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## General Physics

by: Nichole Keebler

36

0

12

# General Physics PHYSICS 208

Nichole Keebler
UW
GPA 3.95

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
12
WORDS
KARMA
25 ?

## Popular in Physics 2

This 12 page Class Notes was uploaded by Nichole Keebler on Thursday September 17, 2015. The Class Notes belongs to PHYSICS 208 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 36 views. For similar materials see /class/205230/physics-208-university-of-wisconsin-madison in Physics 2 at University of Wisconsin - Madison.

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Date Created: 09/17/15
a The story so far dB Magnetic field generated by current A mpere s law B ds 4 surface bmndeu bv Path Com Exam 2 results Grade cutoffs M m ixmna mmmtmm z Ampere s law Sum up component of B around path Equals current through surface Canponmtofs 307ng E lused galars M l 93 quot Ampere s law surface bummed bv path m m 312nm mum Ming 3 Am pere s law in electrostatics j E d5 7 m Work done by Er eld w jam 45 qu As 50 5 u m is Work per Lil ilt charge to bring charge back to Where it started This is zero m m ixmna rmmamm 4 Gauss law in electrostatics Electric ux through surface a charge enclosed Mnat about magneuc mm m m 312nm mum Ming 5 Magnetic flux Magnetic ux is de ned exactly as electric llux Component of B L surface x Area element ltIgtEfBdA l r I l zero ux Maximum ux Si unitof magneuc ux is the Weber 1 Trmz m m xxmna Mememm Magnetic flux What is that magnetic ux through this ace surf A Positive B Negative Mm Mr 3Lme WWGZHX mime 8 iiiir Hi il i l ii i ii Gauss law in magnetostatics Net magnetic ux through any closed surface is always zero lt1 0 mum Corrpare to Gauss law for eiecmc eld l 39 V 39 Datum QIMWA Ea as 1 Sighting diam Mquot m 3mm arm a is x Comparison with ee ctrostatics case law Eiectrostatics Arrpere39s law X Magnemstatics x Mm my 312mx WwiKXZ X team 8 Timedependent fields Up to this point have discussed only magnetic and electric elds constant in time Eerieids arise from char es Berieids arise from movii ig charges currents Faraday s discoveu Another source of electric eld Timervai yii ig magnetic rieid creates eiectric rieid Mm Mr 3Lme WwiKXZ X team 8 m Measuring the ind uced field A changing magnetic ux produces an EMF around the closed path Howto measure this Use a real loop ofwire for the closed path low EIR Current but no battery Electric currents require a battery EMF Faraday Timevarying magnetic eld creates EMF Faradays law EMF around loop rate of change ofmag ux Mm Mr 3Lme WwiKXZ X mime 8 lZ Faraday s law segSEaseedinps eedi BdA t t va EMF aroundow Magne r ux Waugh mute bomded by paw EMF no ionger zero around dosed ioop Mal iii zmnm rimzne mm 3 Quick quiz Wnicn ottnese conducting ioops WiH have currents owing in them Constanti I gt i quot Cnnstant v Cnnstanti Cnnstanti Mal iii mm riimmnmmix l6 Faraday s law Faraday s law Timervaryirig Betieid creates Erfieid Conductor Ee eid creates eiectnc current BiotSavartlaw Eiectnc current creates magnetic neid Lenz s law I induced current produces a magnetic fieid interacts Witn bar magnetiust as anotneroar magnet I LeriZ S iaW induced current generates a magnetic fieid thattries tn cancei the change in the ux Causes repuisivefnrce Result Anotnerrnagnetic rieid created ii is is zmnm rim mm is Quick quiz Quick Quiz vvnat direction force do iteei due to Leriz iaw when i pus themagnetdown 5 Down Left D Right strong magnet Mal iii zmnm rimzne mm 7 A conducting rectanguiar iooo moveS Witn constant veiocityv in tne w direction tnrougn a region or constant magnetic fieid B in tne ez direction as snown wnat is tne direction ottne induced iooo current A CCW B CW Mal iii mm VivsxlmJazureix ix Quick Quiz Conducting rectanguiarioop moves With constant veiocity v m the 7y direction away from a me With a Co stam Currem I as ShOWU What i5 the direction ofthe induced ioop current A CCW C No induced current Bried mquot was ma page arow Low moves to region ofsmale 5 so m decreases Mumow amenme die79639 somustoeate a ddm same man m m 311ms Phwzan mm m 19 Motional EMF Conductor moving in uniform magnetic eld charges in conductor are moving Magnetic eld exerts force x x x X X X X Cnargespiie up atends x XI x x x Static equmbnum Er eid X XL X X X g anceii g X X X magnetic force v x x x x x 15qu X X X X x sum 7 x x Mmmmm EMFWBL m m 311ms Phwzan mm m m Hydrogen atom energies J F 39day Ho ors lecture Prof ChntSprott akes us on a tour Offractais ouanttzeu energy ieveis Eaen urrespunds te unerent Orbit rautus Eiumt Pamete waverunetten Energy Eaen uesenneu by a u tum number n 13 a 74 yea We 2m twee zemenerev Classical vs Quantum Quantum Particle in a box Pamete un ned te a nxeu yegten er space e 9 man in a tune nan muves uniy aiung iengtn L 1 4 classlcally nan buunces back and mm in tube s isa ciasstcai state uttne nan iden n acn state bv Speed mnmmlummassxspeed m kinetic enevev Ciasstcai any mumenturn enevw ispussmie Quantum mumema enevev EYE euanuzeu m um 29 mm meme emu Dnerent m Ciassicai particie bounces back an 0 Sum Etimes veiumty is te ieft semettmes te ngnt 7 t Quantum rnecnantcs Par iEiE represented by We utmns Wavestravehng Quantum wavefunctlon sunEmnsmnn at both a same ume We 2m maven m nA ieftandngnt quantum states Quantum version Quantum state is netn VEiDEiUES at me same nme A2L One new waxsterian L Greune state is a stanan wave made equaiiy at e ma vv Wavetvaeimg ie 2 Art Detevmneu bv stanumu wave cundmun LenoZ gs BX Quantum Wavefunctmn L su erpnsitinn Bf b DLh mutmns W u Different p mv m Dmevent wauetenetn A L Twa he in wavelength meme emu subtecttu standingWae c eeev numbev at nattan n speeds cunespunu tn dmvenn Wavemnchon W A2L mamentum otetat l n unmtmn etenetns nt n the tube we 2m maven m um 29 mm Particle in box question A particle in a box has a mass rn lts Energy is all Kinetic p22rn Just saw that rnernenturn in state n is npa it s Energy levels 0 get eleser teqether at higher Energy m u 29 mi meme mm 7 Particle in box energy levels Oual ltlzed momentum h h vgn m Energy kll letlc z z E i 7 an5 quot5 2m 2m OrQuantized Energy E 15 m u 292nm V39rysuszzuuieLS a Question A particle is in a panlcular quantum state in a box at length L THE box ls rlEIW squeezed El a shorter length U2 The particle remains in the same quantum state The Energy at the particle is now A 2 tin es blgger 2tirnes srnaller rn es srn aller E unehanqeq m u 29 mi meme mm 9 Quantum dot particle in 3D box CdSe quantum dots dlspersed in hexane BaWel ldl group MIT Energy level spacing increases as particle size decreases e 2 2 2 2 n 1 h n h End 7 2 8m 8mL m u 292nm Mummies in Interpreting the wavefunction Probablllstlc ll lterpl etatlol l The square rnaqnituqe er the Wavefunctlon lull2 gives the prepapility errinqinq the particle ata particular spatial leeatien Waveiunction Frobaalh Weefunclnn ZL n t x m um 29 mm name was 11 Higher energy wave functions n p E h h n3 37 l ZL 38 L it i n2 2 2 h s 2L XML l t t i ll quot1 7 h c 2L emu Thu u 292nm inmmemn x2 Probability of nding electron Quantum Corral ind pamcie anywhere on average tor htgh n Ciasstcaiiy equaiiy Mkeiytuf OMrtrue 1 up mm Ouaniumrmechanicai or sivtbulton Ciasstcai disivthuitan t I l 14 a 1 a v P L D L l L n EgeHEWI Zerges in the prgbabvivty 68 ivun atamaaaaempteu min a ctvcuiav Wig Puretv quantum tnterrerenoe erreot The npptes natuethe NYE retteet the eiecivun quantum atateaata ctvcuiav nne ntenerenee etteeta m u 29 mm rmame tame u m ua 292nm rma 2m tame Scanning Tunneling Microscopy Particle in a box again lt7L Q Partrcte centarneo entrretv wrthrn cteseo Lube Wavemnchan prawne Waverummnr n excavevf Oven tap Dam e Ea m enmgh washake ha But at tawenerer es pam ete taYS entrretv within hax overthe tast 2n yrs techneter uevetepeu to eentrpuaptv pesttten ttp and sampie 172 nrn apart Like an eiectranm meat is a very userut rntereseepet rememberphmaeiectnceffecti name mm mm 2m mm ta Two neighboring boxes Quantum mechanics says S meming different other box ts brought nearbv the eiectron rnav otsappearrrorn one wett and Low entrgy appear tn the othen mum The reverse then hap ens and the eiectron osotttates back an form wtthout traverstng the tnterventng otstanoe ouanturn M eehantes some prooaomty of the perme penetratrng s of box39 Low quotHEY Quantumxmtt Nanzera Drahahvivty ar being autxide the hex nu ua 292nm Wampum ta m u 29 mm name maze Question Suppose sepaauon beMeen boxes increases by a factor of two The mnneimg probabmty A increases by 2 Bi Decreases by 2 hig v39 pmbabtttty iow39 pmbabttt ty m NW 191nm News We 15 to Example Ammonia molecule N H Ammonia moiecuie NHJ Nitvooen N nastwu equivaient stabie positions Ouamummechamcaiiv turmeis n as mvevsmn ime asis emst atomic ciock aw K a m NW 191nm Phwzan MM m Atomic clock question Suppose we cnangedtne ammonia moiecuie so tnattne dtstance between tne two stabie positions ottne nitrogen atom iNCREASED Tne ciockwouid A New down B speed up c staythe same m NW 191nm mm m MN 15 11 Tunneling between conductors Make one WeH oee er pamete tunnets ays in ntnerweu m NW 191nm mm m MN 15 22 Scanning Tunneling Microscopy no sampie ae quantum boxes Potenuai difference induces mnnehng Tunnehng abemew sensuve to opnsarrpie spacing amp e mertne iast 2n yrs technoiogy deveioped to controiiaoiy position tip and sampie 172 nrn apart is a very usefui rntemsenpe w NW unto me me MN 15 a lmagescourtesy M LigaM Lrw wm m NW 191nm me me MN 15 a Manipulation of atoms Take advantage ompratom mterachons to Quantum Corral phymcauymove atomsmound onthe surface I 39 39 Hmhwm hsshuwsme assemmy 1 ur a mrcmar cunav by I muvmg mmvmua run 7 a atums run he surfa e at J c 77 391 4 H r p a v I The 777 unentatmn suppuns an 2721an M u Ewen5W 5mm State Wm Ea a C39 8 Hum ammsassemmed mm a meme ma v ca a 7 a be awe me 5 quot3 m Hpmes msmeme ma 727mm 272mm quantum atesuva cwvcu av 7mg Me evence 277227 a EgeHEIM m um 29mm mama man 25 m u 292nm Manama 25 The Stadium Corral game fun 39 I hT IQ X I 39 39 quot a gammy Agam mn an mPPEV m v asassemmedm nve gme quantum than m e edvanwwdundmn um um bewndlhesudmmma mucMn a abserve mam me s m u 29 mm quotmama max 27 Karyn mamquot m angma chm camun Manama man HananDPPEVUM camunMunameuanM mumamm Manama DErgleHEIM za Exercise Parallel Plates Physics 208 Lecture 6 El Find the potential difference between the two large Today s Tom s conductor plates of areaA and separation d I Capacitance Ch 26 5 how I Capacitors and Capacitance d g 1 39 w I Calculating Capacit Icefor I I Answer L parallel plate cylindrical spherical capacitors AV WW I Combinations ofcapacitors I Note AV is proportional to Q I Hope you have prevlewed Realistic case Capacitors El A generic capacitor Demo Charging A Pair of Parallel Conductors El Capacitor are very useful devic s Timing control noise filters energy buffer generatorlselectorlfi frequency lter sensors memories uncharged Charging Capacitance El AV a o ocav c is called capacitance D c QIAV amount of charge per unit of potential diff gt Unit larad F 1 CoulombIVolt gt Parallelplate CznAld gt Cylindrical and Spherical see examples intext l Charging A Capacitor q Armc a Av0c gt dq q uncharged charin charged duAqu D Electric potential energy gained After charging the capacitor stores potential energy u v2 ozlc Discharging A Capacitor a AVQc I a lt1 charged discharin uncharged duAqu D Potential energy released the originally charged capacitor has potential energy u v2 ozlc Combinations of Capacitors n Series Effective Capacitance charge conservation olazlal o CQIAV 1IC 1IC11IC2 rQl Qi mAvlaL gAv2a c I H AV AV effectiver 11cs s 1Ic11ICZ1IC Note one always lt c Combinations of Capacitors In Parallel C1AV1 c2sz 35 AV cP AV I C C2 c1u1u2 Q AVZ 2 effectively AV AV AV1 AV2 AV Effective Capacitance Why AV 39 C1C parallel C 39 C1CzCg Note Cpmne always gt CI Quick Quizexercise Combination of Capacitors El What is the effective capacitance for this combination CHEF C22HF Ca3l1F 1 C6pF c1 2 C311F CZ 3991 3 C15pF 4 None of above

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