Phys Scientists & Engineers II
Phys Scientists & Engineers II PHY 184
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This 24 page Class Notes was uploaded by Quinn Larkin on Saturday September 19, 2015. The Class Notes belongs to PHY 184 at Michigan State University taught by Staff in Fall. Since its upload, it has received 31 views. For similar materials see /class/207637/phy-184-michigan-state-university in Physics 2 at Michigan State University.
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Date Created: 09/19/15
Lecture 17 Chapter 29 Magnetic Fields Magnetic Fields 1 Analogous to electric field a magnet produces a magnetic field B Set up a B field 2 ways Moving electrically charged particles Current in a wire Intrinsic magnetic field Basic characteristic of elementary particles such as an electron Magnetic Fields 2 When charged particle moves through B field a force acts on the particle Magnitude of F3 is where D is the angle between v and B SI unit forB is teslaT Magnetic Fields 3 FB o if Charge q O Particle is stationary v and B are parallel qgt0 or antiparallel q180 F3 is maximum if v and B are J to each other Magnetic Fields 4 FB acting on charged particle is always L to v and B FB never has component H to v FB cannot change v or KE of particle FB can only change direction of v Magnetic Fields 5 Right hand rule For positive Charges the thumb of right hahd poihts ih directior of F5 Wheh the fihgere sweep v ihto B through the smaller ahgle quot For hegative Charges F5 poihts ih opposite directior Magnetic Fields 6 zi 4 39 LL all W U i Checkpoint 1 What is the direction of F3 on the particle with the v and B shown Use righthand rule don t forget charge A z C zero Magnetic Fields 7 Jr J J39 a Check yourself using matrix notation Write vectors for v and B Magnetic Fields 8 Magnetic eld lines Direction of tangent to eld line gives direction of B at that point Denser the lines the stronger the B field Magnetic Fields 9 I I I quotquot Magnetic field lines enter one end south of magnet I 939 39 I mh 3 II and eXIt the other end 1 7 north Opposite magnetic poles attract like magnetic poles repel Magnetic Fields 1 O What happens if there is both an E field and a B field Both fields produce a force on a charged particle If the two fields are L to each other call them crossed fields Magnetic Fields 11 s r afr 101 0 Tun vacmml PIIIE39I39IP Cathode ray tube used in television Can deflect a beam of electrons by E field from charged parallelplates B field from magnet Adjust E and B fields to move electron beam across fluorescent screen Magnetic Fields 12 Checkpoint 2 E field out of page B field to left A Rank 12 and 3 by magnitude of net F on particle greatest first What direction is FE at 1 Out of page Is it the same for all directions of v YES Magnetic Fields 13 What is direction of F3 for 123 and 4 1 FB O 2 FB out of page 3 FB O 4 FB into page A Rank magnitude of net F for 1 2 and 3 2 then 1 amp 3 tie B Which direction could have net F of zero Direction 4 Magnetic Fields 14 Electrons moving in a 1quot wire current can be deflected by a B field called the Hall effect Creates a Hall potential difference V across the wire Can measure the wire s charge density when at equilibrium FE FB v High Magnetic Fields 15 Electrons have drift 1quot velocity vd in direction opposite the current i B field into page causes force F3 to right Electrons pile up on right hand side of strip Leaves charges on left and produce an E field inside the strip pointing to right ml High Magnetic Fields 16 E field on electron produces a FE to the left F l Quickly have equilibrium where FE FB E field gives a V across the strip Left side is at a higher 39 j39 potential 1 131254 x A l A 11quot 1 Magnetic Fields 17 Can measure the number 1quot of charge carriers per unit l dl volume 17 at equilibrium K B K x x X I Kc x x H igh a Low x Magnetic Fields 18 Remember from Chpt 27 that drift speed is E 3 X 21 5 3K M24 x High X a Low r Magnetic Fields 19 Replacing E by PEA 1i X 21 sq X M24 x z High Magnetic Fields 20 Ifl is the thickness of the 1 F dl Strip Finally get initial 7quot 4 Low x Magnetic Fields 21 Checkpoint 3 Have 6 choices for velocity v of rectangle in i x iry and i2 A Rank 6 choices by V across solid greatest first First figure out direction of iv for each v i H gt 3 nquot 3 H For ix F3 is zero 10180 393 For iry F3 is into out of page across distance d For irz F3 is moving up down page across 2d Magnetic Fields 22 A Rank 6 choices by V across solid greatest first FE FB but opposite direction Egt 3 SO V V 31 Found irz to be across 2d iry across d and ix to be zero iziyix Four same point charges at corners of rectangle nternal Resistance 0 Battery nternal Resistance 0 Battery example 39 B ield rom Current Distribution fine potential at center 2 VR l V R 331303 AL39nd mVaSS H idssmioo fax q VR RR ViReiRRi quotW5 q 1dB 0 0 30 39 V zkrSV k 2 b 2 i leq 1 i t 1 AKAUOZgt12mv2qV0 1 1 47 r2 gt 1 I a V t 1 o R R i at d 180 l 2 2 RRi7t l V M I 2 dBZZS O Z SSInE 20gtB20 i I Hollow spherical conductor With surface charge V R 5 R Wm 32 x2 ii fanield ii i kQ Q kQ Rquot Z t R i i r 2 TB 2 8161 77 3 B dB 7 o iRd W gm of WV 2 W 7 l I inside R 478 R outside Power in Eieciric circuits Flesrstance In Parallel have same voltage Momentum o a track flnd momen and speed o 4 R2 2R 4 8R 0 2 current is sum 0 individual p mv B field rom Current distribution 3 CirCUIts Four point charges on corners of square three P IV 1 R szthl EandV R1 1 It n t t Upper half 39 39 vo a e is co 3 an 1 pos and one neg find V at certain point above Energy 1 VemfR i9 l Lg not ll l ll 12r t e 1 2 C m0 CD 2 7395 R 3r Bu e r Gen ter i lkWh 1000W3600s 3 61 06 joules n q Period req and ang req 0 particle in orbit P 12R J 2kg 2 k q q q q T How emp Dependence o the i 2 2i T JEZM m Deuteron in CVC39Otron g 39 dam r a2 a2 62 710 11 Resistance 0 a Light bulb Reg 1 R v qB anf 1 I B Ll0i Bfielid 0 Long Wires find point where B M l 39 quot 1quot POW whenll39ghled Galvanometer as currentmeasuring device f2q B q 1 R 1 4r meld 393 OM 39i gtk 1 PV2RgtRV2P VZ RVl R 7quotquot c 912 39 2612 CZ X quotall nt 1quot max eq IR 2 2 E 2777 I I I I I I R0 L gt V intRi lmaXReq W a f m BR cIgt7r2 st j R2 CD7r2 iu l l l d r 1 is Find V from e uation of volume With certain WT To n Ma netiC field Hall e ect 12gtr1 1 1 1 1 R 9 Final 1 coordinates Dri t velocity 0 e in copper wire R E quot VH VHdhne Vthe r l r 2 av av x vdniz nevd at C1 i i s dv dl B 2 W E 2 Atoms as magnets Ef E Ey E El 8 z A 1m 1 Hall probe find mag o magnetic field 12R 4r 3r Current I i conductzon electrons gt Z R R E E electrons LL l Ll l LL 139 e 6 ve iex2 W2 W nsulating sheet With charge It Volume mt eq s W b 2120 4o 60 F 2 A r r i E aV 2x 2 dlStrlletlon um Orm Ind Change In lelectron 60201023at0ms densityg 10010613m3 R R int 15150170 6021023at0ms densityg 1010 3 I I I Z M Z 7W v 7 1 r ax y V when charge is moved rom atom Xg cms m3 S ii z39 atom Xg mg mg 2 0 oo Magnencmoment ii I av position Ato B m m V ime 0 12R 16 8r ve 2 ver Ey 2xyz e s vd H Circular motion find speed Ha z177 7 8y soc EdA 80 EA EA q 0A neA d d t k 7rr 3V 0 i A orce on a current carrying Wire 3 la 39 3 a 6 Orbitalangularmomentumofe z a Z E WQEdcos0 xzvdt a t qti z39visdrzftvelocity Iquot L rpzrmv Z 280 V 1 2 2eV 01 AWW W Q a d Qi 0 id Chapter 26 CIrCUIts quvBsin9 iijsille 5mg eVgt v m L rm 2H0 2mg f i 2 80 yl 339 7 Kircho s Junction Rule V 39 e M W e AW TQ A B gt F 211351119 F mev2 F vBe MagnencDipoleMoment V 30in oquot fg ni l1 12 l3 orque on a current carrying loop square and circle W r quotmg c e e Surface area of capacitor Ll l 39 Kircho S Loop Ru39e quot i7 4 vBe mevz gt r mev ab 0b Capacitor Defibrillator he sum 0 VOItage drops around a complete C39rCU39t 3900P mUSt TiaB sin9iaB sine 63 B ield inside toroid Cd char ed find capac sum to zero nh 2 2 l uONi A g Wheatstone bridge RargngVa Patter gt iazBsinez iABstne B 2 50 U iCiz Z db R O l i e Magnetic Dipole Momentum 7quot 2 0019 new gtl KiRV uNiA Chapter 29 Electromagnetic Induction 2U loopcbd iuRu igRg iVRV 0 39 Magnetic potential energy in external magnetic field Magnetic ux Changing B ield current inC according to 2 U Bcos9 e e current find induced voltage at loo V junctions A riangle Shaped Loop DB HBdA BAcos6l 2 p I i ii hypotenuse 1WbiT 2 AN7FR nduced em field 0 a Capacitor with mylar between plates find work to 1 g r 39 l If quot m B t B 1 2 4 42 I 39d t39 d 39 d d 1 1 1 l l MESH aradaqus Lawo nduction 0 0 S SO ellOl Ill lll llce em remove mylar and potential difference one Mylar s g v Capacitg ully charged Hde F emf B A econstant V Acosedg due to Changing field IS removed When bridge balanced qtot Vemf Bx 300590 E d1 emf dt B eld of outer solenoid By 3st 397 nduction in a flat loo d AW 2 VVi Wf V KV th 3R3gt1uRu 1VRV CapaCitor discharging 92mm Ad i p Vemf Acos0 BO1 2452 B om WN LJ V R t J F L B pp J UMquot Vemf ACOSQE BCOSQEJ 0 43st df voltage time depend 1 2 1 C 2 I1 lul3 Iv E 21 y Acos0B 24s 22t q g e I 0 39 ZCV 2 K W Finally 0 I Chapter 28 Mag Fields of Movmg Charges Spec39a39 cases at quot3amp9 nduced em Vail011 d A constant Vem Acos6 In uce em Parallel plate capaCItor find charge energy stored zuR IR i q e RC M6906 leld Magneth Fjlop lt3 matter f dt A dch dB 611T LLO 517551110 BB iE39dS Z V Acose area and if filled Withdielectric 211 23133 ime to charge a capacitor dB 2 a o a o A o a ngconsiam V f Bcosg dt emf dt U 1 A dc q VC C K 80A 3 a 47 r Tm B MPH M 01ZmH A B t t V wAB gt ndder m ive qv Z R R 91 q 1 6 RC 4 107 Re lative ermeabz39lz39 cons an equot1f 2 sm 2 80 quot V c 0 0 7 A p y M otion Voltage find induced voltage as a unction 0 time 39 39 Km 1 95 63 lggjlggeter In a Simple CerUIt t RCln1 B leld a Long Stralght ere Magne cpermeabihty AU wd wdvl l f dV I CerUlt SWltCh connected 7238 iquot B r 0 dA di C KW i K ime constant 0 Circuit go i 2an ti1 95mm Kmuo E 430059 emft LE 2 1 39 R 4 B ield rom a Loo u r a Chapter 25 Direct Currents Connected I J RC Z CVemfrlchrV W m p BCOSQW39UZW 39 quot me H 0 I B 0 u l 1 1 1 RRV t 1 2R 39 V vacosOfromOtot l Electric current OlltOPhOFBSlS R 5 R gt Reg R RV M f m Q 1 Wm T
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