Appl M Fall 6 Nuruhr Lcur # r 9/6/6 4 Avanc lcromagnc Thory Lc # : Poynng s Thorm Tm- armonc M Fls Poynng s Thorm Consrvaon o nrgy an momnum Poynng s Thorm or Lnar sprsv Ma Poynng s Thorm or Tm-armonc Fls non o mpanc an Amanc Fosr s Racanc Thorm Lornz Rcprocy Rang: ackson Ch 6.7-6. 9 skp 6. Colln pp. 4. 4.4 Copyrgh 6 Rgns o Unvrsy o Calorna
Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Ovrvw arng rom h work on on a currn sourc s possbl o vlop a consrvaon o nrgy ha nclus h low cross Poynng s cor. Ths approach gnralzs o Momnum usng q v cross B Phasor noaon an vn/o consquncs Lnar sprsv ma Tm-harmonc ls Racanc has posv slop Rcprocy Copyrgh 6 Rgns o Unvrsy o Calorna
Copyrgh 6 Rgns o Unvrsy o Calorna Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Work on on ourc by Fl Work on by ls on sourcs Rplac Us ngraon by pars lk vcor ny nrpraon: Work on by ls on sourcs quals h nrgy low no h voum plus h cras n nrgy sor n h ls n h volum B u u
Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Lnar Momnum F Pmch ρ ε q µ v B ρ B ε Pmch ε B g c rms low _ across _ bounary B Copyrgh 6 Rgns o Unvrsy o Calorna Forc on parcl Momnum orc/m ubsu Many manpulaons ngraon by pars an v horm n momnum g rms a nrpraon: Ra o chang n mchancal momnum plus ra o chang n lnar momnum n volum s qual o low o mnum across h surac no h volum. 4
Copyrgh 6 Rgns o Unvrsy o Calorna 5 Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Fourr Rprsnaon Proprs r s any uncon Fourr Rprsnaon Fourr pcrum Whn s ral π ε w w w c
Copyrgh 6 Rgns o Unvrsy o Calorna 6 Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Fourr Rprsnaon mplcaons Ral naur o sgnals gvs analycal proprs o spcrum n h compl plan ε ε Z Z
Copyrgh 6 Rgns o Unvrsy o Calorna 7 Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Fourr Rprsnaon mplcaons Con. Ral naur o sgnals gvs analycal proprs o spcrum n h compl plan Rprsnaon or R an X conan only vn an o powrs o am s ru or ε n n n n X X R R jo vn jx R Z Z Z
Copyrgh 6 Rgns o Unvrsy o Calorna 8 Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Lnar sprsv Ma Consuv rlaonshp Ral uncon consran ubsu nons usng compl conjuga pl no wo qual pars Mak narrowban appromaon [ ] [ ] [] [ ] [ ] [] { } [ ] {} ε ε ε ε ε ε ε ε m m
Copyrgh 6 Rgns o Unvrsy o Calorna 9 Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Lnar sprsv Ma Con. u u u B m m R R m m µ ε µ ε µ ε
Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Tm-armonc Fls [ ] φ R cos φ R [ ] s rprsn by a compl numbr call a phasor whn roas Proucs hav a m npnn mavrag an a oubl rquncy par Copyrgh 6 Rgns o Unvrsy o Calorna
Copyrgh 6 Rgns o Unvrsy o Calorna Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Tm-armonc Poynng s Thorm Ral Par Tm-avrag my Par s oubl rquncy 4 4 na w w B w w m m
Appl M Fall 6 Nuruhr Lcur # r 9/6/6 mpanc rom Poynng s Thorm na Z R X R jx Ι R X 4 w w na m s surac or sgnal an s h ous surac Tak Ral an my pars or R an X Copyrgh 6 Rgns o Unvrsy o Calorna
Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Fosr s Racanc Thorm Colln 4. X B 4 4 w w w w m m Ι ar wh v o cross rvav o plus rvav o cross ; us v horm Rsul: Th rvav o h racanc an h suscpanc wh rspc o s always posv Thr may b an alrnav rvaon usng h m rvav o h prsson or h mpanc Copyrgh 6 Rgns o Unvrsy o Calorna
Appl M Fall 6 Nuruhr Lcur # r 9/6/6 Lornz Rcprocy Thorm Colln 4. Poson Poson sourc sourc Conucng Objc n Copyrgh 6 Rgns o Unvrsy o Calorna ar wh Lornz rcprocy samn pu n ngral orm; subsu or us v horm argu ngral a nny s zro u o sam ougong rlaonshp bwn an or boh sourcs 4