calculating electromagnetic
|
|
- Justina Evans
- 5 years ago
- Views:
Transcription
1 Theoeal mehods fo alulang eleomagne felds fom lghnng dshage ajeev Thoapplll oyal Insue of Tehnology KTH Sweden
2 Oulne Despon of he poblem Thee dffeen mehods fo feld alulaons - Dpole and monopole mehods fo feld alulaons - Non-unqueness of feld omponens - Felds n ems of appaen hage hd mehod Speal ase of eun soke wh speed of lgh Aknowledgemen: V.A akov and M. Uman Unvesy of Floda Ganesvlle ll
3 Despon of he poblem ghnng g eun soke speed -x 8 ms Cuen se me < -6 s Dsbued soue fas hangng g n boh spae and me Mehods of fndng exa expessons fo emoe ele and magne felds v τ- τ < v. d d E B θ 3
4 El f ld f d l Ele felds fom a dpole Sa Z j β Z e j + m Z E - j - E ω β β θ π 3 os y P θ e - j + m jz - E - j - E ω β θ β β θ π β 3 sn 4 y φ e j + m j H - j - E ω β φ β θ π β sn 4 x j β π 4 d adaon Induon o Ae he feld omponens unque? nemedae
5 Ele felds fom lne soues ne soue seveal dpoles onneed end o end Is possble o defne sa nduon and adaon omponens unquely? How do we defne sa feld? - dsane 3? - The pa of ele feld gven by he gaden of he sala poenal? How do we defne adaon feld? - dsane? - Assoaed wh ae of hange of uen aeleang hages? - ae of hange of veo poenal?
6 Two mehods fo fndng ele felds Monopole mehod Cuen Densy Cuen densy Chage Densy fom onnuy equaon Veo Sala Poenal Veo Poenal fom oen Poenal ondon Sala a Poenal Ele Feld Dpole mehod Expl use of oen ondon Ele Feld Expl use of onnuy equaon Jefmenko
7 ubnsen e al. 989 showed ha fo a exendng sep pulse boh gve denal ele felds numeally. Safaenl and Mna [99] showed ha fo exendng sep pulse boh expessons ae analyally equvalen. Thoapplll and akov showed analyally ha fo any dsbuon of uen and hages on a lghnng hannel he dpole and monopole mehods gve he same ele felds
8 Dpole and monopole mehods fo feld alulaons - Dpole mehod Expl use of oen τ τ ondon o fnd sala A θ τ poenal fom veo 4 poenal φ oen ondon A + d ˆ φ θ Adτ A θ E φ A B A 8
9 Monopole mehod fo feld o opo e e od o e d alulaons - The monopole mehod mehod The onnuy equaon explly used o fnd ˆ 4 τ τ τ θ d A p y hage densy fom uen * ρ. ons ρ + * 4 4 d Q ρ φ φ A E φ Q 9
10 Expessons fo sala poenal Dpole mehod 4 3 d d + + τ τ θ φ Monopole mehod * d Q ρ φ o opo e e od 4 4 d Q τ τ Boh ae analyally equvalen
11 Sample alulaon usng he wo mehods p g lghnng eun soke feld a gound D l h d v Dpole mehod v 3 3sn ˆ V d d E τ τ α + 3sn ˆ d b α sn ˆ d α 3 Sa Monopole mehod 3 * ˆ V d E ρ Induon adaon 3 * ˆ V d d ρ ρ adaon ˆ d
12 Non-unqueness of feld omponens Numeal example - 5 m 3 EV_C & EV_CE EQ_ C 5 m Ele Fe eld Vm EQ_CE EI_CE E_CE E_C - EI_C Tme μs
13 Non-unqueness of feld omponens Numeal example - m 6 EV_C & EV_CE km Ele Feld V Vm 4 EI_C EQ_C EI_CE EQ_CE E_C E_CE Tme moseond
14 Non-unqueness of feld omponens Numeal example - 3 m 3. km.5 EV_C & EV_CE le Feld Vm E E_C & E_CE EI_C & EI_CE Tme μs EQ_C & EQ_CE
15 Ele feld a gound plane Dpole mehod Boh he gaden of he sala poenal and he me devave of he veo poenal onbue o he adaon feld em. Monopole mehod adaon em s ompleely gven by he me devave of he veo poenal. Tme devave of he veo poenal onbue o he nduon feld em. Eleosa and nduon ems ae gven ompleely by he gaden of he sala poenal No one-o-one oespondene beween feld omponens. Howeve oal feld s he same
16 Infeenes Indvdual feld omponens - sa nduon and adaon - ae no unque Toal ele feld s unque Dffeenes beween feld omponens ae sgnfan a lose dsanes and neglgble a fa dsanes Cauon has o be exesed n nepeng measuemen esuls o n makng appoxmaons n alulaons 6
17 elaon beween eaded uen and eaded hage? * ρ?. ons O O ρ Thoapplll akov Uman 997 7
18 elaon beween wo defnons of eaded hage densy os θ ρ ρ * + os θ oal hage densy a eaded me oal hage densy a eaded me as seen by emoe obseve appaen hage densy 8
19 elaon beween appaen hage densy and eaded uen ρ d - τ d τ d v+ 9
20 Felds a gound n ems of appaen g pp hage densy 3 * d E ρ ε π * an 3 d - - ρ ε π an 3 d d v - - ρ ε π * d ρ ε π M d d v ρ ε π 3 d d v ρ ε π
21 Pulse popagaon on a veal anenna above pefe gound exa fomulaon Wha happens f he eun soke speed s speed of lgh and f he uen avels whou any aenuaon and dspeson? I s poved n Thoapplll e al. ha he exa geneal expesson wh effe of pefe gound nluded edues o E θ θˆ θ sn θ B θ ˆ φ θ sn θ θ ˆ θˆ Cooay and Cooay also deve same esuls sang fom he felds of a movng pon hage.
22 Pulse popagaon on a veal anenna exa fomulaon - onnued Poynng veos adally-deed deed wh ogn a pon hage Wave mpedane 377 Ω Pon soue Pefe ondung plane
23 Smlay o he soluon of nfne onal anenna Spheal TEM soluon [Shelkunoff 95] Spheal TEM soluon [Thoapplll e al.] Pon soue Pon soue Pefe ondung plane
24 Infeenes A sem-nfne ondung we of vanshng adus pependula o a ondung plane all onduos beng pefe suppo spheal TEM f he only soue s a pon soue a he boom of he we. The uen eleased fom he pon soue avels unaenuaed wh he speed of lgh. The Poynng veo and enegy flow s n he adal deon fom he soue a he boom of he anenna. The wave mpedane s he fee-spae mpedane 377 Ω a all dsanes fom he anenna.
25 SOME EFEENCES FO MOE INFOMATION [] Uman M. A. D. K. Man and E. P. Kde The eleomagne adaon fom a fne anenna Am. J. Phys [] ubnsen M. and M.A. Uman 989. Mehods fo alulang he eleomagne felds fom a known soue dsbuon: Applaon o lghnng IEEE Tans. Eleomagn. Comp [3] ubnsen M. and M. A. Uman On he adaon feld un-on em assoaed wh avellng uen dsonnues n lghnng J. Geophys. es [4] Thoapplll. V. A. akov and M. A. Uman Dsbuon of hage along he lh lghnng hannel: ll elaon o emoe ele and magne felds fld and do eun-soke models J. Geophys. es [5] Thoapplll. Uman M.A. and akov V.A. Teamen of eadaon effes n alulang he adaed eleomagne felds fom he lghnng dshage J. Geophys. es [6] Thoapplll. and V. A. akov On dffeen appoahes o alulang lghnng ele felds J. Geophys. es [7] Thoapplll. and V.A. akov On he ompuaon of ele felds fom a lghnng dshage n me doman IEEE EMC Inenaonal Symposum Moneal Canada Aug [8] Thoapplll. Compuaon of eleomagne felds fom lghnng dshage Chape n he book The ghnng Flash ed V. Cooay The Insuon of Eleal Engnees ondon 3. [9] Thoapplll. M.A. Uman N. Theehay Ele and magne felds fom a semnfne anenna above a ondung plane J. Eleosas
5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( )
5-1. We apply Newon s second law (specfcally, Eq. 5-). (a) We fnd he componen of he foce s ( ) ( ) F = ma = ma cos 0.0 = 1.00kg.00m/s cos 0.0 = 1.88N. (b) The y componen of he foce s ( ) ( ) F = ma = ma
More informationField due to a collection of N discrete point charges: r is in the direction from
Physcs 46 Fomula Shee Exam Coulomb s Law qq Felec = k ˆ (Fo example, f F s he elecc foce ha q exes on q, hen ˆ s a un veco n he decon fom q o q.) Elecc Feld elaed o he elecc foce by: Felec = qe (elecc
More informationModern Energy Functional for Nuclei and Nuclear Matter. By: Alberto Hinojosa, Texas A&M University REU Cyclotron 2008 Mentor: Dr.
Moden Enegy Funconal fo Nucle and Nuclea Mae By: lbeo noosa Teas &M Unvesy REU Cycloon 008 Meno: D. Shalom Shlomo Oulne. Inoducon.. The many-body poblem and he aee-fock mehod. 3. Skyme neacon. 4. aee-fock
More informationBackcalculation Analysis of Pavement-layer Moduli Using Pattern Search Algorithms
Bakallaon Analyss of Pavemen-laye Modl Usng Paen Seah Algohms Poje Repo fo ENCE 74 Feqan Lo May 7 005 Bakallaon Analyss of Pavemen-laye Modl Usng Paen Seah Algohms. Inodon. Ovevew of he Poje 3. Objeve
More informationMCTDH Approach to Strong Field Dynamics
MCTDH ppoach o Song Feld Dynamcs Suen Sukasyan Thomas Babec and Msha Ivanov Unvesy o Oawa Canada Impeal College ondon UK KITP Sana Babaa. May 8 009 Movaon Song eld dynamcs Role o elecon coelaon Tunnel
More informationLecture 5. Plane Wave Reflection and Transmission
Lecue 5 Plane Wave Reflecon and Tansmsson Incden wave: 1z E ( z) xˆ E (0) e 1 H ( z) yˆ E (0) e 1 Nomal Incdence (Revew) z 1 (,, ) E H S y (,, ) 1 1 1 Refleced wave: 1z E ( z) xˆ E E (0) e S H 1 1z H (
More informationSilence is the only homogeneous sound field in unbounded space
Cha.5 Soues of Sound Slene s he onl homogeneous sound feld n unbounded sae Sound feld wh no boundaes and no nomng feld 3- d wave equaon whh sasfes he adaon ondon s f / Wh he lose nseon a he on of = he
More informationNote: Please use the actual date you accessed this material in your citation.
MIT OpenCuseWae hp://cw.m.edu 6.03/ESD.03J Elecmagnecs and Applcans, Fall 005 Please use he fllwng can fma: Makus Zahn, Ech Ippen, and Davd Saeln, 6.03/ESD.03J Elecmagnecs and Applcans, Fall 005. (Massachuses
More informationCOMPUTER SCIENCE 349A SAMPLE EXAM QUESTIONS WITH SOLUTIONS PARTS 1, 2
COMPUTE SCIENCE 49A SAMPLE EXAM QUESTIONS WITH SOLUTIONS PATS, PAT.. a Dene he erm ll-ondoned problem. b Gve an eample o a polynomal ha has ll-ondoned zeros.. Consder evaluaon o anh, where e e anh. e e
More informationChapter 3: Vectors and Two-Dimensional Motion
Chape 3: Vecos and Two-Dmensonal Moon Vecos: magnude and decon Negae o a eco: eese s decon Mulplng o ddng a eco b a scala Vecos n he same decon (eaed lke numbes) Geneal Veco Addon: Tangle mehod o addon
More informationSound Radiation of Circularly Oscillating Spherical and Cylindrical Shells. John Wang and Hongan Xu Volvo Group 4/30/2013
Sound Radaton of Culaly Osllatng Spheal and Cylndal Shells John Wang and Hongan Xu Volvo Goup /0/0 Abstat Closed-fom expesson fo sound adaton of ulaly osllatng spheal shells s deved. Sound adaton of ulaly
More informationReflection and Refraction
Chape 1 Reflecon and Refacon We ae now neesed n eplong wha happens when a plane wave avelng n one medum encounes an neface (bounday) wh anohe medum. Undesandng hs phenomenon allows us o undesand hngs lke:
More informationModal Analysis of Periodically Time-varying Linear Rotor Systems using Floquet Theory
7h IFoMM-Confeene on Roo Dynams Venna Ausa 25-28 Sepembe 2006 Modal Analyss of Peodally me-vayng Lnea Roo Sysems usng Floque heoy Chong-Won Lee Dong-Ju an Seong-Wook ong Cene fo Nose and Vbaon Conol (NOVIC)
More informationALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS.
GNRAL PHYSICS PH -3A (D. S. Mov) Test (/3/) key STUDNT NAM: STUDNT d #: -------------------------------------------------------------------------------------------------------------------------------------------
More informationElectromagnetic waves in vacuum.
leromagne waves n vauum. The dsovery of dsplaemen urrens enals a peular lass of soluons of Maxwell equaons: ravellng waves of eler and magne felds n vauum. In he absene of urrens and harges, he equaons
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm H ( q, p, ) = q p L( q, q, ) H p = q H q = p H = L Equvalen o Lagrangan formalsm Smpler, bu
More informationTRANSIENTS. Lecture 5 ELEC-E8409 High Voltage Engineering
TRANSIENTS Lece 5 ELECE8409 Hgh Volage Engneeng TRANSIENT VOLTAGES A ansen even s a sholved oscllaon (sgnfcanly fase han opeang feqency) n a sysem cased by a sdden change of volage, cen o load. Tansen
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm Hqp (,,) = qp Lqq (,,) H p = q H q = p H L = Equvalen o Lagrangan formalsm Smpler, bu wce as
More informationOutline. GW approximation. Electrons in solids. The Green Function. Total energy---well solved Single particle excitation---under developing
Peenaon fo Theoecal Condened Mae Phyc n TU Beln Geen-Funcon and GW appoxmaon Xnzheng L Theoy Depamen FHI May.8h 2005 Elecon n old Oulne Toal enegy---well olved Sngle pacle excaon---unde developng The Geen
More informationGalilean Transformation vs E&M y. Historical Perspective. Chapter 2 Lecture 2 PHYS Special Relativity. Sep. 1, y K K O.
PHYS-2402 Chapte 2 Lectue 2 Special Relativity 1. Basic Ideas Sep. 1, 2016 Galilean Tansfomation vs E&M y K O z z y K In 1873, Maxwell fomulated Equations of Electomagnetism. v Maxwell s equations descibe
More informationPendulum Dynamics. = Ft tangential direction (2) radial direction (1)
Pendulum Dynams Consder a smple pendulum wh a massless arm of lengh L and a pon mass, m, a he end of he arm. Assumng ha he fron n he sysem s proporonal o he negave of he angenal veloy, Newon s seond law
More information1 Constant Real Rate C 1
Consan Real Rae. Real Rae of Inees Suppose you ae equally happy wh uns of he consumpon good oday o 5 uns of he consumpon good n peod s me. C 5 Tha means you ll be pepaed o gve up uns oday n eun fo 5 uns
More informationPHYS PRACTICE EXAM 2
PHYS 1800 PRACTICE EXAM Pa I Muliple Choice Quesions [ ps each] Diecions: Cicle he one alenaive ha bes complees he saemen o answes he quesion. Unless ohewise saed, assume ideal condiions (no ai esisance,
More informationPhysics 442. Electro-Magneto-Dynamics. M. Berrondo. Physics BYU
Physis 44 Eleo-Magneo-Dynamis M. Beondo Physis BYU Paaveos Φ= V + Α Φ= V Α = = + J = + ρ J J ρ = J S = u + em S S = u em S Physis BYU Poenials Genealize E = V o he ime dependen E & B ase Podu of paaveos:
More informationChapter Finite Difference Method for Ordinary Differential Equations
Chape 8.7 Fne Dffeence Mehod fo Odnay Dffeenal Eqaons Afe eadng hs chape, yo shold be able o. Undesand wha he fne dffeence mehod s and how o se o solve poblems. Wha s he fne dffeence mehod? The fne dffeence
More informationScattering at an Interface: Oblique Incidence
Course Insrucor Dr. Raymond C. Rumpf Offce: A 337 Phone: (915) 747 6958 E Mal: rcrumpf@uep.edu EE 4347 Appled Elecromagnecs Topc 3g Scaerng a an Inerface: Oblque Incdence Scaerng These Oblque noes may
More information4/12/2018. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105. Plan for Lecture 34: Review radiating systems
PHY 7 Eodynams 9-9:5 M MWF On 5 Pan o u : Rvw adang sysms Souon o Maxw s quaons wh sous Tm pod sous Examps //8 PHY 7 Spng 8 -- u //8 PHY 7 Spng 8 -- u Gna vw -- SI uns mosop o vauum om ( P M ): Couombs
More informations = rθ Chapter 10: Rotation 10.1: What is physics?
Chape : oaon Angula poson, velocy, acceleaon Consan angula acceleaon Angula and lnea quanes oaonal knec enegy oaonal nea Toque Newon s nd law o oaon Wok and oaonal knec enegy.: Wha s physcs? In pevous
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 0 Canoncal Transformaons (Chaper 9) Wha We Dd Las Tme Hamlon s Prncple n he Hamlonan formalsm Dervaon was smple δi δ Addonal end-pon consrans pq H( q, p, ) d 0 δ q ( ) δq ( ) δ
More information8.022 (E&M) Lecture 13. What we learned about magnetism so far
8.0 (E&M) Letue 13 Topis: B s ole in Mawell s equations Veto potential Biot-Savat law and its appliations What we leaned about magnetism so fa Magneti Field B Epeiments: uents in s geneate foes on hages
More informationIn the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal
More informationChapter 6 Plane Motion of Rigid Bodies
Chpe 6 Pne oon of Rd ode 6. Equon of oon fo Rd bod. 6., 6., 6.3 Conde d bod ced upon b ee een foce,, 3,. We cn ume h he bod mde of e numbe n of pce of m Δm (,,, n). Conden f he moon of he m cene of he
More information24-2: Electric Potential Energy. 24-1: What is physics
D. Iyad SAADEDDIN Chapte 4: Electc Potental Electc potental Enegy and Electc potental Calculatng the E-potental fom E-feld fo dffeent chage dstbutons Calculatng the E-feld fom E-potental Potental of a
More informationCHAPTER 10: LINEAR DISCRIMINATION
HAPER : LINEAR DISRIMINAION Dscmnan-based lassfcaon 3 In classfcaon h K classes ( k ) We defned dsmnan funcon g () = K hen gven an es eample e chose (pedced) s class label as f g () as he mamum among g
More informationMobile Communications
Moble Communaons Pa IV- Popagaon Chaaess Mul-pah Popagaon - Fadng Poesso Z Ghassemlooy Shool o Compung, Engneeng and Inomaon Senes, Unvesy o Nohumba U.K. hp://soe.unn.a.uk/o Conens Fadng Dopple Sh Dspeson
More informationCourse Outline. 1. MATLAB tutorial 2. Motion of systems that can be idealized as particles
Couse Oulne. MATLAB uoal. Moon of syses ha can be dealzed as pacles Descpon of oon, coodnae syses; Newon s laws; Calculang foces equed o nduce pescbed oon; Deng and solng equaons of oon 3. Conseaon laws
More information[Griffiths Ch.1-3] 2008/11/18, 10:10am 12:00am, 1. (6%, 7%, 7%) Suppose the potential at the surface of a hollow hemisphere is specified, as shown
[Giffiths Ch.-] 8//8, :am :am, Useful fomulas V ˆ ˆ V V V = + θ+ φ ˆ and v = ( v ) + (sin θvθ ) + v θ sinθ φ sinθ θ sinθ φ φ. (6%, 7%, 7%) Suppose the potential at the suface of a hollow hemisphee is specified,
More informationGo over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration
Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse
More informationRotations.
oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon If we say wh one bass se, properes vary only because of changes n he coeffcens weghng each bass se funcon x = h< Ix > - hs s how we calculae
More informationNanoparticles. Educts. Nucleus formation. Nucleus. Growth. Primary particle. Agglomeration Deagglomeration. Agglomerate
ucs Nucleus Nucleus omaon cal supesauaon Mng o eucs, empeaue, ec. Pmay pacle Gowh Inegaon o uson-lme pacle gowh Nanopacles Agglomeaon eagglomeaon Agglomeae Sablsaon o he nanopacles agans agglomeaon! anspo
More informationPhysics Exam II Chapters 25-29
Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do
More informationName of the Student:
Engneeng Mahemacs 05 SUBJEC NAME : Pobably & Random Pocess SUBJEC CODE : MA645 MAERIAL NAME : Fomula Maeal MAERIAL CODE : JM08AM007 REGULAION : R03 UPDAED ON : Febuay 05 (Scan he above QR code fo he dec
More informationANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 2
Joh Rley Novembe ANSWERS O ODD NUMBERED EXERCISES IN CHAPER Seo Eese -: asvy (a) Se y ad y z follows fom asvy ha z Ehe z o z We suppose he lae ad seek a oado he z Se y follows by asvy ha z y Bu hs oads
More informationI-POLYA PROCESS AND APPLICATIONS Leda D. Minkova
The XIII Inenaonal Confeence Appled Sochasc Models and Daa Analyss (ASMDA-009) Jne 30-Jly 3, 009, Vlns, LITHUANIA ISBN 978-9955-8-463-5 L Sakalaskas, C Skadas and E K Zavadskas (Eds): ASMDA-009 Seleced
More informationIn electrostatics, the electric field E and its sources (charges) are related by Gauss s law: Surface
Ampee s law n eletostatis, the eleti field E and its soues (hages) ae elated by Gauss s law: EdA i 4πQenl Sufae Why useful? When symmety applies, E an be easily omputed Similaly, in magnetism the magneti
More information4/3/2017. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103
PHY 7 Eleodnais 9-9:50 AM MWF Olin 0 Plan fo Leue 0: Coninue eading Chap Snhoon adiaion adiaion fo eleon snhoon deies adiaion fo asonoial objes in iula obis 0/05/07 PHY 7 Sping 07 -- Leue 0 0/05/07 PHY
More informationPHYS 705: Classical Mechanics. Derivation of Lagrange Equations from D Alembert s Principle
1 PHYS 705: Classcal Mechancs Devaton of Lagange Equatons fom D Alembet s Pncple 2 D Alembet s Pncple Followng a smla agument fo the vtual dsplacement to be consstent wth constants,.e, (no vtual wok fo
More information17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other
Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.1 Electic Potential Enegy Electic foce is a consevative foce and so we can assign an electic potential enegy (PE) to the system
More informationLecture 5. Chapter 3. Electromagnetic Theory, Photons, and Light
Lecue 5 Chape 3 lecomagneic Theo, Phoons, and Ligh Gauss s Gauss s Faada s Ampèe- Mawell s + Loen foce: S C ds ds S C F dl dl q Mawell equaions d d qv A q A J ds ds In mae fields ae defined hough ineacion
More informationOn the Physical Significance of the Lorentz Transformations in SRT. Department of Physics- University of Aleppo, Aleppo- Syria ABSTRACT
On he Phsal Sgnfane of he Loen Tansfomaons n SRT Na Hamdan Sohel aa Depamen of Phss- Unes of leppo leppo- Sa STRCT One show all fas ha seem o eqe he naane of Mawell's feld eqaons nde Loen ansfomaons [nsen's
More informationLet s treat the problem of the response of a system to an applied external force. Again,
Page 33 QUANTUM LNEAR RESPONSE FUNCTON Le s rea he problem of he response of a sysem o an appled exernal force. Agan, H() H f () A H + V () Exernal agen acng on nernal varable Hamlonan for equlbrum sysem
More informationp E p E d ( ) , we have: [ ] [ ] [ ] Using the law of iterated expectations, we have:
Poblem Se #3 Soluons Couse 4.454 Maco IV TA: Todd Gomley, gomley@m.edu sbued: Novembe 23, 2004 Ths poblem se does no need o be uned n Queson #: Sock Pces, vdends and Bubbles Assume you ae n an economy
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon Alernae approach o second order specra: ask abou x magnezaon nsead of energes and ranson probables. If we say wh one bass se, properes vary
More informationTime-Dependent Density Functional Theory in Condensed Matter Physics
Exenal Revew on Cene fo Compuaonal Scences Unvesy of Tsukuba 013..18-0 Tme-Dependen Densy Funconal Theoy n Condensed Mae Physcs K. YABANA Cene fo Compuaonal Scences Unvesy of Tsukuba Collaboaos: G.F. Besch
More informationPHY2053 Summer C 2013 Exam 1 Solutions
PHY053 Sue C 03 E Soluon. The foce G on o G G The onl cobnon h e '/ = doubln.. The peed of lh le 8fulon c 86,8 le 60 n 60n h 4h d 4d fonh.80 fulon/ fonh 3. The dnce eled fo he ene p,, 36 (75n h 45 The
More informationSUPPLEMENTARY INFORMATION
do: 0.08/nature09 I. Resonant absorpton of XUV pulses n Kr + usng the reduced densty matrx approach The quantum beats nvestgated n ths paper are the result of nterference between two exctaton paths of
More informationWhen to Treat Prostate Cancer Patients Based on their PSA Dynamics
When o Tea Posae Cance Paens Based on he PSA Dynamcs CLARA day on opeaons eseach n cance eamen & opeaons managemen Novembe 7 00 Mael S. Lave PhD Man L. Pueman PhD Sco Tyldesley M.D. Wllam J. Mos M.D CIHR
More informationPhysics 11b Lecture #2. Electric Field Electric Flux Gauss s Law
Physcs 11b Lectue # Electc Feld Electc Flux Gauss s Law What We Dd Last Tme Electc chage = How object esponds to electc foce Comes n postve and negatve flavos Conseved Electc foce Coulomb s Law F Same
More informationChapter Fifiteen. Surfaces Revisited
Chapte Ffteen ufaces Revsted 15.1 Vecto Descpton of ufaces We look now at the vey specal case of functons : D R 3, whee D R s a nce subset of the plane. We suppose s a nce functon. As the pont ( s, t)
More informationUniversity of California, Davis Date: June xx, PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE ANSWER KEY
Unvesy of Calfona, Davs Dae: June xx, 009 Depamen of Economcs Tme: 5 hous Mcoeconomcs Readng Tme: 0 mnues PRELIMIARY EXAMIATIO FOR THE Ph.D. DEGREE Pa I ASWER KEY Ia) Thee ae goods. Good s lesue, measued
More informationOnline Supplement for Dynamic Multi-Technology. Production-Inventory Problem with Emissions Trading
Onlne Supplemen for Dynamc Mul-Technology Producon-Invenory Problem wh Emssons Tradng by We Zhang Zhongsheng Hua Yu Xa and Baofeng Huo Proof of Lemma For any ( qr ) Θ s easy o verfy ha he lnear programmng
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationChapter 6: AC Circuits
Chaper 6: AC Crcus Chaper 6: Oulne Phasors and he AC Seady Sae AC Crcus A sable, lnear crcu operang n he seady sae wh snusodal excaon (.e., snusodal seady sae. Complee response forced response naural response.
More informationLecture 2 M/G/1 queues. M/G/1-queue
Lecure M/G/ queues M/G/-queue Posson arrval process Arbrary servce me dsrbuon Sngle server To deermne he sae of he sysem a me, we mus now The number of cusomers n he sysems N() Tme ha he cusomer currenly
More informationThe Feigel Process. The Momentum of Quantum Vacuum. Geert Rikken Vojislav Krstic. CNRS-France. Ariadne call A0/1-4532/03/NL/MV 04/1201
The Fegel Pocess The Momenum of Quanum Vacuum a an Tggelen CNRS -Fance Laboaoe e Physque e Moélsaon es Mleux Complexes Unesé Joseph Foue/CNRS, Genoble, Fance Gee Ren Vosla Ksc CNRS Fance CNRS-Fance Laboaoe
More information1 Fundamental Solutions to the Wave Equation
1 Fundamental Solutions to the Wave Equation Physial insight in the sound geneation mehanism an be gained by onsideing simple analytial solutions to the wave equation One example is to onside aousti adiation
More informationEP2200 Queuing theory and teletraffic systems. 3rd lecture Markov chains Birth-death process - Poisson process. Viktoria Fodor KTH EES
EP Queung heory and eleraffc sysems 3rd lecure Marov chans Brh-deah rocess - Posson rocess Vora Fodor KTH EES Oulne for oday Marov rocesses Connuous-me Marov-chans Grah and marx reresenaon Transen and
More informationLightning return stroke current reconstruction or vertical and variable channel shape
nenaona Confeene on Lgnng oeon (CL) Sanga Cna Lgnng eun soe uen eonsuon o vea and vaabe anne sape Ande Cean Adan oos Dan D. Mu Son Spnean Levene Cumb Depamen of ea ngneeng Depamen of Maemas Tena Unves
More informationSuperstructure-based Optimization for Design of Optimal PSA Cycles for CO 2 Capture
Supersruure-asedOpmaonforDesgnof OpmalPSACylesforCO 2 Capure R. S. Kamah I. E. Grossmann L.. Begler Deparmen of Chemal Engneerng Carnege Mellon Unversy Psurgh PA 523 Marh 2 PSA n Nex Generaon Power Plans
More information3/19/2018. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105
PHY 7 Eletodynamis 9-9:5 A WF Olin 5 Plan fo Letue 4: Complete eading of Chap. 9 & A. Supeposition of adiation B. Satteed adiation PHY 7 Sping 8 -- Letue 4 PHY 7 Sping 8 -- Letue 4 Eletomagneti waves fom
More informationCH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal
More informationPHYS 1443 Section 001 Lecture #4
PHYS 1443 Secon 001 Lecure #4 Monda, June 5, 006 Moon n Two Dmensons Moon under consan acceleraon Projecle Moon Mamum ranges and heghs Reerence Frames and relae moon Newon s Laws o Moon Force Newon s Law
More information( ) () we define the interaction representation by the unitary transformation () = ()
Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger
More informationCptS 570 Machine Learning School of EECS Washington State University. CptS Machine Learning 1
ps 57 Machne Leann School of EES Washnon Sae Unves ps 57 - Machne Leann Assume nsances of classes ae lneal sepaable Esmae paamees of lnea dscmnan If ( - -) > hen + Else - ps 57 - Machne Leann lassfcaon
More informationTest 1 phy What mass of a material with density ρ is required to make a hollow spherical shell having inner radius r i and outer radius r o?
Test 1 phy 0 1. a) What s the pupose of measuement? b) Wte all fou condtons, whch must be satsfed by a scala poduct. (Use dffeent symbols to dstngush opeatons on ectos fom opeatons on numbes.) c) What
More informationMay 29, 2018, 8:45~10:15 IB011 Advanced Lecture on Semiconductor Electronics #7
May 9, 8, 8:5~:5 I Advanced Lecue on Semconduco leconcs #7 # Dae Chape 7 May 9 Chape 5.Deec and Cae Cae Scaeng Ionzed mpuy scaeng, Alloy scaeng, Neual mpuy scaeng, Ineace oughness scaeng, Auge / Scaeng
More informationThe Unique Solution of Stochastic Differential Equations. Dietrich Ryter. Midartweg 3 CH-4500 Solothurn Switzerland
The Unque Soluon of Sochasc Dffeenal Equaons Dech Rye RyeDM@gawne.ch Mdaweg 3 CH-4500 Solohun Swzeland Phone +4132 621 13 07 Tme evesal n sysems whou an exenal df sngles ou he an-iô negal. Key wods: Sochasc
More informationCOMPLEMENTARY ENERGY METHOD FOR CURVED COMPOSITE BEAMS
ultscence - XXX. mcocd Intenatonal ultdscplnay Scentfc Confeence Unvesty of skolc Hungay - pl 06 ISBN 978-963-358-3- COPLEENTRY ENERGY ETHOD FOR CURVED COPOSITE BES Ákos József Lengyel István Ecsed ssstant
More informationNumerical Study of Large-area Anti-Resonant Reflecting Optical Waveguide (ARROW) Vertical-Cavity Semiconductor Optical Amplifiers (VCSOAs)
USOD 005 uecal Sudy of Lage-aea An-Reonan Reflecng Opcal Wavegude (ARROW Vecal-Cavy Seconduco Opcal Aplfe (VCSOA anhu Chen Su Fung Yu School of Eleccal and Eleconc Engneeng Conen Inoducon Vecal Cavy Seconduco
More informationExperiment 09: Angular momentum
Expeiment 09: Angula momentum Goals Investigate consevation of angula momentum and kinetic enegy in otational collisions. Measue and calculate moments of inetia. Measue and calculate non-consevative wok
More informationEngineering Mechanics. Force resultants, Torques, Scalar Products, Equivalent Force systems
Engneeng echancs oce esultants, Toques, Scala oducts, Equvalent oce sstems Tata cgaw-hll Companes, 008 Resultant of Two oces foce: acton of one bod on anothe; chaacteed b ts pont of applcaton, magntude,
More informationElectromagnetic Theory 1
/ lectomagnetic Theoy uestion : lectostatic Potential negy A sphee of adius caies a positive chage density ρ constant Obviously the spheical coodinates system is appopiate hee Take - C m - and cm τ a)
More informationEMA5001 Lecture 3 Steady State & Nonsteady State Diffusion - Fick s 2 nd Law & Solutions
EMA5 Lecue 3 Seady Sae & Noseady Sae ffuso - Fck s d Law & Soluos EMA 5 Physcal Popees of Maeals Zhe heg (6) 3 Noseady Sae ff Fck s d Law Seady-Sae ffuso Seady Sae Seady Sae = Equlbum? No! Smlay: Sae fuco
More informationBlock 4 Numerical solution of open channel flow
Numeral Hydrauls Blok 4 Numeral soluon o open hannel low Markus Holzner 1 onens o he ourse Blok 1 The equaons Blok 2 ompuaon o pressure surges Blok 3 Open hannel low (low n rers) Blok 4 Numeral soluon
More informationELG4179: Wireless Communication Fundamentals S.Loyka. Frequency-Selective and Time-Varying Channels
Frequeny-Seletve and Tme-Varyng Channels Ampltude flutuatons are not the only effet. Wreless hannel an be frequeny seletve (.e. not flat) and tmevaryng. Frequeny flat/frequeny-seletve hannels Frequeny
More informationStanford University CS259Q: Quantum Computing Handout 8 Luca Trevisan October 18, 2012
Stanfod Univesity CS59Q: Quantum Computing Handout 8 Luca Tevisan Octobe 8, 0 Lectue 8 In which we use the quantum Fouie tansfom to solve the peiod-finding poblem. The Peiod Finding Poblem Let f : {0,...,
More information( ) ( )) ' j, k. These restrictions in turn imply a corresponding set of sample moment conditions:
esng he Random Walk Hypohess If changes n a sees P ae uncoelaed, hen he followng escons hold: va + va ( cov, 0 k 0 whee P P. k hese escons n un mply a coespondng se of sample momen condons: g µ + µ (,,
More informationFIRMS IN THE TWO-PERIOD FRAMEWORK (CONTINUED)
FIRMS IN THE TWO-ERIO FRAMEWORK (CONTINUE) OCTOBER 26, 2 Model Sucue BASICS Tmelne of evens Sa of economc plannng hozon End of economc plannng hozon Noaon : capal used fo poducon n peod (decded upon n
More informationPhys 201A. Homework 5 Solutions
Phys 201A Homewok 5 Solutions 3. In each of the thee cases, you can find the changes in the velocity vectos by adding the second vecto to the additive invese of the fist and dawing the esultant, and by
More informationESS 265 Spring Quarter 2005 Kinetic Simulations
SS 65 Spng Quae 5 Knec Sulaon Lecue une 9 5 An aple of an lecoagnec Pacle Code A an eaple of a knec ulaon we wll ue a one denonal elecoagnec ulaon code called KMPO deeloped b Yohhau Oua and Hoh Mauoo.
More informationToday - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations
Today - Lecue 13 Today s lecue coninue wih oaions, oque, Noe ha chapes 11, 1, 13 all inole oaions slide 1 eiew Roaions Chapes 11 & 1 Viewed fom aboe (+z) Roaional, o angula elociy, gies angenial elociy
More informationTHIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.
T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson
More informationReflection and Refraction
Chape 3 Refleon and Refaon As we know fom eveyday expeene, when lgh aves a an nefae beween maeals paally efles and paally ansms. In hs hape, we examne wha happens o plane waves when hey popagae fom one
More informationEulerian and Newtonian dynamics of quantum particles
Eulean and ewonan dynas of uanu pales.a. Rasovsy Insue fo Pobles n Means, Russan Aadey of enes, Venadsogo Ave., / Mosow, 956, Russa, Tel. 7 495 554647, E-al: as@pne.u We deve e lassal euaons of ydodynas
More informationNotes 11 Gauss s Law II
ECE 3318 Applied Electicit and Magnetism ping 218 Pof. David R. Jackson Dept. of ECE Notes 11 Gauss s Law II Notes pepaed b the EM Goup Univesit of Houston 1 Eample Infinite unifom line chage Find the
More informationModule 18: Outline. Magnetic Dipoles Magnetic Torques
Module 18: Magnetic Dipoles 1 Module 18: Outline Magnetic Dipoles Magnetic Toques 2 IA nˆ I A Magnetic Dipole Moment μ 3 Toque on a Cuent Loop in a Unifom Magnetic Field 4 Poblem: Cuent Loop Place ectangula
More informationRelative and Circular Motion
Relaie and Cicula Moion a) Relaie moion b) Cenipeal acceleaion Mechanics Lecue 3 Slide 1 Mechanics Lecue 3 Slide 2 Time on Video Pelecue Looks like mosly eeyone hee has iewed enie pelecue GOOD! Thank you
More informationMaximum Likelihood Estimation
Mau Lkelhood aon Beln Chen Depaen of Copue Scence & Infoaon ngneeng aonal Tawan oal Unvey Refeence:. he Alpaydn, Inoducon o Machne Leanng, Chape 4, MIT Pe, 4 Saple Sac and Populaon Paaee A Scheac Depcon
More informationTwo-dimensional Effects on the CSR Interaction Forces for an Energy-Chirped Bunch. Rui Li, J. Bisognano, R. Legg, and R. Bosch
Two-dimensional Effecs on he CS Ineacion Foces fo an Enegy-Chiped Bunch ui Li, J. Bisognano,. Legg, and. Bosch Ouline 1. Inoducion 2. Pevious 1D and 2D esuls fo Effecive CS Foce 3. Bunch Disibuion Vaiaion
More information