411_Equations.Summary

411_Equations.Summary - *********************Physics 411...

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Unformatted text preview: *********************Physics 411 EXAM COVER SHEET.******************* You can write any formulas you like on the printed side of these sheets and bring them to the exam. __________________________________________________________________________________ DÝr Þ= PEÝr Þ 4 6 DÝr, t Þ = 4^k 1 O o _ 0 Ýr, t Þ ßD 1 Ýr, t Þ ? D 2 Ýr, t Þà 6 n = aÝr, t Þ 4 6 BÝr, t Þ = 0 /BÝr, t Þ /t J /DÝr, t Þ + 4^k 2 J J 0 Ýr, t Þ 4 × H Ýr , t Þ = k 2 W o O o Wo k1 /t 4 × EÝr, t Þ = ?k 3 ßB 1 Ýr, t Þ ? B 2 Ýr, t Þà 6 n = 0 n ×ÝE 1 Ýr, t Þ ? E 2 Ýr, t ÞÞ = 0 n × ÝH 1 Ýr, t Þ ? H 2 Ýr, t ÞÞ = FÝr, t Þ 4 6 JÝr, t Þ+ /_Ýr, t Þ = 0; /t x NÝgÝxÞÞ= > NÝdg ? x i Þ i F = qßE +k 3 v × B à; NÝ k ? k v Þ NÝ g ? g v Þ = 1 ®Ýr Þ = k 1 XXX V _Ý r v Þ 3 d x + ®o |r ? r v | k?k v ?Ýg?g v Þtà | dx | x=x i Ý 2^ Þ 4 XXXX all space, time e ?ißr6 d 3 rdt df = dr 6 4fÝr Þ system esu (Electrostatic) emu (Electromag.) Gaussian Heaviside-Lorentz SI (MKSA) SI (MKSA) quantity Ampere Oo = Wo = Wo Oo dq Coul.s ?1 dt 10 7 4^c 2 ?7 DÝr Þ= PEÝr Þ. k2 1 c2 XXX contains r fÝr v ÞN Ý3Þ Ýr ?r v Þdx v dy v dz v = fÝr Þ B k1 1 c2 1 1 4^ 1 4^O o J k3 1 1 c c 1 1 1 1 c 1 c q statcoul. statcoul. statcoul. statcoul 1 1 c2 1 4^c 2 Wo 4^ gauss (G) 1 Coulomb (C) 1 ” V/ohm = V/I tesla ” 10 ?7 c 2 10 ?7 1 8.854 187 10 ?12 Farad/m 1.256 637 10 ?6 Henry/m 376.730 610 5 /c 2 6.582 10 ?16 eVs e2 ci (SI) 4^10 376.730 ohms (IÞ 1.0546 10 ?34 Js ÝSIÞ = 1 137.04 i e e2 4^O o ci 1.602 10 ?19 Coulomb 4.80 10 16 statcoul Ýesu, GaussianÞ Ýesu, GaussianÞ Ýesu, GaussianÞ 0.529177 Å 0.529177 10 ?10 m e2 2r H Bohr radius, r H 4^O o Ý2r H Þ e2 ÝSIÞ = 13.605 eV DÝr Þ = 1 4^ dÝ r Þ = 1 4^ P XXX _ 0 Ýr v Þ Ý r ? r v Þ 3 v d r + D 0 Ýr Þ, SI units |r ? r v | 3 4 6 D 0 Ýr Þ = 0 XX surface aÝr v Þ dS v + d 0 . SI units |r ? r v | _Ýr Þ= aÝr ÞNÝFÝr ÞÞ|4FÝr Þ | ! EÝzÞ = n a 0 2P 1 ^ d Ýr Þ d + Ýr Þ ? d ? Ýr Þ = ? P å nÝr Þ6ÝP 1 E 1 Ýr Þ ? P 2 E 2 Ýr ÞÞ= aÝr Þ; å nÝr Þ6ÝP 1 E 1 Ýr Þ ? P 2 E 2 Ýr ÞÞ= 0; dÝ r Þ = ? 1 P N¸0 ?a 0 z = d x , y , z || Ý Þ 2P lim aÝr, N ÞN = ^ d Ýr Þ; XX ^ d Ýr Þ Ýr ? rÞ 6 dS v = ? 1 P v3 |r ? r | v XX ^ d Ýr Þ dI 4 2 dÝ r Þ = ? 1 _Ý r Þ P 4 2 gÝr, r v Þ = N Ý3 Þ Ýr ? r v Þ; dÝ r o Þ = dÝ r Þ = 1 P XXXß?_Ýr v Þà gÝr, r v Þ d 3 r v ?1 + F Ýr , r 0 Þ 4^|r ? r 0 | gÝr, r 0 Þ = + XXX gÝr, r o Þß?_Ýr Þ/Pàd 3 r volume XX bounding surface ! ßdÝr Þ4gÝr, r o Þ ? gÝr, r o Þ4dÝr Þà6nÝr ÞdS ——————————————————————————————————————————– In the text the Green’s function has a different normalization. (See text Eqs.1.31-1.42). 4 2 G text Ýr, r v Þ = ?4^N Ý3 Þ Ýr ? r v Þ and G text Ýr, r v Þ = dÝ r o Þ = 1 4^ 1 |r ? r v | XXX G text Ýr, r o Þ_Ýr Þ/Pd 3 r volume ?1 4^ XX bounding surface ! ßdÝr Þ4G text Ýr, r o Þ ? G text Ýr, r o Þ4dÝr Þà6nÝr ÞdSà —————————————————————————————————————————— d D Ýr 0 Þ = 1 XXX G D Ýr, r 0 Þß?_Ýr Þàd 3 r + XX dÝr s Þ4G D Ýr s , r 0 Þ 6 dS P volume bounding surface 4 2 G N Ýr, r 0 Þ = N Ý3 Þ Ýr ? r 0 Þ; XX bounding surface ! 4G N Ýr, r 0 Þ 6 nÝr ÞdS=1 dÝ r 0 Þ = 1 P XXX G N Ýr, r 0 Þß?_Ýr Þàd 3 r volume + d avg + XX bounding surface ! G N Ýr, r 0 Þ4dÝr Þ 6 nÝr ÞdS ! ß4G N Ýr, r 0 Þà 6 nÝr Þ = d L?D Ýr o Þ = 4F N Ýr, r 0 Þ + 4 ?1 4^|r ? r 0 | ! 6 nÝr Þ = 1 S tot XX bounding surface dÝr s Þ L?D 4G D Ýr s , r 0 Þ 6 dS; d L?N Ýr Þ = ? XX bounding surface G N Ýr s , r 0 Þ4d L?N Ýr s Þ 6 dS SÝr, t Þ = EÝr, t Þ × HÝr, t Þ; W electron = e 2 /2a Wi = P 2 XXX |4d i Ýr Þ |2 d 3 r volume W ij = P W =1 2 3 XXX 4d i Ýr Þ 6 4d j Ýr Þd r, 3 volume Q i = > C ij V j j=1 N C ii = Qi Vi , Vj= 0 > QiVi= 1 2 i=1 J N > C ij V i V j i,j=1 N Ißf, 4f à = XXX FÝr, fÝr Þ, 4fÝr ÞÞd 3 r G D Ý r , r v Þ = ?1 4^ ?R / r v 1 + v |r ? r | |r ? ÝR 2 /r v2 Þr v | / NF NF ? ? V u Ýr Þ = 0 Nf > /x i NÝ/f//x i Þ > J J i=1 ...
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