E F = q b E (2) E q a r q a q b N/C q a (electric flux line) q a E r r r E 4πr 2 E 4πr 2 = k q a r 2 4πr2 = 4πkq a (3) 4πkq a πk 1 ɛ 0 ɛ 0 (perm

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1 (static electricity) 20 (electric charge) A,B q a, q b r F F = k q aq b r 2 (1) k q b F F q a r?? 18 (Coulomb) 1 N C r 1m N 1C k Nm 2 /C 2 1 k q a r 2 (Electric Field) 1

2 E F = q b E (2) E q a r q a q b N/C q a (electric flux line) q a E r r r E 4πr 2 E 4πr 2 = k q a r 2 4πr2 = 4πkq a (3) 4πkq a πk 1 ɛ 0 ɛ 0 (permittivity) q a ɛ0 4πr 2 E = q a E = ɛ 0 q a 4πr 2 ɛ 0 (4) q a 4πr (electric flux density)d 2 D = ɛ 0 E (5) 2

3 ɛ 0 C 2 /Nm 2 E N/C C/m 2 q b q a W?? W = F r W = F r = q b Er (6) = q b q a 4πrɛ 0 Er (electric potential) (difference of potential) (power voltage)v 1.2 N S A,B p n, p s r F F = k p np s r 2 (7) k C Wb r 1m 107 (4π) = N 2 1Wb k Nm 2 /Wb 2 (magnetic field)h p n, p s (magnetic flux line) 3

4 N S H 1820 (Ørsted) (Ampère) I H H = I 2πr (8) I A H A/m I r H r r s H = I s 4πr 2 (9) 4

5 E ɛ D H (magnetic permeability)µ 0 (magnetic flux density)b B = µ 0 H (10) Wb/m 2 µ 0 N/A 2 4π 10 7 N/A (electrical current) 1A 1 1C ρ v S I I = ρvsq (11) v m α F = ma 2 F = qe α = qe m v T v = qe m T 11 I = ρ qe m Sq E I = ρq2 S m E (12) I V R I = V R (13) 12 E V 1 R 5

6 B I F F B I F = (I B)l (14) l F I B F B I

7 (Faraday) 1831 (electromagnetic induction) V φ t V = φ t (15) φ B S IH(Induction Heating) 1.5 (Maxwell) πr 2 E = qa ɛ 0 r r a q a ɛ0 b 0 7

8 q a n E θ S E a S E E θ E cos θ n E n E n = E n cos θ n = 1 4 s E nds = q a ɛ 0 (16) (electric charge density)ρ q a = ρdv v ɛ 0 E nds = ρdv (17) s v N N S H 0 H µ 0 H nds = 0 s B nds = 0 (18) s 8

9 H = I 2πr B B = µ 0I 2πr 2πrB = µ 0 I Bdr = µ 0 I (19) j S I = jds Bdr = µ 0 s jds (20) de/dt B S I de dt de s dt ds de ɛ 0 s dt ds 20 ( ) de Bdr = µ 0 j + ɛ 0 ds (21) dt s Bdr = µ 0 s ( ) E j + ɛ 0 nds (22) t 9

10 V = φ t V 6 E r E r V = E r V = Edr φ E r V φ B S φ = BdS s Edr = d dt s BdS (23) B Edr = nds (24) s t ɛ 0 E nds = ρdv s v ( ) E Bdr = µ 0 j + ɛ 0 nds s t B nds = 0 s Edr = s B t nds 10

11 E = ρ (25) ɛ 0 ( ) E B = µ 0 j + ɛ 0 (26) t B = 0 (27) E = B t (28) (electromagnetic waves) (wave length)λ c (period)t (frequency)ν T c = λ/t ν 1 ν = 1/T c = νλ Hz µm 0.1nm 10nm 1µm 100µm 10mm 1m 100m 10km γ X 11

12 µm µm µm 1mm 1m 2.2 E = 0 E B = µ 0 ɛ 0 t H = 0 (29) E = 0 (30) E H = ɛ 0 t H E = µ 0 t B H (31) (32) f() z t f() v t 0 z 0 t z 1 v z 0 = z 1 v t 12

13 x t f(z 1 -vt 1 ) t 1 t f(z 0 -vt 0 ) z t 0 v t z 0 z 1 z f(z vt) f(z 1 vt 1 ) = f(z 1 v(t 0 + t)) = f(z 1 vt 0 v t) z 0 = z 1 v t = f(z 0 vt 0 ) (33) f(z 1 vt 1 ) = f(z 0 vt 0 ) f(z vt) f() f(z + vt) (sine wave) sin sin x 2π λ a u(z, t) u(z, t) = a sin 2π (z vt) (34) λ T v λ = vt u(z, t) = a sin 2π( z λ t T ) (35) 2π 2π λ (wave number) k T ω u(z, t) = a sin(kz ωt) (36) (plane wave) k k = (k x, k y, k z ) x r k n z y 13

14 k n r n r u(r, t) = a sin(k r ωt) = a sin(k x x + k y y + k z z ωt) (37)?? π 2 u(r, t) = ae i(k r ωt) (38) i u(r, t) = a cos(k r ωt) + i sin(k r ωt) (39) z xz yz x H y E x z y z E x H y E x = E 0 sin(kz ωt) (40) H y = H 0 sin(kz ωt) (41) 31 z H y z = ɛ E x 0 t 32 (42) E x z = µ H y 0 t 42 z (43) 2 H y z 2 = ɛ 0 E x t H y z = ɛ 0 µ 0 2 H y t 2 43 (44) 14

15 (wave equation) 43 z 2 E x z 2 = µ 0 H y t E x z = ɛ 0 µ 0 2 E x t 2 42 (45) (wave equation) (E 0 sin(kz ωt)) z 2 = ɛ 0 µ 0 2 (E 0 sin(kz ωt)) t 2 k (E 0 cos(kz ωt)) (E 0 cos(kz ωt)) = ωɛ 0 µ 0 z t k 2 (E 0 sin(kz ωt)) = ω 2 ɛ 0 µ 0 (E 0 sin(kz ωt)) k 2 = ω 2 ɛ 0 µ 0 k 2 ω 2 = ɛ 0µ 0 (46) k = 2π 2π λ ω = T v = λ T v = ω k c c c = ω λ = 1 ɛ0 µ 0 (47) c ɛ 0 µ 0 x v 2 y x 2 = 1 v 2 2 y t 2 (48) E H S S = E H (49) S (pointing vector) E H kh 0 cos(kz ωt) = ɛ 0 ωe 0 cos(kz ωt) (50) ke 0 cos(kz ωt) = µ 0 ωh 0 cos(kz ωt) (51) 15

16 k ω k ω = ɛ E 0 cos(kz ωt) 0 H 0 cos(kz ωt) k ω = µ H 0 cos(kz ωt) 0 E 0 cos(kz ωt) (52) (53) µ 0 {H 0 cos(kz ωt)} 2 = ɛ 0 {E 0 cos(kz ωt)} 2 {H 0 cos(kz ωt)} 2 = ɛ 0 µ 0 {E 0 cos(kz ωt)} 2 H0 2 = ɛ 0 E0 2 µ 0 ɛ0 H 0 = E 0 (54) µ 0 E H ν 0 ɛ 0 H 0 E zx yz ɛ 1 µ 1 ɛ 2 µ 2 E vi E vr E hi Ehr x x ε 1, µ 1 θ i θ r z ε 1, µ 1 θ i θ r z ε 2, µ 2 θ t Y ε 2, µ 2 θ t Y E ht E vt zx E vi E vt E vr θ i θ t θ r x 16

17 zx E hi E ht E hr E iv e i(k1n r ωt) n (sin θ i, cos θ i ) r zx (z, x) u iv (z, x, t) k 1 u iv (z, x, t) = E iv e i(k1z sin θi k1x cos θi ωt) (55) z E ivz E ivz = E iv cos θ i n E y y y 54 y H ivy H ivy = ɛ1 µ 1 E iv y z x { Eivz = E iv cos θ i H ivy = ɛ1 (56) µ 1 E iv sinθ i E iv H iv cosθ i sinθ i x cosθ i H ih E ih sinθi sinθ i x cosθ i n θ i cosθ i n θ i z z y E ihy E ihy = E hi H ih n E z H iz H ihz = ɛ1 µ 1 E ih cos θ i { Eihy = E ih H ihz = ɛ1 (57) µ 1 E ih cos θ i u rv (z, x, t) u rv (z, x, t) = E rv e i(k1z sin θr k1x cos θr ωt) (58) 17

18 z E rvz y H rvy { Ervz = E rv cos θ r H rvy = ɛ1 (59) µ 1 E rv E rv sinθ r x cosθ H r rv cosθ r n x cosθ r E rh cosθ r sinθ r H rh n θ r sinθ r θ r sinθ r z z y E rhy z H rhz { Erhy = E rh H rhz = ɛ1 (60) µ 1 E rh u tv (z, x, t) k 2 u tv (z, x, t) = E tv e i(k 2z sin θ r k 2 x cos θ t ωt) (61) z E tvz y H tvy { Etvz = E tv cos θ t H tvy = ɛ2 (62) µ 2 E tv x z x z sinθ t θ E tv t H tv cosθ t cosθ t H th E th sinθ t sinθ t sinθ t cosθ t n cosθ t n y E thy 18

19 z H thz { Ethy = E th H thz = ɛ2 (63) µ 2 E th z x = 0 ωt { E ivz e ik1z sin θi ik1z sin θr ik2z sin θt + E rvz e = E tvz e E ihy e ik 1z sin θ i + E rhy e ik 1z sin θ r = E thy e ik 2z sin θ t (64) z k 1 sin θ i = k 1 sin θ r = k 2 sin θ t (65) θ i = θ r k 1 sin θ r = k 2 sin θ t k 1, k 2 ɛ2 k 1 = ω ɛ1 µ 1, k 2 = ω µ 2 64 { E ivz + E rvz = E tvz (66) E ihy + E rhy = E thy { H ivy + H rvy = H tvy H ihz + H rhz = H thz (67) E iv cos θ i E rv cos θ r = E tv cos θ t E ih E rh = E th ɛ1 ɛ1 ɛ1 µ 1 E iv + µ 1 E rv = µ 1 E ih cos θ i + ɛ1 µ 1 E rh = ɛ2 µ 2 E tv ɛ2 µ 2 E th (68) n n = ɛ2 µ 2 / ɛ1 E rv E iv µ 1 = cos θ i n cos θ t cos θ i + n cos θ t (69) E rh E ih = n cos θ i cos θ t n cos θ i + cos θ t (70) 19

20 E tv 2 cos θ i = (71) E iv cos θ i + n cos θ t E th 2 cos θ i = (72) E ih n cos θ i + cos θ t θ i 0 (Brewster s angle) (polarisation) 3.2 (radiation) (radiant energy) (J) (J/s) (radiant flux) (W) (lm) (radiant exitance) (irradiance) M e Φ S M e = dφ ds (W/m 2 ) (lx = lm/m 2 ) (radiant intensity) (73) 20

21 I dω Φ I e Φ Ω I e = dφ dω I e (W/sr) (cd = lm/sr) α (74) S α r Ω S r Ω = S r 2 (75) sr 4πr 2 4π(sr) ds θ ds cos θ ds cos θ θ ds (radiance) L e I e L e = di e ds cos θ I e = dφ dω L e = d 2 Φ dωds cos θ (76) (77) 21

22 (W/sr m 2 ) (cd/cm 2 ) (radiation) (heat radiation) (black body) (black body radiation) 1859 (Kirchhoff) λ T (Planck) 1900 T < E > < E >= 1 2kT k E P (E) P (E) = Ae E kt (78) A e?? E E = nhν h ν n n 0, 1, 2, n = 0, 1, 2, P (0), P (1), P (2), 0hνP (0) + 1hνP (1hν) + 2hνP (2hν) + (79) 22

23 < E > = = 0hνP (0) + 1hνP (1hν) + 2hνP (2hν) + P (0) + P (1hν) + P (2hν) + hν(0 + e hν kt e 0 + e hν kt + 2e 2hν kt + + e 2hν kt + = hν 0 + x + 2x x + x 2 + x = hν 1 x = hν x 1 hν = e hν kt 1 x = e hν kt M e (λ, T ) c c = νλ M e (λ, T ) = 2πhc2 λ 5 1 e hc kλt 1 T =300[K] 5000[K] (80) (81) (K) 1000(K) 600(K) 300(K) µm 1µm 10µm 100µm 1mm 5900[K] M e L e B B(λ, T ) = 2hc2 λ 5 1 e hc kλt 1 (82) 23

24 hν kt 1 e hν kt 1 e hν kt B(λ, T ) = 2hc2 λ 5 1 e hc kλt (83) (Wien) λ µm T 3200 hν kt hν 1 e kt 1 hν kt B(λ, T ) = 2c kt (84) λ4 (Rayleigh-Jeans) λ = 3mm 30mm (vacuum discharge) 1913 (Bohr) 3 2 E 2 E (energy level) 2 E 2 1 E 1 1 E 2 E 1 (radiation) 24

25 (Excitation) (absorption) 1890 (Rydberg) n m λ ν 1 λ = ν ( 1 c = R n 2 1 ) m 2 R E E = hc λ (85) = hν (86) E = nhν 1905 (Einstein) (photon) µm 10µm 3µm 0.7 3µm

26 aerosol N 2 O 2 CO 2 O 3 N 2 O 2 Ar (Rayleigh scattering) (Mie scattering) I s α θ λ I i dω dω ( ) 128π 5 I s = 3λ 4 α2 /dω 3 4 (I i + cos 2 θ) dω 4π 1/10 ρ N γ (extinction coefficient)k λ K λ = 8π3 (γ 2 1) 2 3λ 4 Nρ λ 4 b K() ( ) 2πb K λ = πb 2 K λ, γ (87) (88) (89) (extinction) 26

27 (emission) λ j λ k λ jλ k λ = B(λ, T ) (90) I λ ds ρ di λ di λ = k λ ρi λ ds (91) di λ = j λ ρds (92) 90 j λ = k λ B(λ, T ) J λ j λ = k λ J λ di λ = k λ ρi λ ds + j λ ρds = k λ ρi λ ds + k λ J λ ρds di λ ρk λ ds = I λ + J λ (93) LOWTRAN AFGL Air Force Geophisics Laboratory MODTRAN 6s(Second Simulation of the Satellite Signal in the Solar Spectrum)

28 µ ) µm 28

29 4.3 θ φ = 2k h cos θ < π 2 h < λ 8 cos θ (94) λ h k(= 2π/λ) Φ π/2 φ = 2k h cos θ < π 8 λ h < 32 cos θ (95) σ σi = P r(4π) 3 R 4 P t G 2 λ 2 (96) P t λ R G P r 29

30 A σ 0 = σ i /A i backscattering coefficient 30

168 13 Maxwell ( H ds = C S rot H = j + D j + D ) ds (13.5) (13.6) Maxwell Ampère-Maxwell (3) Gauss S B 0 B ds = 0 (13.7) S div B = 0 (13.8) (4) Farad

168 13 Maxwell ( H ds = C S rot H = j + D j + D ) ds (13.5) (13.6) Maxwell Ampère-Maxwell (3) Gauss S B 0 B ds = 0 (13.7) S div B = 0 (13.8) (4) Farad 13 Maxwell Maxwell Ampère Maxwell 13.1 Maxwell Maxwell E D H B ε 0 µ 0 (1) Gauss D = ε 0 E (13.1) B = µ 0 H. (13.2) S D = εe S S D ds = ρ(r)dr (13.3) S V div D = ρ (13.4) ρ S V Coulomb (2) Ampère C H =

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