THERMAL PHYSICS. E nc T. W PdV. degrees of freedom. 32 m N V. P mv. Q c. AeT (emitted energy rate) E Ae T Tsurroundings. Q nc p

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1 HRMA PHYSICS PHY 8 Final es: Compehensie Concep and Fomula Shee NB: Do no add anyhing o he fomula shee excep in he space specially assigned. hemodynamic Paamees: Volume V of mass m wih densiy ρ: V m empeaue in Celsius, Kelin and Fahenhei scales: 9 K C 7.5 F 5 C m N V Numbe of moles in a sample of mass m: n M N A V Ideal Gas: Mean fee pah: M 4 N V Ideal Gas aw: PV nr o PV NkB N Pessue by he kineic heoy: P m V Inenal negy (monoaomic gas): nc (monoaomic gas) ms Speed: k B R ms m M (monoaomic gas) Caloimey and Phase changes: Specific hea: Q c m Hea exchanged o ay empeaue: Q cm Hea exchanged duing a phase change: Q m (+ fo added hea, fo eleased hea) negy conseaion in a mixue of n subsances: Q Q... Q n Consans: Aogado numbe: N A = 6. pa./mol Uniesal gas consan: R = 8. J/mol K Bolzmann consan: k B =.8 J/K Sefan-Bolzmann consan: σ = W/m K 4 negy anspo: Rae of hea anspo by hemal conducion: Rae of hea anspo by hemal adiaion: hemodynamic Pocesses: Q A Pc k 4 P Ae (emied enegy ae) 4 4 P Ae suoundings (ne enegy ae) hemodynamics wok done on he gas: V f W PdV he Fis aw of hemodynamics: Q W Mola hea capaciy a consan olume: C V i degees of feedom Mola hea capaciy a consan pessue: C p C R Change in inenal enegy: nc Isobaic pocess: V consan Q nc p Isochoic pocess: P consan, W Q nc R

2 CRICIY AND MAGNISM PHY 8 Final es: Compehensie Concep and Fomula Shee Isohemal pocess: Adiabaic pocess: nopy: Hea engines: PV consan, W nr V V PV V ln f i (wok done by gas) consan, consan, S Qeesible Wok done by a hea engine: W Qho Qcold hemal efficiency: e Qcold Qho Cano efficiency: e cold ho C C, Q p (macoscopic) S k lnw (micoscopic) B lecic Chages, Foces and Fields: Chage quanificaion: q ne Chage densiy: linea ql, suface q A, olume qv Coulomb aw magniude of elecosaic foce: q q q q F k 4 Foce-elecic field elaionship: F q q q Magniude of he field of a poin chage: k (adial) 4 R Field by a coninuous disibuion of chage: dq 4 (in a poin a posiion R elaie o R each elemen of chage dq) whee he chage disibuions can be: linea dq dl, on suface dq da, in olume dq dv lecic dipole: p qd (fom negaie o posiie chage) Dipole elecic field: k p (axial) oque on elecic dipole: p lecic flux: Acos k p (biseco plane) da Gauss s aw: qinside lecic negy: (unifom field) (in geneal) Diffeence of elecic poenial enegy: U q x (only fo q in unifom field ) Conseaion of enegy: K U Wnonconseaie Diffeence of elecic poenial: V U q dv dv dv Field in ems of poenial:,, (Caesian coodinaes) dx dy dz dv d dv d (adial field) Poenial of a poin chage elaie o infiniy: q q V k 4 Consans: lemenay chage: e =.6 9 C lecon mass: m e = 9. kg Poon mass: m p =.67 7 kg Coulomb consan: k = N m /C lecic pemiiiy: ε = 8.85 C /Nm Magneic pemeabiliy: μ = 4π -7 m/a

3 PHY 8 Final es: Compehensie Concep and Fomula Shee Ne poenial by a disibuion of n poin chages: V V V... Vn Poenial diffeence by a coninuous disibuion: Capacios: dq V 4 R Q Capaciance in geneal: C V Deice dependen capaciance paallel plae capacios: C A d quialen capaciance - paallel C C C C... C - seies Cs C C... Cn negy soed by chaged capacio: U QV CV Q C negy densiy: p u Capaciance wih dielecic: C C A d lecic Cuen and Resisos: Cuen and cuen densiy definiions: dq I and J I A o J nqd d Ohm s aw: J J wih σ, ρ = cons. Also R V I cons. Deice dependen esisance: R A empeaue dependence of esisiiy: Powe dissipaed in a esiso: dc Resisie Cicuis: lecomoie foce: IR I P IV I R V R quialen esisance - seies R R R... R s - paallel Rp R R... R Vi Kichhoff ules: - juncion Iin Iou RC dc Cicuis: ime consan: - loop aound a loop RC Chaging egime: - chage on capacio q Q e n (in a poin a posiion R elaie o each elemen of chage dq) (Q imum chage) n n - cuen i Ie (I imum cuen) Dischaging egime: - chage on capacio - cuen q (Q i iniial chage) i Qie Iie (I i iniial cuen)

4 PHY 8 Final es: Compehensie Concep and Fomula Shee Magneic Foces: Magneic foce on moing poin chage: F q B (magniude F = qbsinθ and diecion gien by RHR #) Magneic foce on cuen caying wie: df Id B Foce beween long cuen caying wies: F II Magneic oque on a cuen loop: IA B BIAsin Magneic momen: IA Souces of Magneic Fields: q ˆ Magneic field of a moing chage: B (magniude qsin B, diecion by RHR #) 4 4 Id ˆ Magneic field of a cuen segmen: db (magniude Id sin db, diecion by RHR #) 4 4 (Bio-Saa aw) Ne magneic field (supeposiion): B B B... Magneic field of long cuen: I B (diecion gien by RHR #) Magneic field of a cicula cuen loop: I B R (diecion gien by RHR #) B (in ems of magneic momen) R Magneic field inside a solenoid: B ni (diecion gien by RHR #) Ampee s aw: B d Iencl lecomagneic Inducion: Magneic flux: B B da (fo a unifom field Φ B = BAcosθ) db Faaday s aw: d Moional emf - in geneal: Bdl (Faaday law) - saigh od: B - oaing loop: BA sin Maxwell equaions: q db da encl dl d d B da B dl I d Inducance and Inducos: Muual inducance: M M M NB i N B i Self inducance N B I mf muually induced: M di d M di d Self induced emf: di d Self inducance of solenoid induco: negy soed in induco: n Volume U I (fo a saigh cuen in unifom field, magniude F = IBsinθ and diecion gien by RHR #) encl

5 PHY 8 Final es: Compehensie Concep and Fomula Shee R dc-cicuis: ime consan: R Cuen wih baey in seies: i I e Cuen wihou baey: C dc-cicuis: (I imum cuen) i Iie Fequency: C Oscillaoy chage, cuen and di/d: q Q i I (I i iniial cuen) di d di d cos sin Maxima: I Q lecomagneic Waes: Hamonic waes aeling along x-axis: Speed of ligh: c Componens: cb Poying eco: Inensiy: cos di d, ˆ cos, ˆ cos x y kx B x zb kx S B Q k I Powe Aea S B c cb Foce by M-beam: F IA c (complee absopion) F IA c ac-cicuis: ms cuen and olage: Ims I Vms V RC-seies combinaion: if cuen aies like i I may be de-phased: cos Ohm s law: V IZ Resonance fequency: C ansfomes: V NV N (complee eflecion), he olage V acoss he seies I NI N cos lemen Impedance Z Phase φ XC X R C R X C R X R X XC if XC X if XC X

6 RAIVIY PHY 8 Final es: Compehensie Concep and Fomula Shee Relaiisic ime and space ime dilaion: c Consans: Speed of ligh in acuum: c =. 8 m/s Cusomizaion aea: In he space below you can add exa-infomaion ha you deem useful. Howee, you can add only geneic fomulas and diagams. No explici poblem o quesion soluions such as he ones poided fo he pacice es o pape-based homewok.

r r r r r EE334 Electromagnetic Theory I Todd Kaiser

r r r r r EE334 Electromagnetic Theory I Todd Kaiser 334 lecoagneic Theoy I Todd Kaise Maxwell s quaions: Maxwell s equaions wee developed on expeienal evidence and have been found o goven all classical elecoagneic phenoena. They can be wien in diffeenial