Physics III PH 113
Popular in Course
Popular in Physics 2
This 37 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 15 views. For similar materials see /class/225113/ph-113-rose-hulman-institute-of-technology in Physics 2 at Rose-Hulman Institute of Technology.
Reviews for Physics III
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 10/19/15
Magnetism Lecture 29 Electromagnetic Induction B B gt gt gt gt gt TTTTTTTT V gtgt gt gt TTTTlTTTT Todng Review of the Test 1 The History of Induction Faraday s Discovery Experimental Demonstrations Motional EMF Induced Current in a Circuit In 1831 Joseph Henry a Professor of Mathematics and Natural Philosophy at the Albany Academy in New York discovered magnetic induction In July 1832 he published a paper entitled On the Production of Currents and Sparks of Electricity from Magnetismquot describing his work Because Henry published affer Michael Faraday he did not receive much credit for this discovery which actually preceded Faraday39s Joseph Henry 17971878 Michael Faraday39s ideas about conservation of energy A r r led him to believe that since an electric current could cause a magnetic field a magnetic field should be able to produce an electric current He demonstrated this principle of induction in 1831 and published his results immediately The principle of induction was a landmark in applied science for it made possible the dynamo or generator which produces electricity by mechanical means Michael Faraday 17911867 Physics 113 Dr Renat Letfullin 3 Closing the switch causcs a momentary Faraday had wound Two coils around The same iron in has 16 mm 39m ml mghmml39 ring He was using a currenT flow in one coil To 39 cmmmmr produce a magneTic field in The ring and he hoped ThaT This field would produce a currenT in The oTher coil Like all previous aTTemst To use a sTaTic magneTic field To produce a currenT his aTTempT Omng failed To generaTe a currenT ngirtzg39glfy However Faraday noTiced someThing sTrange In The insTanT when he closed The swiTch To sTarT The currenT flow in The lefT circuiT The currenT meTer in The righT circuiT jumped ever so sligthy When he broke The circuiT by opening The swiTch The meTer GISO Jumped bur in The opposife direc on The Opening the switch causc5a momentary 39 in the left Cll CUil current inth opposite 1 dirccljon effecT occurred when The currenT was sTopping or sTarTing buT noT when The currenT was sTeady Physics 113 Dr Renat Letfullin 4 Faraday replaced The upper coil wiTh a bar magneT He found ThaT There was a momenTary currenT when The bar magnefwas moved in or ouT of The coil Conclusion There is a currenT in The coil if and only if The magneTic field passing Through The coil is changing The currenT in a circuiT due To a changing magneTic field is called induced currenT Faraday placed one coil above The oTher wiThouT The iron ring Again There was a momenTary currenT when The swifch opened or closed Physics 113 Dr Renat Letfullin Push orpu1l coil 0 Was iT necessary To move The magneT Faraday placed The coil in The field of a permanenT magneT He found ThaT There was a momenTary currenT when The call was moved Mott X X E into page g x x X X z lgt X v x x x X X Change carriers in Ihe wire experience an The charge separation creates an chm1c eld in The charge t lon continues until the downward upward force of ma ituLlc F qui Being the canducmn 3 increases as more Charge ows electric force FE 15 large Enough to balance the upward magnetic force F 5 Then the net force n free tn move positive charges ow upward n charge is mm and the current ceases or if you prefer negative charges downward Consider a lengTh lof conducTor moving To The righT in a magneTic field ThaT is inTo The diagram PosiTive charges in The conducTor will experience an upward force and negaTive charges a downward force The neT resulT is ThaT charges will pile upquot aT The Two ends of The conducTor and creaTe an elecTric field E When The force produced by E becomes large enough To balance The magneTic force The movemenT of charges will sTop and The sysTem will be in equilibrium FquvB FEqu FBzFE gt EvB Physics 113 Dr Renat Letfullin 6 Separating Charge a Magnetic forces separate the charges and cause a potential difference between the b Chdemic39dl reactiml cgiaflfaw the Eh gss ends This is a motional emf 2 use a Pquot equot 1 creme Ween the ends This is a chemical emf y l x x x E X X X x x x AV a AV le x x v X x x X 0 X X X Electric field inside the battery Electric field inside the moving conductor l 1 AV Vmp mem IEydy j vBdy v13 0 0 Physics 113 Dr Renat Letfullin 7 DIOCIOI CIickchms onl The square conducTor moves upward Through a uniform magneTic field ThaT is dir39ecTed ouT of The diagram Which of The figures shows The cor39r39ecT disTr39ibuTion of charges on The conducTor39 u n o o o o n o n a u o o u I o n o u o o o I o o o u o u o u u o u u u u o a u n a o a I n u a 0 u o a o a a o a o o a n u o a a c n o o I n a a u u n n u t n a o u n a o o o u a o u a o n o E um 01 page a b 0 Id e Physics 113 Dr Renat Letfullin 8 mm A Battery mm A 60 cm long flashligh r battery has an EMF of 15 V Wi rh wha r speed must a 60 cm wir39e move Through a 010 T magnetic field To create The same EMF E le E 15 V v 250 ms B 006 m010 T Physics 113 Dr Renat Letfullin 9 m Potential Difference am a Rotating Bar A mefal bar39 of lengfh l rofafes wifh angular velocify co abouf a pivof af one end A uniform magnefic field Bis perpendicular To The plane of rofafion Whaf is The pofenfial difference between The ends of The bar39 vzwr EBvBwr AVzV p V plvot j Erdr 0 l l I 130 rdr 2 Ba rdr 2 3012 0 0 The electric field strength increases with r w X X X X X x E Angular velocity cu X x X x x The speed at disfance r is v wr Physics 113 Dr Renat Letfullin 10 Induced 0mm in a Circui39i lThe Charge carriers in the wire are pushed upward by he magnetic force Posiu ve end ofwire Moving wire The figure shows a conducting wir39e sliding X X X with speed v along a Ushaped conducting r39ail X X X The induced emf E will cr39ea re a current I X Xv x X X X around The loop X X X X X X Conducting rail Fixed Negative end E I E to table and doesn t move I 0 wire R R 2 The charge carriers ow around the conducting loop as an induced currenl Physics 113 Dr Renat Letfullin 11 Force and Induc on A pulling force to the right must We have assumed Tha l The balance the magnetic force to keep conductor moves with a constant speed v thew 139 m0V g m mnm39m Wd Thls force does WOlk on the WLre I139 Turns out That a current carrying mm In 392 a magnetic field experiences a force Fmag so we must supply a counterforce Fpull To x x x x x x x x make l39hlS happen X x X X zzx I X X x x x x x x x X gtlt x Fma Fpull l ZBZ x E x x x x x le v1 dlemagzllBB X xgx x x x x x x R R x x x x xgtlt x x x The magnetic force on the curremcurrying wire is opposite the motion Physics 113 Dr Renal Letfullin 12 Ac 12 Lighting A Bulb The figure shows a circuiT including a X x x x x x gtlt x 3 V 15 W lighT bulb connecTed by ideal wires wiTh no resisTance The righT wire X X 13cmx X X X X is pulled wiTh consTanT speed v Through a 3 V x x x x x x x perpendicular 010 T magneTic field 9 gt 15 W x x x X X x x a WhaT speed musT The wure have 01 T To lighT The bulb To full brigthess X x X X x x x x b WhaT force is needed To keep X X X X X X X X The wire moving AV 30 V VZEZB39O WzmomS R 60Q B 010 m010 T I 050 A P 15 W 0 50 A F v1232 300 ms010 m2010 T2 AV 30 V 39 1 R 60 Q 50gtlt10 3 N Physics 113 Dr Renat Letfullin 13 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 14 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 15 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 16 Magnetism The Magnetic Field of a Current B B gt gt gt gt gt TTTTTTTT X X X X X X x x1 x x egg H TMTlTvTTT F F F0 B xxxxxx r 6 Line In regr39als Another form of Amper39e39s Law 6 Example The Magne ric Field Inside a Cur39r39en rCar39r39ying Wir39e Magne ric Field of Solenoids Mo rion of Charge in an Uniform magne ric filed The Ear rh39s Van Allen Bel r The Hall Effec r dickchns ml WhaT is The cur39r39enT dir39ecTion in The loop and which side is The nor39Th magneTic pole a Cur39r39enT cw N pole on Top b Cur39r39enT cw N pole on boTTom c Cur39r39enT ccw N pole on Top d Cur39r39enT ccw N pole on boTTom Physics 113 Dr Renat Letfullin 3 a The line can be dividedinto many small A hne from 1 to f segments The sum of all the As s is the length L of he line A line integral is a special kind of vector integral in which the projection of some vector quantity is projected on a straight or curved linear path connecting two points and the product of vector39s projection times infinitesimal path distance is summed The simplest line integral is just the sum over the path length L f We have prevuously seen this kind of Integration In L ZklAsk lds our discussion of work Physics 113 Dr Renat Letfullin i i 4 Now consider a line inTegr39aI in The a presence of a magneTic field Divide The paTh up inTo ine segmenTs of lengTh f A39s AT The k rh segmenT The magneTic field is is f H I ZBkA k gtj1 d i 39gt gt k i N If E is always in The same dir ecTib n as ds and consTanT over39 The paTh Then The line passes through a magnetic field Magnetic field at segment k f4 f f jBd desBjdsBL b Displacement of segment k Physics 113 Dr Renat Letfullin 5 Line Integrals Made Easy tel If E is everywhere perpendicular If E is everywhere parallel 1390 To The pa rh of integration d39s39 Then The path of integration d39s39 Then f f IECKO JE 23L Physics 113 Dr Renat Letfullin nL pUIHl A special case of a line inTegral is one ThaT runs in a closed paTh and reTurns To where iT sTarTed ie a line inTegral around a closed curve which for a magneTic field is denoTed by gdg Consider The case of The field aT a disTance d Hi rwhm lungem in me irllrgmllun th from a long Slr alghl wme39 B I dumn39lpnxxlllmugh 472 d llu L39llL39llKUkl m39liv I u 2 llliflliilllll s Therefore DEB LE 2 Em ds 27rd 01 7 This resulT is independenT of The shape of The curve around The wire independenT of where The currenT passes 353 Through The curve gt depends only on The amounT of currenT EB d u I 0 through passung Through The InTegraTIon paTh Physics 113 Dr Renat Letfullin Ampere39s Law 7 M The Magnetic Field Inside a WT CWQ Wt By symmetry the magnetic field must be tangent to the circle A wire of radius R carries currenT I Find The magneTic field inside The Currentcarrying wire of radius R wire aT a disTance rltR from The axis Closed 2 integration 1 JA 1 2 1 Pam 7239 hr h t 011g Rz 2 I I is the curith inside radius r llu39migh Field inside Wire Dj m3mdsm2m 2 I Bmax Olthrough 01 R2 2 58m Fie1d outside wire B 01 r uo 21r 27239 R2 47 R2 0 I I 0 R 2R 3R 4R Physics 113 Dr Renat Letfullin of a Solem dl I A solenoid is a helical coil lt of wire consisTing of mulTiple loops all carrying The same currenT One can Think of The field of a solenoid by superimposing The fields from several loops as shown in The lower figure On The axis The Three fields will add To make a sTronger neT field buT ouTside The loop The fields from loops 1 and 3 will Tend To cancel The field from coil 2 When The fields from all The loops are superimposed The resulT is ThaT The field inside The solenoid is sTrong and roughly parallel To The axis while The field ouTside is very weak In The limiT of an ideal solenoid The field inside is uniform and parallel To The axis while The field ouTside is zero Physics 113 Dr Renat Letfullin 9 b A stack of ihree loops 39 hum N Integration path We can use Ampere39s Law to calculate the forAInp re s law field of an ideal long solenoid by choosing the integration path carefully We choose a rectangular LXW loop with one horizontal side outside the solenoid and the vertical sides passing through If the loop encloses N wires then Ifhmugh NI Therefore Ampere39s Law says that mBc zyONI 0000000 0 III 1 MI quotI l 395 I III IEI QQQQQQQQQQQQQ E is tangent b the integration ml d3 BIL 32W BBL 34W path along the bottom edge If n NL is the number of turns per unit length then The first side in inside and parallel to B so 313 Sides 2 and 4 are perpendicular to B no radial B so BZB4O Side 3 is outside the solenoid so 330 Therefore B uoNIL B solenoid 0 quot1 Physics 113 Dr Renat Letfullin 1O m Gm ns a Uniform Magnetic Field We wish To genera re a 010 T magnetic field near39 The cen l39er39 of a 010 m long solenoid How many Turns are needed if The wire can carry a maximum current of 10 A Bsolenoid Hon Therefore N 010 T010 m 4 800 turns 01 47rgtlt10 TmA10 A Physics 113 Dr Renat Letfullin 11 As shown in The figures The mogneTic field of a solenoid looks very much like ThoT of a bar mogneT The nor39Th pole of The solenoid can be idenTified using yeT onoTher39 r39ighT hond r39ule LeT The fingers of your39 r39ighT hond cur39l in The dir39ecTion of The solenoid cur39r39enTs Then your39 Thumb will be poinTing in The dir39ecTion of The mogneTic field and To The nor39Th pole of The solenoid I Solenoid 1 B at magnet Physics 113 Dr Renat Letfullin 12 lid 39 Force is perpendicular To Bv Circular mo rion Solve for39 R xxxxxx x K x x x x x x Uniform B into page Consider a posiTive charged parTicle wiTh mass m and charge q moving aT velociTy v perpendicular To a uniform magneTic field B The parTicle will move in a circular paTh of radius rcyc because of The force F on The parTicle which is i is peqwemlicular In If B into page A 2 mv mv F 1V3 cyc B The magnelic l39urcc is ulwuyx rcyc q perpendicular ll F aiming lhc particle in mmc in u circle v B fcyc 1 1ndependent of rayc and v Z rcyc m 27 Physics 113 Dr Renat Letfullin 14 The Cyclotron Accelerator Because when a charged parTicIe moves in a uniform fieldfcyc is independenT of boTh radius and energy one an quotpumpquot energy inTo The parTicIe as iT cycles using an eecTric field ThaT varies wiTh The frequencyfcyc This is The basic principle of The cycloTron a parTicIe acceleraTor ThaT can increase The energies of charged parTicIes The uTimaTe energy of a cycloTron is deTermined by The radius R of The magneT Em RqB22m Physics 113 The potential AV oscillates at the cyclotron l39requencyf uyu39 Proton source Protons exit here Dr Renat Letfullin m The Radius of claim Motion An elecTr39on is acceleraTed fr39om r39esT Through a poTenTiaI of 500 V Then injecTed inTo a uniform magneTic field B Once in The magneTic field iT compleTes a half r39evoluTion in 20 ns X a X WhaT is The radius of The or39biT X B X X X gmv2 eV00 v l 133x107 ms m X X f i 2 5x108 Hz W T 220gtlt10 9 s 39 0quot 500V Bzsz yc 894X1073 T 4ycm l847x103 m847mm 39 q 6 Physics 113 Dr Renat Letfullin 16 3 Charged particles spiral around the magnetic field lines EarTh s Van Allen Charged parTicles Tend To spiral in a magneTic field moving along field lines in a spiral paTh When The field lines quotpinchquot TogeTher The parTicles quotbouncequot and reverse The direcTion of Their moTion along The field lines This forms a quotTrapquot ThaT can caTch and hold charged parTicles The EarTh39s magneTic field forms such a Trap for elecTro ns and proTo ns emiTTed by The Sun These quot Ifiii gl39 lftjl f g Z j g i jm Trapped charged parTicles form The Van Allen hew 39me radiaTion belTs in The space around The EarTh EnergeTic elecTrons and proTons leaking from The Trap near The EarTh39s magneTic poles ionize The air in The upper aTmosphere and produce The Aurora Borealis in The norThern sky Physics 113 Dr Renat Letfullin httpscience nasagovspacewea rher a agaller y010c r03pageZ h rml The Hall Effect a 1 Th chumc carriers When a charged particle f f m 1 moving in a vacuum i139 is y Am deflec red perpendicular To i139s 1 A 4 velocity by a magnetic field In I 1879 Edwin Hall a graduate C9 quot9 F39 nfgd fm student of Johns Hopkins Univ 39 discovered That The same behavior is True for charged par139icles moving in a conductor J x E c61rk 1 ic1d d c to chum sepiu39ulitin AVH Edw39n Herbert Fm m3 Fe 6E e 1855 1933 c Electron Top surface w L39LIII39L Hl is ncgulivu F 39 AVH wvdB quot J I A I I 13 vd AVszB me me wine wine tne Physics 113 Dr Renat Letfullin 19 M Hell Probe Measurement of Magnetic Field A Hall pr39obe consisTs of a sTr39ip of meTallic bismuTh ThaT is 015 mm Thick and 50 mm wide BismuTh is a poor39 conducTor39 wiTh a charge carrier densiTy of n 135x1025 m393 The Hall volTage on The probe is measured To be 25 mV when The cur39r39enT is 15 A WhaT is The magneTic field and whaT is The elecTr39ic field inside The bismuTh tne BZTAVH 74 25 3 719 15gtlt10 m135gtlt10 m 16X10 Clt00025V 15A 054T AVH 00025 V E w 0005 1n 050 Vm Physics 113 Dr Renat Letfullin 20 Experimental Activity Solenoids and Bar MagneTs As shown in The figures The mogneTic field of a solenoid looks very much like ThoT of a bar mogneT The nor39Th pole of The solenoid can be idenTified using yeT onoTher39 r39ighT hond r39ule LeT The fingers of your39 r39ighT hond cur39l in The dir39ecTion of The solenoid cur39r39enTs Then your39 1 Solenoid 1 Thumb will be poinTing in The dir39ecTion of The mogneTic field and To The nor39Th pole of The solenoid gt8 e fUW B ar magnet Physics 113 Dr Renat Letfullin
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'