The Essence of the Electromagnetic Wave is Not Energy

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "The Essence of the Electromagnetic Wave is Not Energy"

Transcription

1 The Eence of the Electomagnetic Wave i Not Enegy Zeng Qingping Ai Foce Rada Academy Pofeo Abtact The cutomay opinion i: electic ave o light ave i enegy, TYang expeiment i the intefeence of enegy, it hading finge ae the enegy magnitude But, thi aticle ummaize the phyical expeiment to point out: the eence of electic ave i not enegy, and it hading finge ae not the enegy magnitude, but the amplitude magnitude of the vecto field Then, thi aticle ummaize all the expeiment of electomagnetic ave, and deive the concluion that the eence of the electic ave i not enegy No that the eence of electic ave i not enegy, a extenion, thi mean that Maxell vecto E H (enegy flux denity) doe not have the eal phyical implication, thu e can conide that electic field and magnetic field adiate independently key od enegy, vecto field, TYang expeiment, phyical eence, phyical action Intoduction If the adiation of electic ave i the adiation of vecto field, hen uing vecto field to analyze and calculate intefeence, diffaction, the concluion hould be coincident ith the expeiment If it think that the adiation of electic ave i the tanmiion of ave enegy, hen uing ave enegy flux EH o 05 E to analyze and calculate intefeence, diffaction, the concluion hould be coincident ith the expeiment, o it i not the action of ave enegy If the phyical action of electomagnetic ave i not the enegy action of E H, e can not ay that electic field and magnetic field ae mutual geneation O, e think that electic field and magnetic field adiate independently Thi i the tating point hy thi aticle eeache the phyical action of electic ave In the college phyic book, hen it teache omething about the intefeence and diffaction of light, the phyical teache fit intoduce the concept of light intenity I ( I E ), it eem to tell u: the intefeence of light ave i the intefeence of enegy, hading finge ae the enegy magnitude, hich coincide ith Maxell ave enegy and Poynting enegy flux denity EH ( E ), alo coincide ith the ave equation of mechanical ave So, e fit point out: mechanical ave obey Neton mechanic la, the ave enegy tanmitted i conevation Maxell doe analogy fom mechanical ave to electomagnetic ave, uch concept baed on ave enegy, but it i neithe tanmitting ave enegy conevation no adiating vecto field

2 conevation (ee aticle ) Thi aticle pove to indicate: a fo the mechanical ave, it i tanmitted though the ocillation of the medium, o it obey Neton mechanic la, o the ave enegy W K ( V)A that the mechanical ave tanmit i conevation i the ma in the unit volume But a fo the electic field ave o magnetic field ave, the ma in the unit volume i zeo, thee i no medium of ocillation-tanmiion, thee i no foce of ocillation-tanmiion eithe, o it i a kind of adiation, the concluion of aticle [4] i, electic ave i a vecto field that adiate independently, it field intenity i inveely popotional to ditance quae, if it take the adiation ouce a the cente, take the pheical uface S and S So the field quantity hich flo out of the uface S equal the field quantity hich flo out of the uface S, hich i the conevation of adiation vecto field, and obey the invee ditance quae theoem Thi aticle futhe aneed that all the phyical action of electic ave ae the action of independent vecto field, not the action of ave enegy flux E H The pupoe i to futhe negate the concluion of Poynting enegy flux denity E H on the bai of phyical concept, hich i futhe poving that electic ave i the vecto field that adiate independently on the bai of phyical concept Thi aticle tat fom the intefeence of electic ave, tanmiion of electic ave and othe phyical action, analyze and conclude that the adiation of electic ave i not the tanmiion of ave enegy, but the adiation of vecto field The main concluion include: ) The intefeence and diffaction of electic ave ae the intefeence and diffaction of independent vecto field, not the intefeence and diffaction of ave enegy flux E H, it epecially point out that TYang expeiment i jut the intefeence of vecto field, not the intefeence of enegy, hading finge ae the amplitude magnitude of vecto field, but not the cala enegy magnitude, ) The eflection and efaction of electic ave ae the eflection and efaction of independent vecto field, not the eflection and efaction of ave enegy flux E H, 3) The adiation of electic ave i the adiation of independent vecto field, not the adiation of ave enegy flux E H, 4) The eception of electic ave i the eception of independent vecto field, not the eception of ave enegy flux E H, 5) Electic ave adiation vecto field i conevation, but Maxell cul field i neithe tanmitting enegy conevation no adiating vecto field conevation, 6) Sine and coine electic field, magnetic field ae vitual poe, ine and coine electic field, magnetic field ae not enegy Electic field ave and magnetic field ave ae vitual poe, thei eence i not enegy Micoave acting on the object ill be tanfomed into the themal enegy, it i not the diect tanmiion fom one enegy to anothe enegy, but afte the vecto field act on the object, it geneate themal enegy unde Loentz foce, hich i the ame a the photoynthei of the plant, thee exit a tanfomation pocedue, it i alo the ame a the that foce acting on the object to geneate kinetic enegy, thee exit a tanfomation pocedue Foce F foce (electic field foce qe() t, magnetic field foce qvb() t ) ae both not enegy ma and electic ave So the concluion of thi aticle i: all the phyical action of electic ave ae not the action of ave enegy ( EH ), but the action of independent vecto field, The eence of electic field ave and magnetic field ave i not enegy, but the vitual poe, it act a the ave, adiation

3 vecto field conevation, and the light ave ith the ave length cloe to atomic ize can till be calculated by folloing Planck quantum hypothei on quantization teatment The intefeence of light i not the action of enegy, but the action of independent vecto field In the college phyic book, hen teaching omething about the intefeence and diffaction of light, the phyic teache fit intoduce the concept of light intenity (light enegy), it eem to tell u: the intefeence of light i the intefeence of enegy It ue the light enegy a intoduction befoe intoducing TYang expeiment in the cuent college phyic book The textbook decibe belo: becaue of the light intenity I E, the yntheized light intenity of to bundle of coheent light i : I I I II co( ) When I I, thee i I I co( ) 4I co () When i the even multiple of, thee diplay bight finge, hich equal fou time a the ingle light ouce intenity I, When i the odd multiple of, thee diplay dak finge, the light intenity I =0 Then, the college phyic textbook intoduce TYang expeiment It eem to tell people TYang double-lit intefeence i the intefeence of enegy, the hading finge ae the enegy magnitude We can veify: ubtitute deive the bight finge of TYang, ubtitute hen it i the even multiple of into the fomula(), it can not hen it i the odd multiple of into the fomula(), it can not deive the dak finge of TYang eithe Which i that, fomula () doe not comply ith the expeimental eult So, the intefeence of light i not the intefeence of enegy Only hen calculating accoding to the independent vecto field, it can deive the expeimental concluion of TYang, ee fomula (5 6) Which i that, hading finge ae the vecto amplitude magnitude, but not the magnitude of cala enegy The intefeence of light i not the intefeence of ave enegy Suppoe, it ue Poynting vecto P E H o ( EH) e k to denote the enegy flux of to bundle of light, (note: In the fomula, e k i the diection of enegy flux) ee figue Which i: and E0 co ( t ) E0 co ( t ) () ae the dielectic contant and pemeability in the fee pace The yntheized denity at the point o that to enegy fluxe each on the ceen 3

4 E0 co ( t ) co ( t ) () 0 co ( ) co( t ) Hee ( ), in the fomula denote that the enegy flux denity vaie accoding to the angula fequency Fomula () indicate: When k, k,,3, 0 [+ co ( t )], the module value i 0 When (k ), k,,3, 0 [ co( t )], the module value i till 0 The enegy denity unde thee to ituation ae the ame, thee i no intefeence finge But in fact: hen k, k,,3, thee diplay the bight point, hile hen (k ), k,,3, thee diplay the dak point, and exit the intefeence finge, o double-lit intefeence uch phyical action i not the action of ave enegy Obviouly, afte Maxell tin enegy flux EH i negated, hethe E c can be ued to decibe the intefeence of light micoave? The ane i no S S ( ) ( ) o Figue intefeence of ave enegy Let have a ty, uppoe to bundle of electic field enegy denity hich each the ceen ae epectively E0 co ( t ) E0 co ( t ) In the fomula, c 0 i the light peed in the vacuum The yntheized denity hich to enegy fluxe each at the point o of the ceen i E0 co ( t ) co ( t ) (3) 4

5 0 co ( ) co( t ) Hee ( ), in the fomula denote that the module value of enegy flux denity vaie accoding to the angula fequency of The above fomula indicate: When k, k,,3, 0 [+ co( t )], the module value i 0, hen (k ), k,,3, 0 [- co( t )], the module value i till 0 The enegy denity unde to ituation ae the ame, thee ae no intefeence finge But in fact, thee exit intefeence finge unde the above to ituation, o double-lit intefeence, uch a phyical action i not the action of ave enegy, o, the eence of ave i not enegy, but the field In fact, it i eay to pove, all the intefeence (including equal inclination intefeence, plitte intefeence, film intefeence, Michelon intefeence, and Neton ing, bipim intefeence, Lloyd mio and Laue pot and o on) ae all not the action of ave enegy Intefeence of light i the intefeence of independent vecto field Intefeence of light ave i the intefeence of independent vecto field Thee ae many kind of light ave intefeence, no it take the double-lit expeiment of TYang a the example A hon in the figue, the intefeence finge ae the phyical phenomena hich uch phyical action happen Invetigating uch phyical phenomena, hich i the calculation of finge, can be baed on the viepoint of vecto field, alo the viepoint of ave enegy If thee deive the ame concluion on thee to kind of viepoint, e can ay that it ha thee to kind of chaacte imultaneouly O, it i not (4) d S E S E ( ) ( ) o x D Figue intefeence of the vecto field In uch phyical action, hen e analyze baed on the viepoint of field vecto, the electic field vecto of to bundle of electic ave eaching ceen i denoted a E E t E E t 0co( ) 0co( ) In the fomula, and ae the epective ave path The yntheized field vecto of the electic ave afte upepoition i E EE If the electic ave vecto have the ame (5) 5

6 diection, the yntheized field intenity at the point o on the ceen i: E E0co( t ) E0co( t ) E0 co[ ( )] co[ t ( )] E0 co co[ t ( )] (6) Hee ( ), a fo the fomula (6), thee i:when k, k 0,,,3, E E0 co t ( )], thee diplay bight finge on the ceen When (k ), k,,3, E 0, thee diplay dak finge on the ceen xd Notice that - d in d tg, o D xd When k, k 0,,,3, E E0 cot ( )], thee diplay bight finge on D the ceen xd When (k), k,,3, E 0, thee diplay dak finge on the ceen The D inteval among the finge i d D The above i analyzed by independent vecto field, hich i coincident ith the expeiment And it pove that TYang expeiment i the expeiment of independent vecto field In othe od, TYang intefeence expeiment pove that the intefeence of light i the intefeence of vecto field, hich pove that fomula (6) i coect So, double-lit intefeence obey E vecto upepoition pinciple, hich i the intefeence of the vecto field, hich belong to the action of field vecto In fact, it i eay to pove, all the intefeence (including equal inclination intefeence, plitte intefeence, film intefeence, Michelon intefeence, and Neton ing, bipim intefeence, Lloyd mio and Laue pot and o on) obey vecto upepoition pinciple of independent field, hich i the action of field vecto The above analyi i uing independent electic field E to decibe, and it i the ame to ue independent magnetic field H vecto to analyze 3 The adiation of electic ave i not the action of ave enegy, but the action of independent vecto field 3 The adiation of electic ave i not the tanmiion of ave enegy Let u ee the micoave adiation and the adiation pocedue duing the adio communication 6

7 Enegy tanmiion 3 i Voltage amplification u Amplitud e diplay 4 Emiion 5 Reception Suppoe thee i a emiion ocillato and eception ocillato, and it i fa beteen the eception antenna and emiion antenna, Figue 3 if it i the enegy tanmiion dl In the communication application, if the adiation of electic ave i the adiation of ave enegy, hon in the figue 3, hen the enegy denity act on the eception antenna( a thin ie), it doe not geneate the ignal cuent, becaue i pependicula to the eception antenna In addition, if the eception antenna eceive electomagnetic enegy, it i not impotant fo the eception antenna to paallel ith the emiion antenna But, it i athe impotant in fact Actually, the eception antenna in the figue i not pocket, hich alo can not eceive ave enegy In ode to explain futhe, the eception ignal doe not eceive the enegy, pleae efe to (a) and (b) in the figue 4, in each figue, the left ignal ouce and ight ignal ouce have the ame fequency and phae, alo the cicuit ae identical Wie ab i beteen to emiion antenna, and paallel to the emiion antenna, hich can be conideed a the eception antenna a i(ω) ~ ~ i(ω) emiion b emiion Figue (a) Equal ditance a U U emiion b Figue (b) Equal ditance emiion Figue 4 Tanmiion ith the identical fequency, 7 amplitude, phae, and ymmety

8 No that all the action of electic ave volatility ae the action of independent vecto field, but not the action of coexitent E H enegy, o it i eaonable fo u to detemine, electic ave adiating vecto field i conevation, hich i, each adiation vecto field of electic field ave and magnetic field ave ae conevation Actually hat the E H deived fom Maxell cul theoy i the polynomial of ditance, hich i neithe the conevation of tanmitting ave enegy, no the conevation of adiation vecto field, but a negative enegy value, hich i obviouly not complying ith the objective fact Suppoe (in the figue 4), if the adiation of electic ave i the tanmiion of enegyw, the eception antenna ill eceive thew fom the left ide, and alo eceive thew fom the ight ide Becaue enegyw i cala, o the eception antenna ab totally eceive W, hich i that, the eceived ignal cuent inceae tice compaed ith unde the ingle tanmitte But, it i actually oppoite, it can completely pove that the cuent on the ie ab in the figue i zeo, hy? Becaue e think (the fact hould have been like thi), the adiation of electic ave i the adiation of vecto field, the eception of electic ave i the eception of vecto field Becaue vecto ha diection, the vecto field on the ie ab ae jut counteacted to be zeo So, e tongly think: the eception of ignal i not the eception of ave enegy 3 Electic ave adiation i the adiation of independent vecto field Suppoe thee i an emiion ocillato and eception ocillato, hon in the figue 5 The eception antenna and emiion antenna ae fa fom each othe, dl, o, the electic ave eached to the eception antenna can be conideed a hea ave, pleae note, thee ae thee paamete on eaching to the eception antenna: E, H, A fo the adiation of electic ave, hethe it diectly adiate E and H? O it diectly tanmit enegy flux denity? It negate the eceiving ave enegy uch opinion peviouly, the viepoint baed on field vecto adiation ae dicued belo: Ditance Bt () i Voltage amplification u Amplitud e diplay Emiion Reception Et () Figue 5 Figue of the emiion and eception of the electic ave-----field vecto adiation 8

9 Accoding to hat aticle and dicu, the adiating time vaiable electic field E () t, adiating time vaiable magnetic field B () t, metal electon on the eception antenna unde E (t) and B (t), ill be foced by Loentz electic foce ee () t and Loentz magnetic foce e( c0 ) B ( t), metal electon move up and don, and geneate the ignal cuent So the magnitude of ignal cuent i( t), cuent multiplying impedance i the voltage, the amplitude U m i added to ocillocope, afte being amplified by the voltage, the amplitude U m i added to ocillocope, hich i the invee ditance quae theoem familia ith eveyone Hee, ou concluion i, adiation action i the adiation of vecto field, eception action i eceiving the vecto field In ode to futhe pove that uch concluion i coect, pleae efe to (a) and (b) of the figue 6, in each figue, the left ignal ouce and ight ignal ouce have the identical fequency, phae, and the cicuit ae alo identical Wie ab i beteen the to emiion antenna, and paallel to the emiion antenna, hich can be conideed a the eception antenna It can tet, the cuent on ie ab i zeo, hich i the eult of the upepoition (counteact) of the poitive and negative vecto i( ) ~ a ~ i( ) Emiion b Emiion Figue (a) a U U Emiion b Figue (b) Emiion Figue 6 field vecto counteact in the ymmetic adiation Suppoe, if it adiated the enegy, hat ould be the enegy that the eception antenna ab in the 9

10 figue eceive? It doe not comply ith the fact So thi aticle think, electic ave i not the action of enegy The above analyi i uing independent electic field E to decibe, and it i the ame to ue independent magnetic field H vecto to analyze 4 The eence of time vaiable electomagnetic field i not enegy Since the bith of Maxell theoy, ave equation and Poynting vecto, people have alay been thinking that micoave adiate the ave enegy The cuent theoy think: EH c E ch ha the dimenion of enegy flux denity, the mean value of the ave enegy hich flo though the ectional aea, ithin the time t,i c Emt Accoding to it, it eem that micoave black box can toe ave enegy, micoave heating i the enegy exchange We alo uually hea the aying of micoave enegy, and thee i the teminology of micoave enegy tanfoming into the heat and o on It eem to ay that micoave itelf i enegy, and hen uch kind of micoave act on the object, the enegy i diectly paed to the object Though the explanation belo, e ill ealize that, time vaiable electomagnetic field i vitual poe, the micoave itelf doe not have the chaacte of ave enegy, it acting on the object i afte the vecto field activate the object, it i tanfomed into heat, not the diect tanmiion of the ave enegy Hee, e need to note, vecto field activate into heat and ave enegy exchange into heat ae to diffeent phyical change pocedue and phyical concept + VS - I + VR - Figue 7 Sine and coine electomagnetic field i vitual poe A fo the intenive paamete element (cicuit ize i fa le than ave length), the cicuit that contain eactance, the olution i: full epone equal tanient epone + table epone What e ae inteeted i the phyical chaacte of ine and coine micoave, geneated by uch ine and coine table epone A it i knon, in the pot cicuit compoed of eactance, unde ine and coine table tate, the pot voltage i v( t ) =Vmco( ωt+ ), pot cuent i i( t) I mco( t I ), and the elative complex poe i P Vm Im co( V I ) j Vm Im in( V I ) In the fomula, V i the voltage angle, I i the cuent angle The ight fit tem i eal poe, and the econd tem i vitual poe Real poe conume enegy, and the vitual poe doe not conume enegy Solving uch cicuit to deive, the aveage complex poe that the poe pot povide i: + VLC - 0

11 V R C P ( RC) ( LC ) m V LC j ( RC) ( LC ) 3 m -j VmC ( RC) ( LC ) (7) The aveage complex poe of the eitance pot i : P Vm R C R 0 ( RC) ( LC ) j The aveage complex poe of the inductance i (being poitive) 3 P Vm LC L 0 j ( RC) ( LC ) The aveage complex poe of the capacity pot i (being negative) P 0 V C j ( RC) ( LC ) m Epecially in the eonance, becaue LC, o, the elative aveage complex poe i: ) The aveage complex poe of the inductance pot i (being poitive) ) The aveage complex poe of the capacity pot i (being negative) Vm PL j R C Vm PC j R C The concluion i belo though the calculation and analyi above: unde the ine table tate, the enegy hich voltage ouce povide fully act on the eitance, hile although thee continuouly geneate time vaiable electic field and time vaiable magnetic field in the LC pot, they don t conume enegy, hich i the vitual poe If thee exit a cetain kind of exchange beteen them, it ill be beteen the poitive vitual poe in the inductance and the negative vitual poe in the capacity Expand L, C in the figue, and it adiate to the fee pace, hich indicate that the time vaiable electomagnetic field in the fee pace i vitual poe, not the enegy 5 Epilogue Thi aticle invetigate the natual chaacte of electic ave itelf, centeed on the intenal connection beteen phenomenon and eence, and the neceay connection beteen action and theoem When e ay that intefeence i not the chaacte of enegy, it mean that the intefeence of electic ave i not the action of enegy Alo, uch phyical action can not calculated, analyzed and decibed though the viepoint of ave enegy O, if it ue enegy o enegy flux denity to decibe the intefeence, it ill not comply ith the objective fact When e ay that the tanmiion of electic ave doe not obey the enegy conevation of electic ave, it mean that, the tanmiion of electic ave i not the tanmiion of enegy, but the tanmiion of vecto field, hich alo mean that uch phyical action can not be calculated, analyzed and decibed though the viepoint of enegy O, if it ue enegy o enegy flux denity to decibe eflection and efaction, it ill not deive the eflection and efaction equation, even thee ill come out enegy inceae When e ay that the tanmiion of electic ave i not the tanmiion of enegy, it mean that the ubtance hich electic ave tanmit i vecto field, not the ave enegy O, if the tanmitted ubtance i ave enegy, hen uing enegy to invetigate the eceived light intenity, it ill not comply ith the fact Maybe, if the tanmiion of light i not C

12 only the tanmiion of field, but alo the tanmiion of enegy, hen uing thee to viepoint to decibe the light intenity, the ane hould be the ame, but, it i actually oppoite Baed on many of the analyi above, e have poof to think, the adiation of electic ave i not the adiation of enegy What i othhile to note i, hen the electic ave i unde a cetain condition and acting on a pecial object, it can be tanfomed into enegy, hich i the leap fom quantitative change to qualitative change Thi chapte i not dicuing the pocedue of qualitative change, but dicuing the natual chaacte of electic ave befoe that leap Whethe electic field, magnetic field, o foce field, hen they act on the pecial object unde a cetain condition, they mut be tanfomed into a cetain enegy, hich i no doubt Once it i tanfomed into enegy, the enegy i conevation, hich i alo unavoidable Foce (contant foce o time vaiable foce) act on the object, it can be tanfomed into kinetic enegy, but the eence of foce (contant foce o time vaiable foce) i not enegy, hich eem to eemble electic field, magnetic field In the pat, the tudy hich people did on the action of foce a pefect, and it doe not need to impove anymoe No, the tudy that people doe on the action of field jut tat, and it need futhe eeach Becaue the mechanim hich field and ubtance inteact i not completed debunked yet, o that ome people conide the individual phenomena a tuth, to miundetand electic ave i enegy, and I have to ay that it i a vey egetful thing To ay the above concluion imply, electic ave doe not diectly adiate ave enegy, but adiate vecto field Such concluion ha nothing to do ith the ave paticle duality and quantum hypothei We ay that the electic ave itelf i ucceive, but e don t diagee ith quantifying uch ucceive tuff-----fo example, ave, photon Becaue, it doe not matte hethe quantification o digitalization, they ae both convenient to calculation Epecially the high fequency light ave, ultaviolet, x ay and ay, the highe the fequency i, the moe paticle eence it diplay O, hen eaching x ay uch a fequency limit, becaue the ave length can be compaed ith the electon ize, it mainly ho the paticle chaacte, o to ay that it i mainly the paticle Although light ave and the ay ith highe fequency ha paticle chaacte, hich ha been accepted by many people, and become vey popula, but it doe not influence the concluion the adiation of electic ave i the adiation of field vecto, and obey the adiation vecto field conevation, becaue the paticle chaacte belong to cope of duality Fo example, the diffaction of the electon flo emitted fom the cathode diplay the hape of concentic ing, although the diffaction ha the avelike phenomena, e can not ay that the motion of electon flo tanmit ave enegy Thee i a kind of hotgun in China, thee i filled ith the mall ize metal ball in the boe, afte hooting, thee diplay concentic pot on the taget, although it ha the ame volatility, e can t ay that the motion of metal ball tanmit the ave The ame thing, fo example, the dipole emiion antenna ith the poe one kiloatt, fequency one megahetz, adiate the vecto field hich ae E and B to the fee pace epectively, e can 4 4 only ay that it adiate vecto field, and can t ay that it adiate paticle When e ay the

13 adiation of electic ave doe not have enegy chaacte, it mainly mean that duing the adiation, it adiate in the vacuum a the eence of vecto field, but hen it inteact ith the object, it might diplay the paticle chaacte in ome cicumtance, and be tanfomed into enegy Thi ection negate electic ave enegy theoy It can pove actually, all the electic ave action can not be analyzed by the viepoint of ave enegy Many phyical expeiment indicate, all the action of electic ave ae the action of independent field vecto, but not the diect action of ave enegy Of coue, light ave acting on the black body can geneate heat adiation, light ave acting on potaium oxide diode can geneate cuent, light ave acting on the kin can make people feel hot, light ave acting on the plant can geneate photoynthei, light ave acting on the electon can geneate diffaction, and o on, thee qualitative change happen beteen the light ave and object, duing the qualitative change, thee geneate heat o othe kind of enegy, the minimum unit of tanfomation can be calculated accoding to enegy quantum hf In othe od, in ode to calculate moe conveniently, it can be quantified The oding in the aticle can be modified, the length of the aticle can be compeed Refeence Zeng Qingping The Summay of Natual Science Pinciple-- Intepetation about the impotant difficult poblem of phyic la Science publihe of Hubei, in Wuhan,China,0096 Zeng QingpingSummaization of Quetion on EM Theoy, Poceeding of ILLMC 994 3Zeng QingpingSummaization of Negative to Maxell EM Theoy, Poceeding of ILLMC 995 4Zeng QingpingPoblem on Demontation of the Electic Field Poducing the Magnetic FieldPoceeding of ICMMT 98 (ISTP) 5Zeng QingpingPoblem on Demontation of the Magnetic Field Poducing the Electic Field Poceeding of ICMMT 98 (ISTP) 7Zeng QingpingQuetion on Maxell Electomagnetic Field Theoy Poceed-ing of ICEEA 94 (SCI) 7Zeng QingpingNegative Viepoint to Maxell Electomagnetic Field The-oyChinee Jounal of Radio Science, o Poceeding of ICRS' 95, p7~3 8Zeng QingpingOn Theoy of Relativity in Ma Spectomete Poceeding of CMSC 99, in China 9Zeng QingpingQuetion on EM Theoy and the Sepaative Viepoint on Elec-tic field and Magnetic field, Jounal of Ai Foce Rada Academy, VoL Zeng Qingping Summaization of Quetion on EM Theoy, Poceeding of ILLMC 00 Zeng Qingping Summaization of Negative to Maxell EM Theoy, Poceeding of ILLMC 00 Expecting the efeence that you publihed []Dipute Exiting in the Phyical Natual of Electomagnetic Induction []Veification of Geneal Loentz Magnetic Foce [3]Expeimental Method to Negate Maxell Theoy [4]Mathematical Model of Independent Radiation Magnetic Field [5]The Eence of Electic Wave I not Enegy [6] About the Phyical Eence of Michelon-Moley Expeiment 3

14 [7] Light Velocity Obey Galileo Relativity Pinciple [8] Compton Scatteing Expeiment of Roentgen Ray Obey Neton La [9] Clock Becoming Sloe I the Neceity of Neton La [0] Eintein Loentz Tanfomation I a Math Game 4

Chapter 30: Magnetic Fields Due to Currents

Chapter 30: Magnetic Fields Due to Currents d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.

More information

Newton s Shell Theorem

Newton s Shell Theorem Newton Shell Theoem Abtact One of the pincipal eaon Iaac Newton wa motivated to invent the Calculu wa to how that in applying hi Law of Univeal Gavitation to pheically-ymmetic maive bodie (like planet,

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

Effect of Unemployment Insurance Tax On Wages and Employment: A Partial Equilibrium Analysis

Effect of Unemployment Insurance Tax On Wages and Employment: A Partial Equilibrium Analysis Effect of Unemployment nuance Tax On Wage and Employment: atial Equilibium nalyi Deegha Raj dhikai, Oklahoma Employment Secuity Commiion ynn Gay, Oklahoma Employment Secuity Commiion Jackie Bun, Texa &

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

More information

Forces & Magnetic Dipoles. r r τ = μ B r

Forces & Magnetic Dipoles. r r τ = μ B r Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent

More information

Parameter Identification of DC Motors

Parameter Identification of DC Motors Paamete dentification of DC Moto utho: Dipl.-ng. ngo öllmecke dvantage of the Paamete dentification Method Saving time and money in the teting poce: no anical coupling neceay Full infomation: Entie chaacteitic

More information

Mechanics 1: Work, Power and Kinetic Energy

Mechanics 1: Work, Power and Kinetic Energy Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).

More information

Standardized Coefficients

Standardized Coefficients Standadized Coefficient Ta. How do ou decide which of the X ae mot impotant fo detemining? In thi handout, we dicu one poile (and contoveial) anwe to thi quetion - the tandadized egeion coefficient. Fomula.

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses, 3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

1D STEADY STATE HEAT

1D STEADY STATE HEAT D SEADY SAE HEA CONDUCION () Pabal alukda Aociate Pofeo Depatment of Mecanical Engineeing II Deli E-mail: pabal@mec.iitd.ac.in Palukda/Mec-IID emal Contact eitance empeatue ditibution and eat flow line

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee

More information

Small Hydropower Plant with variable speed PM generator

Small Hydropower Plant with variable speed PM generator Witold MAZGAJ, Zbigniew SZULAR, Tomaz WĘGEL, Tadeuz SOBCZYK Politechnika Kakowka, ntytut Elektomechanicznych Pzemian Enegii Small Hydopowe Plant with vaiable peed PM geneato Abtact. Thi pape peent a new

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

Solutions to Problems: Chapter 7

Solutions to Problems: Chapter 7 Solution to Poblem: Chapte 7 P7-1. P7-2. P7-3. P7-4. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b.

More information

Economics 326: Input Demands. Ethan Kaplan

Economics 326: Input Demands. Ethan Kaplan Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly

More information

Purchase and rental subsidies in durable-good oligopolies* 1

Purchase and rental subsidies in durable-good oligopolies* 1 Hacienda Pública Epañola / Review of Public Economic, 3-(/05): -40 05, Intituto de Etudio Ficale DOI: 0.7866/HPE-RPE.5.. Puchae and ental ubidie in duable-good oligopolie* AMAGOIA SAGASTA JOSÉ M. USATEGUI

More information

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

SECTION 5-3 Angles and Their Measure

SECTION 5-3 Angles and Their Measure 5-3 Angle and Thei Meaue 357 APPLICATIONS Appoximating. Poblem 93 and 9 efe to a equence of numbe geneated a follow: If an n-d egula polygon i incibed in a cicle of adiu, then it can be hown that the aea

More information

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuent-caying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to

More information

Ch. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth

Ch. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth Ch. 8 Univesal Gavitation Pat 1: Keple s Laws Objectives: Section 8.1 Motion in the Heavens and on Eath Objectives Relate Keple s laws of planetay motion to Newton s law of univesal gavitation. Calculate

More information

DSC Baseline Improvements Obtained by a New Heat Flow Measurement Technique

DSC Baseline Improvements Obtained by a New Heat Flow Measurement Technique DS Baeline Impovement Obtained by a New Heat Flow Meauement Technique obet L. Danley, Pete A. aulfield TA Intument, 109 Luken Dive, New atle DE 19720 ABSTAT Nealy all diffeential canning caloimety (DS)

More information

Chapter 13 Fluids. Use the definition of density to express the mass of the gold sphere: The mass of the copper sphere is given by:

Chapter 13 Fluids. Use the definition of density to express the mass of the gold sphere: The mass of the copper sphere is given by: Chapte Fluid 5 One phee i ade of gold and ha a adiu and anothe phee i ade of coppe and ha a adiu. f the phee have equal a, hat i the atio of the adii, /? ictue the oble We can ue the definition of denity

More information

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2 Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the

More information

THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen

THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen THE PRINCIPLE OF THE ACTIVE JC SCATTERER Seppo Uoukaie VTT Buildig ad Tapot Ai Hadlig Techology ad Acoutic P. O. Bo 1803, FIN 02044 VTT, Filad Seppo.Uoukaie@vtt.fi ABSTRACT The piciple of fomulatig the

More information

Modelling and simulation of a signal injection self-sensored drive

Modelling and simulation of a signal injection self-sensored drive Modelling and imulation o a ignal injection el-enoed dive Alen Poljugan Faculty o Electical Engineeing and Computing, Depatment o electic machine, dive and automation, Univeity o Zageb Unka, Zageb, Coatia,

More information

Worked Examples. v max =?

Worked Examples. v max =? Exaple iction + Unifo Cicula Motion Cicula Hill A ca i diing oe a ei-cicula hill of adiu. What i the fatet the ca can die oe the top of the hill without it tie lifting off of the gound? ax? (1) Copehend

More information

Solution Derivations for Capa #8

Solution Derivations for Capa #8 Solution Deivations fo Capa #8 1) A ass spectoete applies a voltage of 2.00 kv to acceleate a singly chaged ion (+e). A 0.400 T field then bends the ion into a cicula path of adius 0.305. What is the ass

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams

More information

Optimizing Supply Chain Collaboration Based on Negotiation and Bargain Power for Single Retailer And Single Supplier

Optimizing Supply Chain Collaboration Based on Negotiation and Bargain Power for Single Retailer And Single Supplier Poceeding of the Intenational MultiConfeence of Enginee and Compute Scientit 20 Vol II,, Mach -, 20, Hong Kong Optimizing Supply Chain Collaboation Baed on Negotiation and Bagain Powe fo Single Retaile

More information

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013 PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0

More information

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation

More information

Using Model Checking to Analyze Network Vulnerabilities

Using Model Checking to Analyze Network Vulnerabilities Uing Model Checking to Analyze Netwok Vulneabilitie Ronald W. Ritchey Paul Ammann * National Secuity Team Infomation and Softwae Engineeing Depatment Booz Allen & Hamilton Geoge Maon Univeity Fall Chuch,

More information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit

More information

Space Vector Modulated Direct Torque Controlled (DTC SVM) Inverter Fed Induction Motor Drive

Space Vector Modulated Direct Torque Controlled (DTC SVM) Inverter Fed Induction Motor Drive Waaw niveity of Technology Faculty of Electical Engineeing Intitute of Contol and Indutial Electonic Ph.D. Thei acin Żelechowki,. Sc. Space Vecto odulated Diect Toque Contolled (DTC SV) Invete Fed Induction

More information

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 Problem Set 8 Autumn 2004 Solutions PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate Systems L. M. Kalnins, March 2009 Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean

More information

Relativistic Quantum Mechanics

Relativistic Quantum Mechanics Chapte Relativistic Quantum Mechanics In this Chapte we will addess the issue that the laws of physics must be fomulated in a fom which is Loentz invaiant, i.e., the desciption should not allow one to

More information

Lecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3

Lecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3 Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each

More information

AP Physics Electromagnetic Wrap Up

AP Physics Electromagnetic Wrap Up AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle

More information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics

More information

PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary

PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8 - TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC

More information

A r. (Can you see that this just gives the formula we had above?)

A r. (Can you see that this just gives the formula we had above?) 24-1 (SJP, Phys 1120) lectic flux, and Gauss' law Finding the lectic field due to a bunch of chages is KY! Once you know, you know the foce on any chage you put down - you can pedict (o contol) motion

More information

Skills Needed for Success in Calculus 1

Skills Needed for Success in Calculus 1 Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell

More information

Problem Set 6: Solutions

Problem Set 6: Solutions UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 16-4 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente

More information

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy

More information

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to . Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

8-1 Newton s Law of Universal Gravitation

8-1 Newton s Law of Universal Gravitation 8-1 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,

More information

NUCLEAR MAGNETIC RESONANCE

NUCLEAR MAGNETIC RESONANCE 19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES

2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES . TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES In ode to etend the definitions of the si tigonometic functions to geneal angles, we shall make use of the following ideas: In a Catesian coodinate sstem, an

More information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere. Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming

More information

v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t

v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement

More information

Unit 11 Using Linear Regression to Describe Relationships

Unit 11 Using Linear Regression to Describe Relationships Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory

More information

Do Vibrations Make Sound?

Do Vibrations Make Sound? Do Vibations Make Sound? Gade 1: Sound Pobe Aligned with National Standads oveview Students will lean about sound and vibations. This activity will allow students to see and hea how vibations do in fact

More information

Valuation of Floating Rate Bonds 1

Valuation of Floating Rate Bonds 1 Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned

More information

Coordination and Risk Sharing with Considering Supply Chain External Quality Fault

Coordination and Risk Sharing with Considering Supply Chain External Quality Fault COMPUTER MODELLING & NEW TECHNOLOGIES 14 18(1C) 445-45 Abtact Coodination and Rik Shaing with Conideing Supply Chain Extenal Quality Fault Li Yongfei 1,* 1 School of Economic and Management, Xian Univeity

More information

Physics 505 Homework No. 5 Solutions S5-1. 1. Angular momentum uncertainty relations. A system is in the lm eigenstate of L 2, L z.

Physics 505 Homework No. 5 Solutions S5-1. 1. Angular momentum uncertainty relations. A system is in the lm eigenstate of L 2, L z. Physics 55 Homewok No. 5 s S5-. Angula momentum uncetainty elations. A system is in the lm eigenstate of L 2, L z. a Show that the expectation values of L ± = L x ± il y, L x, and L y all vanish. ψ lm

More information

VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY OF BIO-DIESEL FUELS VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

More information

MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION

MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION K.C. CHANG AND TAN ZHANG In memoy of Pofesso S.S. Chen Abstact. We combine heat flow method with Mose theoy, supe- and subsolution method with

More information

rotation -- Conservation of mechanical energy for rotation -- Angular momentum -- Conservation of angular momentum

rotation -- Conservation of mechanical energy for rotation -- Angular momentum -- Conservation of angular momentum Final Exam Duing class (1-3:55 pm) on 6/7, Mon Room: 41 FMH (classoom) Bing scientific calculatos No smat phone calculatos l ae allowed. Exam coves eveything leaned in this couse. Review session: Thusday

More information

Your Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :(

Your Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :( You Comments Llamas, and why it is so difficult to get someone to buy me one as a pet. All ask is that it beathes fie. have simple needs people. Seiously. p.s. this lectue was had. did not undestand any

More information

Mechanics 1: Motion in a Central Force Field

Mechanics 1: Motion in a Central Force Field Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.

More information

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

More information

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.

More information

Financing Terms in the EOQ Model

Financing Terms in the EOQ Model Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad

More information

Symmetric polynomials and partitions Eugene Mukhin

Symmetric polynomials and partitions Eugene Mukhin Symmetic polynomials and patitions Eugene Mukhin. Symmetic polynomials.. Definition. We will conside polynomials in n vaiables x,..., x n and use the shotcut p(x) instead of p(x,..., x n ). A pemutation

More information

UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

More information

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013 PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80-kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,

More information

Poynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions

Poynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions Poynting Vecto an Enegy Flow in a Capacito Challenge Poblem Solutions Poblem 1: A paallel-plate capacito consists of two cicula plates, each with aius R, sepaate by a istance. A steay cuent I is flowing

More information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request. Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to

More information

Your Comments. during the last couple lectures its been getting really noisy and hard to hear, especially for the last couple rows.

Your Comments. during the last couple lectures its been getting really noisy and hard to hear, especially for the last couple rows. You Comments lease explain the ight hand ule when thee ae two wies and ou ae ting to find the diection of the foce I am getting confused with all these ight hand ules So do ou have an age-old advice fo

More information

Introduction to Electric Potential

Introduction to Electric Potential Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic

More information

Physics 111. Exam #1. January 24, 2014

Physics 111. Exam #1. January 24, 2014 Phyic 111 Exam #1 January 24, 2014 Name Pleae read and follow thee intruction carefully: Read all problem carefully before attempting to olve them. Your work mut be legible, and the organization clear.

More information

Chapter 17 The Kepler Problem: Planetary Mechanics and the Bohr Atom

Chapter 17 The Kepler Problem: Planetary Mechanics and the Bohr Atom Chapte 7 The Keple Poblem: Planetay Mechanics and the Boh Atom Keple s Laws: Each planet moves in an ellipse with the sun at one focus. The adius vecto fom the sun to a planet sweeps out equal aeas in

More information

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE 1 INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of

More information

Experimental DTC of an Induction Motor Applied to Optimize a Tracking System

Experimental DTC of an Induction Motor Applied to Optimize a Tracking System Euopean Aociation fo the Development of Renewable Enegie, Envionment and Powe Quality (EA4EPQ) Intenational Confeence on Renewable Enegie and Powe Quality (ICREPQ 2) Santiago de Compotela (Spain), 28th

More information

UNIVERSIDAD DE CANTABRIA TESIS DOCTORAL

UNIVERSIDAD DE CANTABRIA TESIS DOCTORAL UNIVERSIDAD DE CANABRIA Depatamento de Ingenieía de Comunicaciones ESIS DOCORAL Cyogenic echnology in the Micowave Engineeing: Application to MIC and MMIC Vey Low Noise Amplifie Design Juan Luis Cano de

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

Complex Envelope Vectorization for the solution of mid-high frequency acoustic problems. A. Sestieri

Complex Envelope Vectorization for the solution of mid-high frequency acoustic problems. A. Sestieri Complex Envelope Vectoization fo the solution of mid-high fequency acoustic poblems A. Sestiei Depatment of Mechanical and Aeospace Engineeing Univesity of Rome la Sapienza Pesentation layout - Low fequency

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

1.4 Phase Line and Bifurcation Diag

1.4 Phase Line and Bifurcation Diag Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes

More information

Nontrivial lower bounds for the least common multiple of some finite sequences of integers

Nontrivial lower bounds for the least common multiple of some finite sequences of integers J. Numbe Theoy, 15 (007), p. 393-411. Nontivial lowe bounds fo the least common multiple of some finite sequences of integes Bai FARHI bai.fahi@gmail.com Abstact We pesent hee a method which allows to

More information

Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!

Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360! 1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

Lab M4: The Torsional Pendulum and Moment of Inertia

Lab M4: The Torsional Pendulum and Moment of Inertia M4.1 Lab M4: The Tosional Pendulum and Moment of netia ntoduction A tosional pendulum, o tosional oscillato, consists of a disk-like mass suspended fom a thin od o wie. When the mass is twisted about the

More information

Strength Analysis and Optimization Design about the key parts of the Robot

Strength Analysis and Optimization Design about the key parts of the Robot Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design

More information

EXPERIMENT 16 THE MAGNETIC MOMENT OF A BAR MAGNET AND THE HORIZONTAL COMPONENT OF THE EARTH S MAGNETIC FIELD

EXPERIMENT 16 THE MAGNETIC MOMENT OF A BAR MAGNET AND THE HORIZONTAL COMPONENT OF THE EARTH S MAGNETIC FIELD 260 16-1. THEORY EXPERMENT 16 THE MAGNETC MOMENT OF A BAR MAGNET AND THE HORZONTAL COMPONENT OF THE EARTH S MAGNETC FELD The uose of this exeiment is to measue the magnetic moment μ of a ba magnet and

More information

NETWORK TRAFFIC PRIORITIZATION USING MAP OF ARRIVALS

NETWORK TRAFFIC PRIORITIZATION USING MAP OF ARRIVALS Seion 1. Statitic Method and Thei Alication Poceeding of the 11 th Intenational Confeence eliability and Statitic in Tanotation and Communication (elstat 11), 19 22 Octobe 2011, iga, Latvia,. 82-87. ISBN

More information

ESCI 340 Physical Meteorology Cloud Physics Lesson 2 Formation of Cloud Droplets

ESCI 340 Physical Meteorology Cloud Physics Lesson 2 Formation of Cloud Droplets ESCI 40 Phyical Meteorology Cloud Phyic Leon 2 Formation of Cloud Droplet Reference: A Short Coure in Cloud Phyic, Roger and Yau Reading: Roger and Yau, Chapter 6 The objective of thi leon are: 1) Undertand

More information