n the fa (left) wie will eel the fa wie, since the cuents se each the. Use Eq. - t calculate the fce e unit length. F F F T A.A nea l nea nea 3 d l d.8 nea nea nea F T A.A fa l fa fa 3 d l d.6 fa fa fa clse. N, attact. N, eel Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 9

14 Chate Magnetis. The Eath s agnetic field is esent at bth lcatins in the ble, and we assue it is the sae at bth lcatins. The field east f a vetical wie ust be inting eithe due nth due suth. The cass shws the diectin f the net agnetic field, and it changes f 3 E f N t E f N when taken inside. That is a suthely change (athe than a nthely change ), and s the field due t the wie ust be inting due suth. See the diaga. F the angles, 3,, and 8 and s 3 and. Use the law f sines t find the agnitude f, and then use Eq. -6 t find the wie agnitude f the cuent. sin wie Eath wie Eath sin sin sin sin sin 3 Eath. T. 9. A sin sin T A Since the field due t the wie is due suth, the cuent in the wie ust be dwn. Eath net wie. The agnetic field at the l due t the lng wie is int the age, and can be calculated by Eq The fce n the segent f the l clsest t the wie is twads the wie, since the cuents ae in the sae diectin. The fce n the segent f the l fathest f the wie is away f the wie, since the cuents ae in the site diectin. ecause the agnetic field vaies with distance, it is difficult t calculate the ttal fce n eithe the left ight segents f the l. Using the ight hand ule, the fce n each sall iece f the left segent f wie is t the left, and the fce n each sall iece f the ight segent f wie is t the ight. f left and ight sall ieces ae chsen that ae equidistant f the lng wie, the net fce n thse tw sall ieces is ze. Thus the ttal fce n the left and ight segents f wie is ze, and s nly the aallel segents need t be cnsideed in the calculatin. Use Eq. -. F F F l l l net nea fa nea fa d d d d nea fa nea fa T A 6. A..6 N, twads wie.3.8. (a) The agnetic fce exeted n the lwe wie ust be uwads, and ust be the sae agnitude as the gavitatinal fce n the lwe wie. Cnside a length L f the ce wie. t Cu d g d L g Cu Cu Cu Cu F F g L g Cu Cu Cu d L L d Cu t g Cu t Cu t Cu kg. 9.8 s T A 8A 6A The cuents ust be in the sae diectin f the agnetic fce t be uwad, s the cuent is t the ight. (b) f the wie is dislaced slightly dwnwad, the agnetic fce wuld be less than the fce f gavity, s the bject wuld cntinue t ve dwnwad and it wuld fall. Thus the lwe wie is nt in stable equilibiu. (c) ecause the wies ae the sae distance aat, the cuent ust be the sae, 6A. The cuent in the ue wie ust nw be t the left s that the agnetic fce is uwads. f the Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

15 Giancli Physics: Pinciles with Alicatins, 6 th Editin wie is nw dislaced uwads, the agnetic fce deceases, and the bject stats t fall, ving twad its iginal sitin. f the wie is dislaced dwnwads, the agnetic fce inceases, and the bject wuld ve back twad its iginal sitin. Thus the wie is in stable equilibiu. 3. The agnetic fields ceated by the individual cuents will be at ight angles t each the. The field due t the t wie will be t the ight, and the field due t the btt wie will be ut f the age. Since they ae at ight angles, the net field is the hytenuse f the tw individual fields. t. T t btt net t btt. btt T A.A.A. (a) Use Eq. -6 t calculate the field due t a lng staight wie. (b) at A A at A A t T A.A. t A T. T T A.A T.3 6 T. (c) The tw fields ae nt equal and site. Each individual field is due t a single wie, and has n deendence n the the wie. The agnitude f cuent in the secnd wie has nthing t d with the value f the field caused by the fist wie. (d) Use Eq. - t calculate the fce due t ne wie n anthe. The fces ae attactive since the cuents ae in the sae diectin. F F n A due t n due t A A A A t T A.A.A l l d..6 N. N These tw fces e unit length ae equal and site because they ae a Newtn s Thid Law ai f fces.. The fces n wie M due t the the wies ae eelling fces, away f the the wies. Use Eq. - t calculate the fce e unit length n wie M due t each f the the wies, and then add the fce vects tgethe. The hizntal ats f the fces cancel, and the su is vetical. FM net y FMN FMP cs3 cs3 l l l M M M cs3 d M N M P MN d MP cs3 F MP 3 3 F MN T A 8.A cs 3.8 N, 9.38 Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

16 Chate Magnetis The fces n wie N due t the the wies ae an attactive fce twads wie P and a eelling fce away f wie M. Use Eq. - t calculate the fce e unit length n wie N due t each f the the wies, and then add the fce vects tgethe. F the syety, we exect the net fce t lie exactly between the tw individual fce vects, which is 6 belw the hizntal. F N net y F NM cs3 M N d MN cs3 T A 8.A cs3.9 N F F sin 3 F N net x NM NP.68 N F F F.38 T A 8.A T A 8.A sin F.9 3. N tan tan 3 F.68 N net y N net N net x N net y N net x F NM 3 9 F NP The fces n wie P due t the the wies ae an attactive fce twads wie N and a eelling fce away f wie M. Use Eq. - t calculate the fce e unit length n wie P due t each f the the wies, and then add the fce vects tgethe. F syety, this is just a i iage f the evius slutin, and s the net fce is as fllws. F P net 3. N F PN 9 3 F PM 6. Thee will be thee agnetic fields t su ne f each wie. Each field will int eendiculaly t the line cnnecting the wie t the idint. The tw fields due t M and N ae dawn slightly seaated f each the, but shuld be cllinea. The agnitude f each field is given by Eq net M N P M P N P M T A 8.A 8. T.9 T A 8.A T cs 3 cs 6 8. T cs 3.86 T cs 6 net x M P. T sin 3 sin 6 8. T sin 3.86 T sin 6 net y M P. T x y. T. T. T net net net N P 6 3 N M M P Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

17 Giancli Physics: Pinciles with Alicatins, 6 th Editin net y tan tan net net y. T. T The net field ints slightly belw the hizntal diectin.. The left wie will cause a field n the x-axis that ints in the y-diectin, and the ight wie will cause a field n the x- axis that ints in the negative y-diectin. The distance f the left wie t a int n the x-axis is x, and the distance f the ight wie is d x. net x d x x d x A gah f the abve functin is shwn hee Use Eq. -8 f the field inside a slenid. N l T A.A T 9. Use Eq. -8 f the field inside a slenid. l.38t.3 N l N T A 9 9.3A. The field due t the slenid is given by Eq. -8. Since the field due t the slenid is eendicula t the cuent in the wie, Eq. - can be used t find the fce n the wie segent. F l l wie wie slenid wie wie. N slenid l slenid N A.3 T A 33A.. Since the ass f ce is fixed and the density is fixed, the vlue is fixed, and we designate it as V L A. We call the fixed vltage V. The agnetic field in the slenid is given by Cu Cu Cu Cu Cu Eq. -8. N N V N V N A V N Cu Cu Cu V L R L L sl Cu sl RCu Cu L L L L L RCu sl Cu RCu sl Cu sl A V N Cu Cu L L RCu sl Cu Cu The nube f tuns f wie is the length f wie divided by the cicufeence f the slenid. L N L V N V V Cu Cu Cu Cu Cu sl Cu Cu L L L L L L sl RCu sl Cu RCu sl Cu RCu sl sl Cu Cu Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 3

18 Chate Magnetis The fist fact in the exessin f is ade f cnstants, s we have L L sl sl Cu. Thus we want the wie t be sht and fat. Als the adius f the slenid shuld be sall and the length f the slenid sall.. (a) Each l f wie duces a field alng its axis, siila t Figue -9. F ath, with all the ls taken tgethe, that syety leads t a agnetic field that is the sae anywhee alng the ath, and aallel t the ath. One side f evey tun f the wie is enclsed by ath, and s the enclsed cuent is N. Aly Eq. -9. l N R N N R (b) F ath, each l f wie ieces the enclsed aea twice nce ging u and nce ging dwn. Aee s law takes the diectin f the cuent int accunt, and s the net cuent thugh the aea enclsed by ath is. l N R (c) The field inside a tid is nt unif. As seen in the esult t at (a), the field vaies invesely as the adius f the tid, and s the tid, and weakest at the utside wall. R. The field is stngest at the inside wall f 3. (a) Aee s Law says that alng a clsed ath, l. F the ath chse a cicle f encl adius, centeed n the cente f the wie, geate than the adius f the inne wie and less than the adius f the ute cylindical baid. ecause the wie is lng and staight, the agnetic field is tangent t the chsen ath, and s. The cuent enclsed by the ath is. l l l encl (b) We ake a siila aguent, but nw chse the ath t be a cicle f adius, geate than the adius f the ute cylindical baid. ecause the wie and the baid ae lng and staight, the agnetic field is tangent t the chsen ath, and s. The cuent enclsed by the ath is ze, since thee ae tw equal but sitely diected cuents. encl l l l encl. f the face f the l f wie is aallel t the agnetic field, the angle between the eendicula t the l and the agnetic field is 9. Use Eq. - t calculate the agnetic field stength..3 N NA sin. T NAsin 6.3A. sin 9. n sectin -, it is shwn that the deflectin f the galvanete needle is tinal t the duct f the cuent and the agnetic field. Thus if the agnetic field is deceased t.86 ties its iginal value, the cuent ust be inceased by dividing the iginal value by.86 t btain the sae deflectin. 3. A initial initial initial 6.6 A initial final final.86 final Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. initial

19 Giancli Physics: Pinciles with Alicatins, 6 th Editin 6. F the galvanete discussin in sectin -, the aunt f deflectin is tinal t the ati f the cuent and the sing cnstant:. Thus if the sing cnstant deceases by %, k the cuent can decease by % t duce the sae deflectin. The new cuent will be % f the iginal cuent. final.. 36 A A initial. F sectin -9, we see that the tque is tinal t the cuent, s if the cuent ds by %, the utut tque will als d by %. Thus the final tque is.88 ties the initial tque. 8. The agnetic dile ent is defined in Eq. - as M NA. The nube f tuns, N, is. The cuent is the chage e unit tie assing a given int, which n the aveage is the chage n the electn divided by the eid f the cicula tin, e T. f we assue the electn is ving in a cicula bit f adius, then the aea is. The eid f the tin is the cicufeence f the bit divided by the seed, T v. Finally, the angula entu f an bject ving in a cicle is given by L v. Cbine these elatinshis t find the agnetic ent. e e e v ev ev e e M NA v L T v 9. (a) The tque is given by Eq. -. The angle is the angle between the -field and the eendicula t the cil face. NAsin 9. A.8. T sin 3. N (b) n Exale - it is stated that if the cil is fee t tun, it will tate twad the ientatin s that the angle is. n this case, that eans the nth edge f the cil will ise, s that a eendicula t its face will be aallel with the Eath s agnetic field. 6. The adius and agnetic field values can be used t find the seed f the tns. The electic field is then fund f the fact that the agnetic fce ust be the sae agnitude as the electic fce f the tns t have staight aths. qv v v q F F qe qv E v q E Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 9.6 C.66T. c. V 6.6 kg The diectin f the electic field ust be eendicula t bth the velcity and the agnetic field, and ust be in the site diectin t the agnetic fce n the tns. 6. The agnetic fce n the ins causes the t ve in a cicula ath, s the agnetic fce is a centietal fce. This esults in the in ass being tinal t the ath s adius f cuvatue. qv v q v q v cnstant 6 u.8 c. 6 u.6 6 u u u..6. c.8 c.6 c.8 c 6 u 6 u.9. 3 u.9..9 c.8 c. c.8 c u The the asses ae u, u, 3 u, and u.

20 Chate Magnetis 6. The lcatin f each line n the fil is twice the adius f cuvatue f the in. The adius f cuvatue can be fund f the exessin given in sectin -. q E E E q q.6 kg.8 V C.68 T..6 3 The distances between the lines ae f the ins ae dubly chaged, the value f q in the deninat f the exessin wuld duble, and s the actual distances n the fil wuld be halved. Thus the distances between the lines wuld als be halved The aticles in the ass sectete fllw a seicicula ath as shwn in Fig A aticle has a dislaceent f f the int f enteing the seicicula egin t whee it stikes the fil. S if the seaatin f the tw lecules n the fil is., the diffeence in adii f the tw lecules is.. The ass t adius ati is the sae f the tw lecules. qv v q v CO N cnstant 8.6 u 8.3 u.. 6. The velcity f the ins is fund using enegy cnsevatin. The electical tential enegy f the ins beces kinetic enegy as they ae acceleated. Then, since the ins ve eendiculaly t the agnetic field, the agnetic fce will be a axiu. That fce will cause the ins t ve in a cicula ath. v qr qr q R qr qv v qv v R V 6. The field inside the slenid is given by Eq. -8 with N l 3 T A 3 A. T elaced by the eeability f the in. 66. The field inside the slenid is given by Eq. -8 with elaced by the eeability f the in. N l l N.T A. T A Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 6

21 Giancli Physics: Pinciles with Alicatins, 6 th Editin 6. The agnetic fce duces centietal acceleatin. qv v v q q 6.8 kg s C. The agnetic field ust int uwad t cause an inwad-inting (centietal) fce that stees the tns clckwise. 68. The kinetic enegy is used t deteine the seed f the aticles, and then the seed can be used t deteine the adius f the cicula ath, since the agnetic fce is causing centietal acceleatin. KE e KE v v v v qv KE q KE e q e.6 kg 3 9. kg.8 KE 3.T KE q q q 69. We assue that the hizntal cnent f the Eath s agnetic field is inting due nth. The Eath s agnetic field als has the di angle f. The angle between the agnetic field and the eastwad cuent is 9. Use Eq. - t calculate the agnitude f the fce. F l sin 33 A. T sin 9 E. N Using the ight hand ule with the eastwad cuent and the Eath s agnetic field, the fce n the wie is nthely and 68 abve the hizntal.. The ailane is a chage ving in a agnetic field. Since it is flying eendicula t the agnetic field, Eq. - alies. F 6 6 qv C s. T 9.3 N ax. The agnetic fce ust be equal in agnitude t the weight f the electn. g qv v g q 9. kg 9.8 s C. T 6. s The agnetic fce ust int uwads, and s by the ight hand ule and the negative chage f the electn, the electn ust be ving west.. (a) The velcity f the ins is fund using enegy cnsevatin. The electical tential enegy f the ins beces kinetic enegy as they ae acceleated. Then, assuing the ins ve eendiculaly t the agnetic field, the agnetic fce will be a axiu. That fce will cause the in t ve in a cicula ath. PE qv KE qv v v qv initial final v 68 F Eath N Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

22 Chate Magnetis qv v V q q q 6.6 kg V 9.6 C. T (b) The eid is the cicufeence f the cicula ath divided by the seed. T V q v qv q 6.6 kg. s 9.6 C. T The acceleating fce n the ba is due t the agnetic fce n the cuent. f the cuent is cnstant, the agnetic fce will be cnstant, and s cnstant acceleatin kineatics can be used. v v a x a v v x x v 3 a x v. kg 8 s F a L.6A net L L xl...t Using the ight hand ule, f the fce n the ba t be in the diectin f the acceleatin shwn in Fig. -6, the agnetic field ust be dwn.. Each f the btt wies will eel the t wie since each btt cuent is site t the t cuent. The eelling fces will be alng the line diectly f the btt wies t the t wies. Only the vetical cnents f thse fces will be cunteacting gavity. Use Eq. - t calculate the agnetic fces. The ass f the wie is its density ties its vlue. The length f the wie is eesented by L. btt Cu g F cs3 L d g Lcs3 Cu Cu d 3 d dg 89 kg s Cu Cu Cu btt T A 9A cs3 F 9A 3 3 g F. (a) Thee will be ne fce n the d, due t the agnetic fce n the chage caies in the d. That fce is f agnitude F l, and by Newtn s nd law is equal t the ass f the d ties its acceleatin. That fce is cnstant, s the acceleatin will be cnstant, and cnstant acceleatin kineatics can be used. l v v v L F F l a a v t net t t (b) Nw the net fce is the vect su f the agnetic fce and the fce f kinetic fictin. F F F l F l g a net f k N k l v v v L a g v g t k k t t (c) Using the ight hand ule, we find that the fce n the d is t the east, and the d ves east. Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 8

23 Giancli Physics: Pinciles with Alicatins, 6 th Editin 6. The seed f the electns is fund by assuing the enegy sulied by the acceleating vltage beces kinetic enegy f the electns. We assue that thse electns ae initially diected hizntally, and that the televisin set is iented s that the electn velcity is eendicula t the Eath s agnetic field, esulting in the lagest ssible fce. Finally, we assue that the agnetic fce n the electns is sall enugh that the electn velcity is essentially eendicula t the Eath s field f the entie tajecty. This esults in a cnstant acceleatin f the electns. (a) Acceleatin: PE KE ev v v initial final x x Deflectin: tie in field: x v t t field x field field qv field ev Eath 3 x Eath e V F qv a a y x Eath y y 3 Eath 3 3 e V x field e V y 3 Eath 3 Eath x x v x e ev y a t x v ev vx x y e 8V Eath x 9.6 C kg V. T (b) e.6 C y x 8V 8 9. kg 3, V 9. T. Eath 3 3. Nte that the deflectin is significantly salle than the hizntal distance taveled, and s the assutins ade abve ae veified.. (a) The fequency f the vltage ust atch the fequency f cicula tin f the aticles, s that the electic field is synchnized with the cicula tin. The adius f each cicula bit v is given in Exale - as. F an bject ving in cicula tin, the eid is q given by T v, and the fequency is the ecical f the eid. v v q T f v v q n aticula we nte that this fequency is indeendent f the adius, and s the sae fequency can be used thughut the acceleatin. Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe. 9

24 Chate Magnetis (b) F a sall ga, the electic field acss the ga will be axiately cnstant and unif as the aticles css the ga. f the tin and the vltage ae synchnized s that the axiu vltage ccus when the aticles ae at the ga, the aticles eceive an enegy incease f KE qv as they ass each ga. The enegy gain f ne evlutin will include the assing f gas, s the ttal KE incease is qv. (c) The axiu kinetic enegy will ccu at the utside f the cycltn. q v KE ax 9 q q..6 C.T ax ax v ax.6 kg ev MeV.66 J 8MeV J ev 8. Each individual wie wuld cause a agnetic field given by Eq. -6 with the aiate distance. The fu individual agnetic fields ae shwn in the diaga. Nte that all fu agnitudes ae the sae. Als and, but in the diaga they ae shwn as 3 slightly dislaced f each the. The vetical cnents all cancel, and s the net agnetic field is ties the hizntal cnent f ne f the individual fields. 3 l net cs, left l l l The tns will fllw a cicula ath as they ve thugh the egin f agnetic field, with a adius f cuvatue given in v Exale - as. Fast-ving tns will have a q adius f cuvatue that is t lage and s they will exit abve the secnd tube. Likewise, slw-ving tns will have a adius f cuvatue that is t sall and s they will exit belw the secnd tube. Since the exit velcity is eendicula t the adius line f the cente f cuvatue, the bending angle can be calculated. L sin 9 L Lq..6 C.33T sin sin sin sin.8 9. v.6 kg. s L Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

25 Giancli Physics: Pinciles with Alicatins, 6 th Editin 8. (a) The electagnet ust dissiate. kw f we if the we suly is t suly that we. Use that we with the vltage acss the electagnet t find the esistance f the electagnet. Then calculate hw uch ce wie is needed t vide that esistance. The ce wie is a squae f side length d, and the ce wie has length L. V V L L L P R R N Cu Cu R P A d N Rd 3 L Rd V d V.6 Cu 3 P Cu Cu W.6 tuns (b) T calculate the agnetic field at the cente f the cil, the cuent ust be knwn, and it can be fund f the we and the vltage since P V. N NP 3 T A.6. W. T V.6 V N (c) t wuld aea f that an incease in N wuld incease, but the incease in N ust aise f a lnge wie, which has e esistance, and s the cuent is lwe. We need t exess in tes f the nube f tuns alne. V N N N Rd d R cnstant V R R The agnetic field will eain cnstant. Cu Cu 8. F ble 8, with ne tun f wie, we have T T A. Use the adius f the Eath f. 9 A 8. F Eq. 8-9(a) we calculate the s cuent, given the we and the s vltage, assuing that each wie vides half the we. P. P V s s s Vs 3 6 P W 83A ax 3 V V s F the geety f the ble, we can calculate the agnetic field that is exected. Nte that the dawing is NOT t scale tan.86 3 left ight Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.

26 Chate Magnetis net left x ight x cs T A 83A cs.86 T 3. This is caable in agnitude t the Eath s field. 83. (a) F the bea f electns t be undeflected, the agnitude f the agnetic fce ust equal the agnitude f the electic fce. We assue that the agnetic field will be eendicula t the velcity f the electns s that the axiu agnetic fce is btained. E,V 3 3 F F qv qe E 6.83 T. T v.8 s (b) Since the electic field is inting u, the electic fce is dwn. Thus the agnetic fce ust be u. Using the ight hand ule with the negative electns, the agnetic field ust be ut f the lane f the lane fed by the electn velcity and the electic field. (c) f the electic field is tuned ff, then the agnetic field will cause a centietal fce, ving the electns in a cicula ath. The fequency is the ecical f the eid f the tin. v q qv v q 9 v q qe.6 C,V f.8 Hz 3 6 T v 9. kg.8 s 8. The seed f the tn can be calculated based n the adius f cuvatue f the (alst) cicula tin. F that the kinetic enegy can be calculated. KE v q q q qv v v 9 q.6 C.T 3 3 KE kg. J.3eV 8. The field inside a slenid is given by Eq. -8. l.3t.3 N l N T A. A.3 tuns 86. Thee ae thee fces n each wie its weight, the agnetic fce f eulsin f the the wie, and the tensin in the attached sting. See the diaga. The agnetic fce is given by Eq. -. The ass f the wie is its density ties its vlue. The length f the wie is eesented by L. The net fce in bth the vetical and hizntal diectins is ze. g F F sin F cs g F T T T cs F g F T Peasn Educatin, nc., Ue Saddle Rive, NJ. All ights eseved. This ateial is tected unde all cyight laws as they cuently exist. N tin f this ateial ay be educed, in any f by any eans, withut eissin in witing f the ublishe.