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# Electromagnetic Fields and Devices II ECE 342

CSU

GPA 3.8

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This 5 page Class Notes was uploaded by Sarina Wintheiser on Tuesday September 22, 2015. The Class Notes belongs to ECE 342 at Colorado State University taught by Carmen Menoni in Fall. Since its upload, it has received 32 views. For similar materials see /class/210279/ece-342-colorado-state-university in ELECTRICAL AND COMPUTER ENGINEERING at Colorado State University.

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Date Created: 09/22/15

EE341 Formulas for the exams Rev Dec 2006 Chapter 1 Z 1 aA IAI W IAlaz WAVE AA1c71 A252 A3313 JAf A Vectors AxBABsina N ABsina N AgtltB AgtltB 0N AB 5m 0 Agtlt 3 131272 71xz x13x yry1Ey 42272932 611 a2 as M A1 A1 A3 Bl Bl BS Coordinate Systems Cartesian Cylindrical dSdl1dlzsinadllgtltdl2 d1drard a dzaz 5133511de ird dza didxajdy cz ydz a ds idrdza idy y Xdz zidyd25x irdrd az d5 idZEZde5xidde5y dVrdrd dZ dxaxgtltdyay dxdyaz rzm deldllodlzxdl3 Fungi dVdxdydz x x r cos y r sin Flux lines z z drrd dz E Fy F2 F F F2 Electric Field Intensity E Electric Flux Density D E D oE free space 1 Point Charge In nite Line E Q 5 a pL K 47239s0 R2 R r 2723980r m Ring of radius a on axis at distance 1 Dipole d1p012 Q 3 4ngoa2zz5 m 12112006 Q2 V E d V ar20089a sin 4 6 am ABAlB1 AZB2 A3B3 1A B 7 081111521121522 A3B3 AB 0COS C AleAl lBlCOSOl Al A2143 ZExE 13113233 C1 C2 C3 Spherical di dramn95 rsint9d 5 i r2 sing d6d 5r i rsint9 drd 5 i 61654 2 alVr2 sin drd6d r x2y2z2 39 tan391 1 x rs1n cos x y rsint9 sin 9tan Z Z 1xy zrcost9 z rsin6d E F9 F4 In nite charged sheet amp a 28 0 N EE341 Formulas for the exams Rev Dec 2006 Magnetic ux density B Magnetic Field Intensity H BuoH Magnetic forcegn a current Magnetic force on a charge Ef e IdeaR dFId xB FqVXB 47 R2 E qix E Infinte current line Finite line of length a2al Loretnz Force 01 01 3 2727 M B 4WCOSOl1 cosa2a FFEFMqE 7XB ocl ocz angles subtended by lines from a1 and a2 to the point of interest Infinite current sheet Ring of radius b on the axis a distnce Z u 2 B az B quotJ5Xan 222b2 Chapter 2 Electric W JB E 611 Electric Potential Magnetic Flux Work AB q 39 B A VABVA VBj Edl llBSISB43 A Maxwell s equations in integral form d Edli Bdgdl Faradayslaw emf l C dt S dt dt H 511 J 4339 D 43 Ampere s law Continuity equation or charge C S dt S Conservation fSDdSJVpdvQlV Gauss law JdSiindvii Dds 3 dl V dl B as o 5 Law of conservation of charge i J dS 0 S Chapter 3 Maxwell s equations in differential form Divergence Theorem Continuity Equation 51 VxE 5 Ad5jVAdv VJ6p at s V a Stokes Theorem I 0D V X H J at A7dzj x2yds c s V D 390 V V X A 0 V B 0 d DidS Vx lim C 7 V5lim S A A5 AHo AV max 12112006 EE341 Formulas for the exams Rev Dec 2006 Time varying Fields Infinite Plane sheet Jstax Wave equation 77 Z Z gt 0 62E 62E Exzt 0Jst X I g r 2 VP 2 lt 0 622 0 0 61 2 J z Z gt 0 Hyzt i SO 2 VP 2 lt 0 1 a VP 080 3X10 m S Harmonic fields Jso costh aX E77t7 J c0sat z x z 0 r70 0 1207r377Q go J Hi 7 cos mt zay Amplitude ofH wt z 2 6 a w r4 Lip 61 27239 62 Polarization Wave propagating in z direction E Egg1C cosat z linear E EEC IX cosat zE15y sinat z circular if E0E1 else elliptical Poynting Vector 13 W m2 Jso2 E X H zi 77 cos 2 wti z 32 Z gt 0 l Time averaged power transmitted 7 ltP gt3ReEXH by the wave Poynting theorem 6 J39lgHZdV Power dissipation density associated with conduction pd 0E2 61 355 jEJdv 3jlgE2dv S V V 2 V 1 2 Electric energy dens1ty WE 38E 1 Magnetic energy density Wm E uH 2 Chapter 4 Drift velocity y mobility Dielectric materials er 39 Va E LlE Vd LlEE for electrons Jo GE p Qd dlpOIC moment m 1 NAV Magnetization o le N2 el conductors Polanzanon P p N J m IA an Magnetic moment 0 uh Nh le 2 N2 8 I M Magnetization semiconductors P 5390 12 E 1 NM M m N m AV 1 M 1m 5 D 80EP 1zm g7 8r1lz gym B B alzma M 0 12112006 3 EE341 Formulas for the exams Rev Dec 2006 Wave equation for a material medium Solution for the specific problem of a a w E 1 1 2 71 E current sheet 150 located at 20 2 mg J0E DgE H Jm7 I Ezt7778 quot coswt 82139aX z gtlt 62E VzE 72E 622x 72 ml gt4 2 w 1i 1 5 J50 7 H t i m r gtlt0 Exzt ReExze j Z 2 e 005w Bzay Z U 7 431 Hyzl7ReHyzef 1 losstangent 605 77Jjau0 ja806 PzEXH ltPgtER6EXH N 77 l e I pd 2 0E2 1504 l 77 7ng WEESE2 URe j le j y7 1 2 77 50 77 150 Wm Boundary conditions Perfect Dielectrics Imperfect Dielectrics 0 quot X E E2 0 aw42 a y 02 VP 0 QEEJ178QZEZ S M8 2 U g I 1 anD1D2p 7777 1 w Wlt8wz z a 8 N u 30 2 oquot aquot BI 32 0 BC at Interface between 2 perfect Good Conductors BC at the surface of a erfect conductor dielectrics 5nXEE20 aJ7 ua avg1 an D ps anx171 172o 02 0 aw aanJs anB0 0 a anDl D20 a 1 anE EH fW Perfect Conductors ogtoo a 0 5 0 Re ection and transmission of uniform plane Total impedance method waves at normal incidence 2H 7 W Fe for F m 7m 1 91311 713327511 7 7 E H Z 1quot12 1 1 gtZ7lnnzcos lljnlsm ll E1 772 771 HT 1771 cos llJrjnZ sin ll f E2 1 f L is a distance to the left of the interface E F Dielectric n1 sandwiched between air no 2 1f and another dielectric 113 HT 772 V773770 d2n114 12112006 4 EE341 7 Formulas for the exams Rev Dec 2006 Canadian Cunnilan x y z Am M Ax Cylindrlul Cuumlnam a 4 z A FlyA a A r av lav av vv n BF PMM 6sz la 13 VA 7 P5PWD pm 31 l a m I1 6 a a VXA 3 11 a AP PM A m 31 m 1 a M 1 131 5 ap 3 p 310 ad 11 10 161V57V Np pap 11319 5x1 12112006 Sphavlell cunrdlnalu r a 41 A Ar39r Am 43 17V 15V V W Equotrmsa quot 1 a z 1 VA rAr a 0 1 Mo madam nine m quotanew a a 39 5 A 1A nian 1 a m 1 la a 4 A quotin9aeA mn9 M Lmew growa 1 4 0344 a R 5 av 1 v 1 51v 2 6 er lt39 Br 1 sin 069 m 59 19W

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