MIT OpeCueWae hp://cw.m.eu 6.13/ESD.13J Elecmagec a pplca, Fall 5 Pleae ue he llwg ca ma: Maku Zah, Ech Ippe, a Dav Sael, 6.13/ESD.13J Elecmagec a pplca, Fall 5. (Maachue Iue Techlgy: MIT OpeCueWae). hp://cw.m.eu (accee MM DD, YYYY). Lcee: Ceave Cmm bu- Ncmmecal-Shae lke. Ne: Pleae ue he acual ae yu accee h maeal yu ca. F me ma abu cg hee maeal u Tem Ue, v: hp://cw.m.eu/em
6.13 Fal Exam Fmula Shee Decembe 1, 5 Caea Cae (x,y,z): Ψ = x y z x y z x y = z x y z z y x z y = x y z y z x z x x y Ψ= x y z Cylcal cae (,φ,z): Ψ = φ 1 z φ z 1 ( ) 1 φ = z φ z φ z 1 z φ z 1 ( φ ) = 1 z φ z = e φ z φ z φ ( ) Ψ = 1 1 φ z Sphecal cae (,,φ): Ψ = 1 1 φ φ ( ) ( ) 1 1 1 φ = φ 1 ( φ) 1 1 ( ) 1 ( ) φ φ = φ φ φ = 1 e φ ( ) ( ) Ψ = 1 1 1 φ Gau Dvegece Theem: ec lgeba: G v = G a = x x y y z z B= xbx yby zbz Ske Theem: ( ) = ( G ) a = G ( ) = ( ) C φ φ z Page 1 4
Bac Equa Elecmagec a pplca Fuameal = q( E v μ H) [ N] (Fce p chage) E1// E// = E = B H1// H// = J E = B a B1 B = c H = J D ( D D ) =ρ H = J a D a c D=ρ D a = ρv 1 = σ = 1 Elecmagec Quaac E = Φ( ), Φ ( ) = ( ( ) /4 ) ρ πε v ρ Φ= ε B= B a = J = ρ E = elecc el (m -1 ) C = Q/ = ε/ [F] H = magec el (m -1 ) L = Λ/I D = elecc placeme (Cm - ) () = C v()/ B = magec lux ey (T) v() = L ()/ = Λ/ Tela (T) = Webe m - = 1, gau w e = Cv ()/; w m = L ()/ ρ = chage ey (Cm -3 ) L le = N μ/w J = cue ey (m - ) τ = RC, τ = L/R σ = cucvy (Seme m -1 ) Λ = B a (pe u) J = uace cue ey (m -1 ) KCL : I () = a e ρ = uace chage ey (Cm - ) KL : () = au lp ε = 8.85 1-1 Fm -1 Q = ωwt / P = ω / Δ ω μ = 4π 1-7 Hm -1 ω.5 = LC c = (ε μ ) -.5 3 1 8 m -1 e = -1.6 1-19 C η 377 hm = (μ /ε ).5 / R = kt Elecmagec Wave ( με ) E = [Wave Eq.] με E = [Wave Eq.] E y (z,) = E (z-c) E - (zc) = R e {E y (z)e jω } ( k ) E =, E = E e H x (z,) = η -1 [E (z-c)-e - (zc)] [(ω-kz) (-z/c)] ( ) ( ε μ ) jk k = ω(με).5 = ω/c = π/λ E H a E H v k x k y k z = k = ω με = J v (Pyg Theem) v p = ω/k, v g = ( k/ ω) -1 E = Mea a Buae / = / = / D =ε EP ( / ) D, c = =ρ τ=εσ.5 k k = a ε / ε TM ε E =ρ ρ z p c E ETe α x > = jk z P = ρ p, J =σe k = k jk B=μ H =μ H M Γ = T 1.5 ε ω =ε 1 ωp ω, ω p ( Ne m ε ) TTE = / 1 η c / η c = (plama) ( [ ]) = ( 1 j / ε ) TTM = / ( 1 [ η c / η c] ) ε ε σ ω e B Sk eph δ = ( ωμσ ).5 [ ] / m Page 4
Raag Wave 1 μj c 1 Φ ρ Φ = c ε = = Φ= ( / ) μj c ρ 4π ( / ) c 4πε E = Φ, B = Wele Cmmuca a Raa G(,φ) = P /(P R /4π ) R 4π P = P φ,, φ P ec = P (,φ) e (,φ) (,) e φ = G(,) φλ 4π G(, φ ) = 1.5 (Heza Dple) π μ/ ε e R = PR () = 3 λ ΦωμεΦ= ρε, jk jkxx jkyy ( xyz,,, ) Re (,, ) Φ = Φ xyze ω jk ω με = μj, E = je λ E (x, y)e xy Ê z = a Ee = (eleme ac)(aay ) E b ~4 1 - [J] Z = Z ecpcy 1 1 xyz (,,, ) = Re xyze (,, ) ω ω, w e = w m jk Φ () = ρ() e /4 ( πε ' ) w e = E 4 ε v ( jk ' () = μj e 4π ' ) ' w = μ H 4 v ' μ jk ( E = H = jηki 4π) e ε φ T m Q = ω w P =ω α.5 mp = c ma b p Fce, M, a Geea = jω - α J =σ ( E v B) [ -1 F= I B Nm ] (ce pe u legh) cuc E= v B e peecly cucg we ( σ ) Max / = B /μ, D /ε [Nm - ] w v T z P = P p, U = u p = ρ u = ( ) u = 1ρ c p = ma = (mv)/ P = v = Tω (Wa) k p= k = ω c =ω ρ γ P T = I ω/ c v v ( P ) ( K ).5.5 p g = = = γ ρ ρ RT I= m η = p/u = ρ c = (ρ γp ).5 ρ RT gae FE = λe Nm Fce pe u legh le chage λ η 1 λ 1 q WM ( λ, x) = ; WE ( q, x) = L x C ( x) WM 1 1 L x M ( λ, x) = = λ ( 1/ L( x) ) = I x x x λ WE 1 1 C x E ( q, x) = = q ( 1/ C( x) ) = v x x x q = (ρ K).5 l, lqu p,u cuu a buae - jkz jkz p(z) = p e p-e, p(z,) = Re p(z)e ω -1 -jkz jkz û z =η (p e - p-e ), u z(z,)= Re u z(z)e ω up a ρ u p γp Page 3 4
Opcal Cmmuca E = h, ph ph h/c = mmeum [kg m -1 ] = B Tam Le Tme Dma v(z,)/ z = -L (z,)/ (z,)/ z = -C v(z,)/ v/ z = LC v/ 1 v(z,) = ( z/c) - ( z/c) (z,) = Y [ ( z/c) - ( z/c)] c = (LC) -.5 = (με) -.5 Z = Y -1 = (L/C).5 Γ L = - / = (R L Z )/(R L Z ) Fequecy Dma ( /z LC)(z) = ω -jkz jkz (z) = e -e, vz (, ) = Re ( ze ) jω -jkz jkz I(z) = Y [ e - -e ], z (, ) = Re I( ze ) jω k = π/λ = ω/c = ω(με).5 Z(z) = (z) I(z) = Z Z (z) [ ] [ ] Z (z) 1 (z) 1 (z) R jx = Γ Γ = jkz [ ] [ ] Γ (z) = e = Z (z) 1 Z (z) 1 Z(z) = Z Z jz a kz Z jz a kz L L SWR = max m Page 4 4