Physics III PH 113
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This 33 page Class Notes was uploaded by Jalon Willms on Monday October 19, 2015. The Class Notes belongs to PH 113 at Rose-Hulman Institute of Technology taught by Renat Letfullin in Fall. Since its upload, it has received 17 views. For similar materials see /class/225113/ph-113-rose-hulman-institute-of-technology in Physics 2 at Rose-Hulman Institute of Technology.
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Date Created: 10/19/15
Magnetism Lecture 07 Electromagnetic Induction B B gt gt gt gt gt TTTTTTTT V gtgt gt gt TTTTlTTTT Toddyt q t Experimental Demonstrations Magnetic flux Force and Induction Energy Considerations Eddy Currents Magnetic Flux Lenz s Law Faraday s Law in the terms of Flux Examples How much of something is passing through some surface Ex How many hairs passing through your scalp Two ways to define 1 Number per unit area eg 10 hairsmmz 2 Number passing through an area of interest eg 48788 hairs passing through my scalp This is what we are using here Physics 113 Dr Renat Letfullin Electric Flux Field Perpendicular For a constant eld perpendicular to a surface A Electric Flux is de ned as Physics 113 Dr Renat Letfullin 4 Electric Flux Non perpendicular Physics 113 Dr Renal Letfullin For a constant eld NOT perpendicular to a surface A Electric Flux is defined as Air Flow and Fltnx a Dimuiun of airflow 00 39I l 2mg h lmaglnc huldmg u r39uclzmgular Imp m WII C in mm ul 1 fun Sum wuh Ihu loup lacenu m IIIL mmcnun ul nir nw Ihun Iill mu lnup as hnmn un1i il in hnrimllul c Loup seen facing lhc fan I b Luup scan from the side 0 w T111 angle huw luugtm sum 0 0 I n a u u i n U bcns I I I g Am Nb Am Albums A 0 The amounT of air39 flow Through The loop depends on The or39ienTaTion of The loop wiTh respecT To The airflow dir39ecTion Aeff abcos6 Acos6 Physics 113 Dr Renat Letfullin The number of arrows passing Through The loop depends on Two focTors 1 The densiTy of arrows which is proporTionoI To B mm xhe side 0 90 2 The effecTive area x Aeff A cos 6 of The loop quot X x x x X Sacnindicdiraclinn X gt X x x X X X x x X X Xux x X oflhcmngncnc cld z x Xx x We use These ideas To x x X x x quot x define The magneTic fIUXI Loop pcrpclldln ulurufleid Luopmtumdlnnughaugki Loop mum 90 Nnurmm Maximum number m39armm rcucr arrow pass mvnngh pass ihxnugh Flux Pm E AeffB AB c056 Flux units 1 weber 1 Wb 1 Tm2 Physics 113 Dr Renat Letfullin 7 Area Vector b B a quot1 Loop of area A Thearea vector is The magnetic perpendiculal to the flux through loop 115 magnitude the 109p is is the area of the loop I A 39 B The angle 0 between ltl and gig the angle at which the loop has been tilted Define The area vecTor A of a loop such ThaT iT has The loop area as iTs magniTude and is perpendicular To The plane of The loop If a currenT is presenT The area vecTor poinTs in The direcTion given by The Thumb of The righT hand when The fingers curl in The direcTion of currenT flow If The area is parT of a closed surface The area vecTor poinTs ouTside The enclosed volume WiTh This definiTion gt gt Pm EAe BzABcos zAB Physics 113 Dr Renal Letfullin m A Circular Loop Rotating in a Magnetic Field 7 The figure shows a 10 cm diameter loop rotating in a uniform 0050 T magnetic field What is the magnitude of the flux through the loop when the angle is 900 300 600 and 900 Circular 100p A 7Z39R2 7r 005m2 785x10 3 m2 393x10 4 beor 6 0 340x1041 beor630 196x1041 be0r660 Obe0r690 QDm 21430056 2 Physics 113 Dr Renat Letfullin Mm c Flux I m a NamMom Fiend X x X X X x So far we have assumed ThaT L 0PX X X X The loop is in a uniform field WhaT x X if ThaT is noT The case The souTion isTo break up The X Small area dA ar39ea mTo mfmITeSImal pieces each a gt Flux through this so small ThaT The field wiThin iT is X3 X little areg is essenTiaIIy consTanT Then drbm BdA X X X X x gt X X x x dcpm1 d Increasing field strength CDm j EdI areaofloop Physics 113 Dr Renat Letfullin 10 Magnetic Flux from a Long Straight Wire 0 Long slmigh wire gt The near edge of a 10 cm x 40 cm r ecTanguIar loop is 10 cm from a long sTr39aighT wir39e ThaT carries a cur39r39enT of 10 A as shown in The figure WhaT is The magneTic flux Through The loop 0 7 10 cm 10 cm Decreasing 0 21 a 0 dx I I 39 E 39 39 Smpofareanmbdi 6L4 7 dx B 61 B 6 2117 7 alpnsiionx Magnetic 39 ux ihlnugll um ml is IgtHIBJA ca C111 om amp21b 1 21b1nx 21b1n 47239 C x 47r C 47f quot Vecmr 11K is wmmg I u muofllxepuge om 555x10 g Wb Physics 113 Dr Renat Letfullin 11 Law I 2 Tle imp nerd m d gcnurnlu 2m A bar magnci pusth inm a nap lucrcmtx m ux lilmugh 1h mm and Induces a Clll39l Clll 0 How Docs llk imluccd L39IIrran How L ianWihi m39 L39uunlerclnckwisequot 1 Heinrich Friedrich Emil Lenz 11133 SILK 18041865 duwnwurd as His magnet appmaches painlng mugnclic htld In 1834 Heinrich Lenz announced a rule for determining The direction of an induced current which has come To be known as Lenz39s Law Here is The s139a139emen139 of Lenz39s Law There is an induced currenf in a closed conducfing loop if and only if fhe magnefic fux fhrough fhe loop is changing The direcfion of fhe induced currenf is such fhaf fhe induced magnefic fied opposes fhe change in fhe ux Physics 113 Dr Renat Letfullin Levin s Low 2 a b I 39 The bar magnet is moving 2 Adownwm dpmmmg eld IS away from the loop net39dcdilu oppose the change Current meter l Downward ux Is decreasing 3 A dmvnwzu39dpnuniug eld is induced by 394 CW Current If The field of The bar39 magneT is already in The loop and The bar39 magneT is removed The induced cur39r39enT is in The dir39ecTion ThaT Tr39ies I To keep The field consTanT N lil uPer ggsuc ng b If The loop is a superconducfar39 a per39sisTenT l l l l sTanding cur39r39enT is induced in The loop and The s field remains consTanT Magnet Physics 113 Dr Renat Letfullin 13 Sixlnducedmtmos 3 up and steady E No induced current 5 up and steady I No change in ux I No induced eld I No induced current E III and Increasing Binduccd B Induced current E up and increasing l Change in ux T Induced eld i I Induced current cw Physics 113 Dr Renat Letfullin E P and decreasing B induced Induced current 5 up and decreasing I Change in flux 1 I Induced eld T I Induced currem ccw Sixlnducedmtmos E down and steady No induced current B 3 down and steady I No change in ux I No induced field I No induced current 3 down and Increasing E induced Induced current B 3 down and increasing I Change in flux Jr I Induced eld T I Induced current ccw Physics 113 Dr Renat Letfullin 3 do and decreasing B iner Induced current B 5 down and decreasing I Change in ux T I Induced eld i I Induced current cw Sixlnduced mm B No induced current 3 up and steady N0 induced current B 5 down and steady Binduccd gt B Induced current 3 up and increasing E Induced 39 Induced CUITBHI B E down and increasing Physics 113 Dr Renat Letfullin Scenarios Bindnwd B Induced current 1 un and decreasing B induced gt Ind CU B 5 down and decreasing I Change in flux T l Induced field i I Induced current cw uced n39ent m Lenin s Law a b 0 The mugnclic eld of 19 upper IUUP pninls up but i ix demonshigh ll quotml in the circuit rapidly dcucuscs The flux through the loop is Switch opens up and decreasing OThc induced field needs lu pninl upwurd l0 oppose lhc 39lmnge in ux 0 A row current induum an upward magnetic eld The swiTch in The circuiT shown has been closed for39 a long Time WhaT happens To The lower loop when The swiTch is opened Physics 113 Dr Renat Letfullin 17 Q291 A circular loop of wire is in a region of spaTially uniform magneTic field The magneTic field is direcTed inTo The plane of The figure If The X magneTic field magniTude is consTanT A The induced emf is clockwise B The induced emf is counTerclockwise C The induced emf is zero D The answer depends on The sTrengTh of The field A291 A circular loop of wire is in a region of spaTially uniform magneTic field The magneTic field is direcTed inTo The plane of The figure If The X magneTic field magniTude is consTanT A The induced emf is clockwise B The induced emf is counTerclockwise C The induced emf is zero D The answer depends on The sTrengTh of The field Q292 A circular loop of wire is in a region of spaTially uniform magneTic field The magneTic field is direcTed inTo The plane of The figure If The X magneTic field magniTude is decreasing X A The induced emf is clockwise B The induced emf is counTerclockwise C The induced emf is zero D The answer depends on The sTrengTh of The field A292 A circular loop of wire is in a region of spaTially uniform magneTic field The magneTic field is direcTed inTo The plane of The figure If The X magneTic field magniTude is decreasvhg X A The induced emf is clockwise B The induced emf is counTerclockwise C The induced emf is zero D The answer depends on The sTrengTh of The field Q293 A circular loop of wire is placed nexT I To a long sTraighT wire The currenT I in The long sTraighT wire is increasing 0 WhaT currenT does This induce in The circular loop A a clockwise currenT B a counTerclockwise currenT C zero currenT D noT enough informaTion given To decide A293 A circular loop of wire is placed negtltT I To a long sTraighT wire The currenT I in The long sTraighT wire is increasing WhaT currenT does This induce in The circular loop A a clockwise currenT B a counTerclockwise currenT C zero currenT D noT enough informaTion given To decide M Leon s Low 9 Flu lhmugh mil i 0 Induced l39ield needs to lcl l gm increasing puinl right to oppose 5 he 111ng in ux 3 h 0 Magnelic I39icld 0 solenoid is lel39l Coill CoilZ 39 x I I l I Ii In 111 LA A A A I I l i I l I I I quot n a l llrlllllll u Jill ll l B l l l39l l l39 I mum 0 I 0 Currcnl direction lTlll Q Elli f l quot lll i induce SwiLch held in the right c Induced current The figure shows Two solenoids facing each oTher39 When The swiTch for39 coil 1 is closed does The cur39r39enT in coil 2 flow from righT To lefT or39 from lefT To righT Physics 113 Dr Renat Letfullin 24 gxaglc A Rotating Loop A loop of wire is iniTially in The xy plane in a uniform magneTic field in The x direcTion IT is suddenly roTaTed 9OO abouT The y axis unTi iT is in The yz plane In whaT direcTion will be The induced currenT in The loop Initial position of loop IniTially There is no flux Through The coil AfTer roTaTion The coil will be Threaded by magneTic flux in The x direcTion The induced currenT in The coil will oppose This change by producing flux in The x direcTion LeT your Thumb poinT on The x direcTion and your fingers will curl clockwise Therefore The induced currenT will be clockwise as shown in The figure Physics 113 Dr Renat Letfullin 25 Lew Ma netic ux I AB 913 Consuder39 The loop shown g x x x x x x x gtlt cpmjBd BAzle x X x x x x x x Faraday39s Law I ch d dx ND 1 x x x a x x x gt5 gtlt 39 B I V m leBl Emi NM x x x x x x x x dz dz dz Lem5 dx Law x x x x x X x x E BZV B where Nnumber of turns X X X X X X X X t d BA magnetic flux 95 B external magnetic field Induced current A area of CO d Therefore E d The minus sign denotes Lenz39s Lawt d Ernf is the term for generated or induced voltage This is Faradayis Law IT can be stated as follows An emf E is induced in a conducfng oop if f Ie magnefc fUX QDm fhrough fhe oop changes wfh fme so fhafE IdQDmd l39l for Me oop The emf M be in Me direc on fhaf w drive f Ie induced currenf f0 oppose f Ie fux change as given by Lenzis Law Physics 113 Dr Renat Letfullin 26 Q294 x A flexible loop of wire lies in a uniform magneTic field of X magniTude Bdir39ecTed inTo The plane of The picTur39e The loop is X pulled as shown r39educing iTs area The induced cur39r39enT X l X rgtltr X X A flows downwar39d Thr39ough r39esisTor39 pr39opor39Tional To B B flows upward Thr39ough r39esisTor39 Rand is pr39opor39Tional To B C flows downwar39d Thr39ough r39esisTor39 Rand is pr39opor39Tional To 82 D flows upwar39d Thr39ough r39esisTor39 Rand is pr39opor39Tional To 32 E none of The above A294 A flexible loop of wire lies in a uniform magneTic field of magniTude BdirecTed inTo The plane of The picTure The loop is X pulled as shown reducing iTs area The induced currenT x x V gtlt X A flows downward Through resisTor Rwandis proporTional To B B flows upward Through resisTor Band is proporTional To B C flows downward Through resisTor Band is proporTional To B D flows upward Through resisTor Band is proporTional To 32 E none of The above m Electromagnetic Induction in o Circular Loop B decreases from 10 T The magnetic field shown in the figure t00 4Tin12 S decreases from 10 T to 04 T in 12 s A 60 R 00100 cm diameter loop with a resistance of 0010 Q X X quot3X X X X x is perpendicular to the field What is the size and direction of the current induced in the loop 2 E dQDm d7rr B Z rz dB all all dt d B 0396 T 050 Ts dt At 12 s 2 2 3 E 7n 7r003 m 050 Ts 141gtlt10 V The current direction is t such as to reinforce the 3 I E 141gtlt10 V 2014114 diminishing B field R 0010 Q Therefore the current I Physics 113 Dr Renat Letfuiiinw39 be CIOCkW39Se39 29 m Electromagnetic Induction in o Solenoid A 20 cm diameTer39 loop wiTh a r39esisTance a 20cm1000turns gt DDDDDDUUDDDDD of 0010 Q is placed in The cenTer39 of a solenoid The solenoid is 40 cm in diameTer39 20 cm long and is wound wiTh 1000 Tur39ns of 533 square insulaTed wire The cur39r39enT Thr39ough h T e solen0Id ere as a funcTIon of Time Is wwkw gEEEXXNXEKKHEEKKKKKKKEEE shown in b 20 41 391 Find The Induced cur39r39enT In The loop C39 39amm39 quotOp d1 b B 0leol dr 10 As unt11 t10 s and 0 after that l Solenoid cum I IsolA q BA OAleol E 197gtlt10395 Vuntil t10 s and 0 after that 0 m 1 61 quot uDAN 611501 Iloop ER 197 mA until t10 s and 0 after that r quotmm E 1 dt 2 61 5d 1 0 s 3 dt 197 gtlt10 6 Physics 113 Dr Renat Letfullin 30 a b Wire loop Induced current V S No force is needed lo pull the loop when the wires are outside the magnetic field A pulling forec is needed to balance the magnelic force on the induced current Suppose ThaT a rigid square copper loop is beTween The poles of a magneT If The loop moves as long as no conducTors are in The field of The magneT There will be no currenT and no forces BUT when one side of The loop enTers The magneTic field a currenT flow will be induced and a force will be produced Therefore a force will be required To pull The loop ouT of The magneTic field even Though copper is noT a magneTic maTerial However if we cuT The loop There will be no force Physics 113 Dr Renat Letfullin 31 Ts 2 AnoTher way of looking aT The sysTem is To consider The Magnetic eld dueto magneTic field produced by meinduced mm The currenT in The loop The lm I currenT loop is effecTively a N J s AAA ing edlcun em ows dipole magneT wiTh a S pole l f mm 6 mp near The N pole of The 5 I magneT and vice versa T M 2 The current is a magnetic dipole The aTTracTive forces S 1 fg fgg 511 1fo36 beTween These poles musT be Magnet g iquot q I overcome by an exTernal Opposite poles attract so a magnetic force 0 pull me loop cm of Ef cixfiliiilii l i 5 Z f g The magneT loop out of the magnetic fiech Physics 113 Dr Renat Letfullin 32 Ts 3 a Eddy currents are induced when 1 The magnetlo force on the eddy a metal Sh el ls pulled through currents ix opposite in direction in ll a magnetic eld Metal sheet Region between the pennanentmagnel s poles Now consider a sheeT of conducTor39 pulled Through a magneTic field There will be induced cur39r39enT jusT as wiTh The wire buT There are now no welldefined cur39r39enT paThs As a consequence Two quotWhirlpoolsquot of cur39r39enT will cir39culaTe in The conducTor39 3 These are called eddy currenfs39 do Rail A magneTic braking sysTem Physics 113 Dr Renat Letfullin 33
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