Sources of Magnetic Field Chapter 28. A Very Large Magnet Application

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Biot-Svt Lw lets use clculte the mgnetic field of moving chge Conside mgnetic field of cuent-cying conducto The

1 3//13 Souces of Mgnetic Field Chpte 8 Chpte-7 foces on moving chge in mgnetic field How is the mgnetic field geneted by moving chge? Biot-Svt Lw lets use clculte the mgnetic field of moving chge Conside mgnetic field of cuent-cying conducto The mgnetic field of long, stight, cuent-cying conducto The mgnetic foce between cuent-cying conductos Conside the mgnetic field of cuent loop Ampee s Lw is the mgnetic nlog to Guss s Lw 1 A Vey Lge Mgnet Appliction 1

2 3//13 The mgnetic field of moving chge A moving chge will genete mgnetic field eltive to the velocity of the chge. 3 Mgnetic Field of Moving Chge Mgnitude of B q vsin B (8-1) 4 Diection of B detemined by v x The vecto fom: Pemebility of fee spce 4x

3 3//13 Foce between two moving potons Two potons moving t the sme velocity (much less thn speed of light) in opposite diections. The electic foce F E is epulsive. The ight-hnd ule indictes the mgnetic foce F M is epulsive. (i x k=-j) Find the tio of the mgnitude of the foces. F B F F B E q v 4 v c The tio of the two foces. Whee c=speed of light. Theefoe: F E >>F B 6 3

4 3//13 Mgnetic Field of Cuent Element Totl mgnetic field of sevel moving chges = vecto sum of fields cused by individul chges Let dq = chge in wie segment dl Let A = coss section e of wie segment dl Let n = chge density in wie segment dl dq = nqadl I = nqv d A Figue 8-3 dqvd sin nqvd Adl sin db 4 4 Idl sin db Biot-Svt Lw 4 Diection of db detemined by Idl x Vecto fom of Biot-Svt Lw Bee-oh Suh-v 7 8 4

5 3//13 Mgnetic field of stight cuent-cying conducto Biot nd Svt contibuted to finding the mgnetic field poduced by single cuent-cying conducto. 9 Mgnetic Field of Cuent-Cying Conducto Figue 8-5 Bsed upon symmety ound the y-xis the field will be cicle If x Idl sin db 4 sin sin( ) dl dy db Idy x x x y 4 ( x y ) 4 ( x y x y Ix dy B 3/ 4 x y Ix dy Ix 1 y I B 4 x x y 4 x x I B 4 x I x using n integtion tble 1 ) 3/ 5

6 3//13 Mgnetic Field of Cuent-Cying Conducto Figue 8-6 whee = pependicul distnce fom the cuent-cying wie

7 3//13 13 Foce between Pllel Conductos Only field due to I shown Ech conducto lies in the field set up by the othe conducto F I ' L B ' ' ' I sin F I LB I LB I L ' II F L ' F II L Substitute fo B Note: If I nd I e in the sme diection, the wies ttct. If I nd I e in opposite diections, the wies epel. See Exmple 8.5 Pge

8 3//13 15 Mgnetic Field of Cicul Cuent Loop Idl sin db 4 sin sin9 1 Figue 8-1 B x I 4 ( x ) db I dl 4 ( x ) x I db 4 ( x ( ) 3/ 3/ dl I dl 4 ( x ) ( x ) x db cos 1/ ) cos B y = 16 8

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10 3//13 Mgnetic Field of Cicul Cuent Loop NI B x 3/ ( x ) (on the xis of N cicul loops) (x=) x Figue 8-13 Figue Applictions of Ampee s Lw Exmple 8-9 Field of Solenoid N n l tuns/mete whee N = totl coil tuns l = 4 = totl coil length Figue 8-1

11 3//13 Applictions of Ampee s Lw Exmple 8-9 Field of Solenoid (mgnetic field is concentted in side the coil) n = tuns/mete Figue 8- Bdl I encl nli b Bdl Bdl Bdl Bdl B b c b c Bdl B dl dl dl dl BL BL nli b d c d B ni c d N I l d dl Figue 8-1 (8-3) N n l tuns/mete whee N = totl coil tuns l = totl coil length 1 11

12 3//13 3 Applictions of Ampee s Lw Exmple 8-1 Field of Tooidl Solenoid (field is inside the tooid) Figue 8-3 Pth N tuns Bdl I encl NI Bdl B B ( ) NI dl B( ) Pth 1 Bdl I encl Pth 3 NI B (8-4) B Bdl I encl B Cuent cncels No cuent enclosed 4 1

13 3//13 5 Ampee s Lw I specific then genel Simil to electic fields if symmety exists it is esie to use Guss s lw 6 13

14 3//13 Ampee s Lw II The line integl equls the totl enclosed cuent The integl is the sum of the tngentil B to line pth Ampee s Lw (Chpte 8, Sec 6) Figue 8-15 Fo Figue 8-15 Bdl Bcos dl Bdl B dl I B dl I Bdl B( ) ( ) I Fo Figue 8-15b B dl I Fo Figue 8-15c Bdl Bdl Bdl Bdl B b dl B1 dl dl B dl Bdl b c b B d c d I I Bdl ( 1 ) ( ) 1 c b d c 8 d dl dl 14

15 3//13 Ampee s Lw Figue 8-16 d I Bdl ( ) I d Bdl Bdl cos dl d B I I Bcos dl Bdl ( d ) I d 9 Mgnetic mteils The Boh mgneton will detemine how to clssify mteil. Feomgnetic cn be mgnetized nd etin mgnetism Pmgnetic will hve wek esponse to n extenl mgnetic field nd will not etin ny mgnetism Dimgnetic shows wek epulsion to n extenl mgnetic field Boh Mgneton- In toms electon spin cetes cuent loop, which poduce mgnetic thei own field 3 15

16 3//13 Feomgnetism nd Hysteesis loops The lge the loops the moe enegy tht is lost mgnetizing nd demgnetizing. Soft ion poduce smll loops nd e used fo tnsfomes, electomgnets, motos, nd genetos Mteil tht poduces lge loops e used fo pemnent mgnet pplictions M B Q8.1 A positive point chge is moving diectly towd point P. The mgnetic field tht the point chge poduces t point P A. points fom the chge towd point P. B. points fom point P towd the chge. C. is pependicul to the line fom the point chge to point P. D. is zeo. E. The nswe depends on the speed of the point chge. 16

17 3//13 Q8. Two positive point chges move side by side in the sme diection with the sme velocity. Wht is the diection of the mgnetic foce tht the uppe point chge exets on the lowe one? +q v +q v A. towd the uppe point chge (the foce is ttctive) B. wy fom the uppe point chge (the foce is epulsive) C. in the diection of the velocity D. opposite to the diection of the velocity E. none of the bove Q8.3 A long stight wie lies long the y xis nd cies cuent in the positive y diection. y A positive point chge moves long the x xis in the positive x diection. The mgnetic foce tht the wie exets on the point chge is in A. the positive x diection. O v +q x B. the negtive x diection. I C. the positive y diection. D. the negtive y diection. E. none of the bove 17

18 3//13 Q8.4 Two long, stight wies e oiented pependicul to the xy plne. They cy cuents of equl mgnitude I in opposite diections s shown. At point P, the mgnetic field due to these cuents is in A. the positive x diection. B. the negtive x diection. C. the positive y diection. D. the negtive y diection. E. none of the bove Q8.5 The long, stight wie AB cies 14.-A cuent s shown. The ectngul loop hs long edges pllel to AB nd cies clockwise 5.-A cuent. Wht is the diection of the net mgnetic foce tht the stight wie AB exets on the loop? A. to the ight B. to the left C. upwd (towd AB) D. downwd (wy fom AB) E. misleding question the net mgnetic foce is zeo 18

19 3//13 Q8.6 A wie consists of two stight sections with semicicul section between them. If cuent flows in the wie s shown, wht is the diection of the mgnetic field t P due to the cuent? A. to the ight B. to the left C. out of the plne of the figue D. into the plne of the figue E. misleding question the mgnetic field t P is zeo Q8.7 The wie shown hee is infinitely long nd hs 9 bend. If cuent flows in the wie s shown, wht is the diection of the mgnetic field t P due to the cuent? A. to the ight B. to the left C. out of the plne of the figue D. into the plne of the figue E. none of these 19

20 3//13 Q8.8 The figue shows, in coss section, thee conductos tht cy cuents pependicul to the plne of the figue. If the cuents I 1, I, nd I 3 ll hve the sme mgnitude, fo which pth(s) is the line integl of the mgnetic field equl to zeo? A. pth only B. pths nd c C. pths b nd d D. pths, b, c, nd d E. The nswe depends on whethe the integl goes clockwise o counteclockwise ound the pth.

(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?

(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m? Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the