A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B

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2 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A y B B x A x B B C y C y + A x B y A x A y A C x C = C x C B y x B y B C x C y C A x A y A B B x B y B x B y B = C C C x C y C x C y C x C y C = A A x A y A x A y A B x B y B.7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C x y B C = B x B y B = x B y C B C y y B x C B C x + B x C y B y C x C x C y C x y A B C = A x A y A B y C B C y B x C B C x B x C y B y C x = x {A y B x C y B y C x + A B x C B C x } y {A x B x C y B y C x A B y C B C y } + { A x B x C B C x A y B y C B C y } = x {B x A y C y + A C C x A y B y + A B } + y {B y A x C x + A C C y A x B x + A B } + {B A x C x + A y C y C A x B x + A y B y } = x {B x A x C x + A y C y + A C C x A x B x + A y B y + A B } + y {B y A x C x + A y C y + A C C y A x B x + A y B y + A B } + {B A x C x + A y C y + A C C A x B x + A y B y + A B } = A x C x + A y C y + A C B x x + B y y + B A x B x + A y B y + A B C x x + C y y + C = A CB A BC 3 x = cos, y = sin x + y = cos + sin = A = sin x + cos y = sin x + cos y = 4.34 l = = = O xy = l = π π = = π

3 5.39 θ = θ = sin θ θ = sin θ O > l sin θ = /l π l [ ] l = sin θ = π sin θ = π l l = πl 6.4 V = h = = h h π [ V = = πh ] = π h 7.43 V = sin θθ O π π [ ] V = sin θθ = π [ cos θ] π 3 = 4π3 3 3 A = x + y = x y A = B = x + y + c = x y c B = + + c. E = x y 4πε + x y c 3 4πε + + c 3 = 4πε c 3/ x + c c 3/ y c 3/ E y = E = + = P c 3/ c = P c 3/ P.. c = P = 3/ + 4 = =, ± 5 5, = 5 B. < E = l + 4πε { + } 3/ t = C. C. E = l 4πε = l 4πε t t + 3/ l 4πε t l t + 4πε tt t + 3/ t + = l 4πε, + + +

4 ' 3 3 = l l = l =, =, =, = + E = 4πε 3 = l 4πε + 3/ = L L C. E = L l 4πε L + 3/ L l 4πε L = l L πε = = l + πε + 3/ L + L L E πε 4 = l = l '= l ' ' L O L = l ' = ' ' l = l = l l = l = l E =, = + E = l 4πε + 3/ = π E = π l 4πε + 3/ = l 4πε + 3/ π x = φ ' φ ' l 4πε + 3/ l ' = φ ' = ' π y = cos x + sin y π E = = l π 4πε + cos x + sin y = 3/ π = l ε + 3/ π = E = 3 E = E = l ε E = l ε cos x + π + > 3/ = = l + 3/ ε + 5/ sin y = E/ E < / > / = / E = / E E mx = l / ε {/ + } = = 3/ l 3 3ε

5 ' 4 5 = s = s E =, = + E = s 4πε + + 3/ = =, = π φ ' y E = s π 4πε + 3/ s π + 4πε + 3/ s = 4πε π + = s sgn ε + x φ ' ' = ' = ' ' ' φ ' E s ε sgn 6 = s = s x y, =, = x x + y y, = x x y y, = + x + y E = 4πε = sx y 3 4πε s E = 4πε W W x x y y + x + y 3/ x x y y + x + y 3/ y x x, y x, y x,y x, y 4 s W y s E = πε + x + y x 3/ = πε s W x = πε + x = [ ] s W x tn πε W y x s W ' y ' + x + x + y = s πε tn W x ' W ' = x' x y' y W tn x lim x + tn x = π/ E = s W tn = s W tn sgn s π πε πε πε sgn = s sgn ε 3 E = ± s ε = kx x + y y + x = y = x =, y = xy

6 5 = = sin θ cos x + sin θ sin y + cos θ = sin θθ = = = cos θ, = sin θ cos + sin θ sin + cos θ = cos θ + Ψ Ψ = D = = 4π = π π π π π 4π 3 sin θθ cos θ sin θθ cos θ + 3/ cos θ sin θθ cos θ + 3/ x ' = O = y R = cos θ + θ RR = sin θθ + Ψ = + R RR = + + R = R 3 4 R 4 > Ψ = 4 < Ψ = 4 [ + + ] [ ] = = [ R R enclose y = π π = 4π π sin θ θ = π 3. D = D = enclose y 4π = sin θ θ enclose y = L π = πl 3.4 D = D = enclose y = πl ] +

7 6 3.7 xy 3.8 enclose y = = A + = A D = D 3.6 D = D = D sgn = enclose y sgn = A 4 O sgn < : s enclose y = 3.4, 3.3 E = ε D = enclose y 4πε = > : s enclose y = s 4π 3.4, 3.3 E = ε D = enclose y 4πε = s 4π 4πε = s ε 5 O 3.5 < : enclose y = 4 3 π3 3.4, 3.3 E = D = enclose y ε 4πε = 4 3 π3 4πε = 3ε > : enclose y enclose y = 4 3 π3 3.4, 3.3 E = D = enclose y ε 4πε = 4 3 π3 4πε = 3 3ε

8 7 6 L 3.6 < : enclose y = 3.4, 3.5 E = ε D = enclose y πε L = > : enclose y L enclose y = s πl 3.4, 3.5 E = D = enclose y ε πε L = s πl πε L = s ε 7 L 3.6 < : L enclose y enclose y = π L 3.4, 3.5 E = D = enclose y ε πε L = π L πε L = ε > : enclose y L enclose y = π L 3.4, 3.5 E = D = enclose y ε πε L = π L πε L = ε 8 xy A 3.8 < : enclose y = A 3.4, 3.7 E = ε D = enclose y ε A sgn = A ε A sgn = ε > : enclose y = A 3.4, 3.7 E = ε D = enclose y ε A sgn = A ε A sgn = sgn ε

9 8 9.4,,,,.4 A = A + A,, + A +,, A,, + A +,, { + } = + A +,, A,, A = A,, A + A, +, + A,, + A, +, = A, +, A,, A = A A,, + A,, + + A,, + A,, + = A,, + A,, A = A.4 = A = lim = A + 3. = + A = lim A + A A + A + A.5, θ,, θ,.5 A = θ + θ+ θ A + A, θ, + A +, θ, + + A, θ, sin θ θ + A +, θ, { + sin θ θ } + + = + A +,, A, θ, sin θ θ A sin θ θ = A

10 9 + θ + θ+ θ + A, θ, θ + A, θ + θ, θ θ θ+ θ A, θ, sin θ θ + A, θ +, { sinθ + θ θ } = sinθ + θa θ, θ + θ, sin θa θ, θ, θ θ sin θ θ sin θa θ sin θ θ = sin θ θ sin θa θ A, θ, + A, θ, + + A, θ, θ + A, θ, + θ = A, θ, + A, θ, θ A sin θ sin θ θ =.5 = + θ+ θ + θ sin θ + θ + θ 3. A = lim = A + 3.c A sin θ sin θθ = {cos θ cosθ + θ} 3 θ θ + θ sin sin θ θ A = lim sin θ θ sin θa θ + A + A sin θ sin θ θ sin θa θ + A sin θ 4 C = cos x + sin y π/3 C E = 4sin x + cos y, W = = 8 A B π/3 π/3 E = = = sin x + cos y sin 3 + cos 3 = 8 [ = 8 cos cos sin x + cos y sin x + cos y sin sin3 3 π/3 ] π/3 { cos sin + sin cos } = = V = 4πε x + y + + 4πε x + y + + = 4πε x + y + = x + y x + y + = x + y + + = xy

11 E = F, F = ε V = E = ε F = [ ε F = ε F F ε = ε + ε = ] ε F E = F, F = = ε V = E = ε F = [ ] ln F + ln F ε ε = } {ln ln + ln ε ε = ε ln + ε ln E = sgn F = sgn, V = = ε = ε ln ln ε F, F = = = sgn E = sgn F = [ F ε ε = V = ε = ] + ε + ε + = + ε F ε + 4 B = A V 5 V = A B = s ε E = A B sgn s ε sgn = s ε [ + ] = s ε + +

12 V = s ε + s ε + = s ε + s ε s ε V = V = s = s V =, = + V = 4πε = s 4πε + =, = π V = π = s 4πε π π s 4πε + = s 4πε [ ] + = s + ε V = V V = s ε B = A V 3 6 A A V = E = E + + = E B B > s V = E = ε = s ε = s [ ] ln ε = s ln ε < s V = E E = ε = s ε = s [ ] ln ε = s ln ε 6 B = A V 3 7 A A V = E = E + + = E B B > V = E = ε = ε = [ ] ln ε = ln ε < V = E = = ε ε E = E = ε ε [ [ ln ] ε ] ε ln + = ε

13 7 A B 3 4 > A A V = E = E + θ θ + sin θ = E B B s V = E = ε = s ε = s [ ] = s ε ε < s V = E E = ε = s ε = s [ ] = s ε ε 8 A B 3 5 > A A V = E = E + θ θ + sin θ = E B B 3 V = E = 3ε = 3 3ε = 3 [ ] = 3 3ε 3ε < V = E = 3 3ε [ ] E = 3ε [ ] 3 3ε = 3 3ε 3ε = = 3ε 6ε ε 3 3ε 9 R, R P V = + 4πε R R R P, θ, φ + θ + x + x / x + 3 x x / x O R y R = R = + cos θ = cos θ + + cos θ + 3 cos θ + cosπ θ = + cosπ θ + 3 cos π θ / = + cos θ + 3 cos θ 3 / cosπ θ + = cos θ + 3 cos θ 3

14 3 V 4πε [{ + cos θ } { + 3 cos θ + 3 cos θ } + 3 cos θ ] 3 = 3 cos θ = 3 cos θ 4πε 3 4πε [ 3 E = V = V V θ θ = 4πε 3 cos θ [ = 3 cos θ 3 4πε 4 ] 3 cos θ sin θ 4 θ = 3 4πε 4 { 3 cos θ + sin θ cos θ θ } cos θ ] θ θ V, 4.35, 4.36 V = V = = l πε [ l ln ] = πε [ ] ln = l πε [ l ln πε = l πε = ] l ln πε 5 < < E > c E V V enclose y = > c 3.4, 3.3 E = ε D = enclose y 4πε = 4πε = E enclose y = < < 3.4, 3.3 V E = ε D = enclose y 4πε = V = c c E = 4πε = E 4πε = 4πε c V c c V = E E = 4πε 4πε = 4πε + c < < c

15 4 enclose y = > c 3.4, 3.3 E = ε D = enclose y 4πε = 4πε = E enclose y = < < E = V V = c V V = c E = E c 4πε = c E = 4πε c 4πε = 4πε c < < c 3 enclose y = > c E = enclose y = < < 3.4, 3.3 E = ε D = enclose y 4πε = V = V = c c E = 4πε = E E E E = c 4πε = 4πε O < < enclose y = 3.4, 3.3 E = ε D = enclose y 4πε = 4πε = = + θ θ + sin θ V = E = E = V = V 4πε = V = V / / V / / / / = V / / 4πε = [ ] = 4πε 4πε

16 5 3 E E = A + B cos θ C + D cos θ A CE + B DE cos θ = θ cos θ A CE = B DE = f θ = E = A C = B D A A = = cos θ / = P P V V = 4πε A P + 4πε A P = ' ' θ = A O y = A P A P x P =, P = A P = A P A P = A A P + P = cos θ + A P = A P A P = A A P + P = cos θ + = cos θ + cos θ = = + cos θ + cos θ = / P,, / = A P = A P = 3 E = V = s = D = = ε E = sin θθ t = E + F cos θ E + F cos θ 3/ = E = = A P 4πε A P 3 + = A P 4πε A P = A P 3 4πε A P + 3 { } 4πε A P 3 A P A P A P 3 4πε A P

17 6 s = ε E = = = 4π + cos θ 3/ { } 4π A P 3 i i = s = = = 4π = π π s sin θθ = 4π [ ] π π + cos θ 4 > 3.4, 3.3 π = D = enclose y 4π = 4 3 π3 4π = 3 3, E = D = 3 ε 3ε < 5.5, 5.6, 3.3 D = enclose y 4π = 4 3 π3 4π > 3 V = E = 3ε = 3 3ε < V = E E = = 3, E = ε ε D = 3 3ε 3ε ε π 3ε ε = 3ε + 6ε ε sin θθ + cos θ 3/ = D = D = εe = ε V = ε V D = ε V = ε V = ε V = ε V = /ε 6 x E x = E x E sin θ = E sin θ E D = D θ ε x ε E cos θ = ε E cos θ θ E ε E, E E sin θ = = ε cos θ E sin θ ε cos θ

18 7 tn θ tn θ = ε ε 7 P = > P = < = P,, > E > = 4πε πε + 3 < P = > ε P,, < ' ' > ε = E < = 4πε 3, = = = x x + y y = + = x + y + ' ε < E > = = x x + y y 4πε x + y + 3/ + x x + y y + 4πε x + y + 3/ E < = = x x + y y 4πε x + y + 3/ = x y ε + ε = ε P.5. = + = P.5. P.5. P.5., = ε ε ε + ε, = ε ε + ε P F = 4πε 3 = 6πε = 6πε ε ε ε + ε ε > ε F

19 8 8 ε, ε L l 3.5 D = enclose y = πl ll πl = l π 5.5, 5.6 ε ε c E = ε ε D = E = ε ε D = l πε ε l πε ε < < c c < < E,mx = E,mx E,min = E,min l πε ε = l πε ε c l πε ε c = l πε ε ε ε = c, ε ε = c c = V = c E = = l πε c l E = πε ε ε ln c + ε ln c C = l V = 4πε /ε + /ε ln/ c l πε ε = l + ln 4πε ε ε 9 E ε, ε l L D 3. ε ε E π L + ε ε E π L = l L c ε ε E = l πε ε + ε V V = l E = πε ε + ε = = l πε ε + ε ln

20 9 C = l V = πε ε + ε ln/ O E ε, ε ε = π π/6 π/6 sin θθ = π sin θθ = π [ cos θ] π/6 = 3π ε = π π π sin θθ = π sin θθ π/6 π/6 = π [ cos θ] π π/6 = + 3π 3. ε ε E + ε ε E = E = ε ε + ε = V πε { 3ε + + 3ε } V = E = πε { 3ε + + 3ε } = = πε { 3ε + + 3ε } C = V = πε { 3ε + + 3ε } / / x ε π 6 O ε Close ufce y t + σ ε = e σ/εt e σ/εt = t t t = = = e σ/εt

21 = εe = ε E, I = J = σe = σ E V = C = V = ε E + E / + E { / + } { CR = ε E E, R = V + / I = E σ + / } E σ E = ε σ E 7 7. AB P,, xy =, = x x + / y, I = Ix x, R = = x x / y +, R = R = x + / + H AB = I R = Ix x { x x / y + } 4πR 3 4π{x + / + } 3/ = I y + 4π x {x + / + } 3/ H AB = I 4π y + / / = I y + π x {x + / + } = I 3/ π x {/ + } x + / + / D I x C y + / = I y + π C. H BC H CD H DA H = H AB + H BC + H CD + H DA = I π + /4 + / x O H = I R 4πR = x x, R = x R = x O A B x {x + / + } 3/ / {/ + } / + O 7.3 = = π = H = I 4π π = I 4 O y y x

22 3 A P 7.3 A P N A N A I N A P I N B H A = N A I + 3/ B P A B H B = N B I { + } 3/ H H = H A + H B = I [ ] N A + + N B 3/ { + } 3/ = / H = H H / =/ = H = I [ ] 3/ + N A 3/ + N 5/ { + } 5/ B = = / = + / / = / 3/ 5 /4 5/ N A + 3/ 5 /4 5/ N B = N A / = N B / 4 J = J C I net though = J = π J = π J 7.8 H = H = I net though = J π C xy C < I net though = 7.9 H = I net though = π > I net though = I 7.9 H = I net though = π I π

23 6 w 7.7 x = J s = I/w x = J s = I/w x I x = x > H top = J s x = {I/w } x = I w y x < H top = J s x = {I/w } x = I w y O w I y x = x > H ottom = J s x = { I/w } x = I w y x < H ottom = J s x = { I/w } x = I w y < x < H = H top + H ottom = I w y + I w y = I w y 7.4,,,, C = C C = + + = + + = = = A = A + A + A + A C + + C = : = =, = = : = =, = + = : = =, + = : = =, = + + = + = + = + = = + A A + A A,, + + A, +, + = A,, + A, +, = A, +, A,, A = A

24 3 A + A A,, + A, +, + + = A,, + A,, + 7. A A = A = lim = A,, + A,, A = A C A = A A C = C C = + + = + + = = = A = A + A + C + A + + A C = : = =, = + = : = =, + = : = =, = : = =, = = = = + = = + = + A A + + A A,, + + A,, + = A,, + + A,, A + A A,, + 7. A A = A = lim = A,, + A,, A = A + A +,, + = A,, + A +,, = A +,, A,, A = A A = A C A

25 4 C = C C = + + = + + = = =.38c 7. A = A + A + A + A C + + C = : = =, = = + + = : = =, = = + = : = =, + = = + + = : = =, = = A A + A A,, + + A +,, + = A,, + A +,, { + } = + A +,, A,, A + A A, +, + 7. A A = A = lim A = A + A,, + = A, +, + A,, = A, +, A,, A = A C A = , θ,, θ, [ A A ] C = C C = + θ+ θ θ = + θ+ θ θ sin θθ sin θ θ

26 5 = = sin θθ A = A + A + A + A C θ θ+ θ + C θ = : = = sin θ, = : = θ = θ θ, = = θ θ+ θ θ + θ = : = = sin θ, θ sin θ = sin θ + θ θ = θ = θ + = : = θ = θ θ, = + + θ sinθ + θ = sinθ + θ θ θ = θ θ+ θ A A + θ A A, θ, + A, θ + θ, θ+ θ θ θ+ θ = A, θ, sin θ + A, θ + θ, { sinθ + θ } A + A A, θ, + 7. A A = A = lim = sinθ + θa, θ + θ, sin θa, θ, θ θ sin θ θ sin θa sin θ θ = sin θ θ sin θa + A, θ, + + = A, θ, θ θ + A, θ, + θ θ = A θ, θ, + A θ, θ, θ A θ sin θ sin θ θ = A sin θ C A = [ sin θ θ sin θa A ] θ C θ θ = C θ θ C θ θ = + + θ = + + sin θ sin θ θ = θ = sin θ A = A + A + A + A C θ + + C θ

27 6 = : = = sin θ, = : = =, = = + = + + = : = = sin θ, = + + = : = =, = + + sin θ = sin θ + sin θ = + sin θ + = A A + A A, θ, + A +, θ, + + = A, θ, sin θ + A +, θ, { + sin θ } A + A A, θ, + 7. A θ A θ = A θ = lim θ = + A +, θ, A, θ, sin θ A sin θ = A θ + A, θ, + + = A, θ, + A, θ, + = A, θ, + A, θ, A sin θ sin θ = A sin θ θ θ C θ A = [ sin θ A ] A C = C C = θ+ θ + θ = θ+ θ + θ θ θ = = θ.39c 7. A = A + A + C θ A + + A θ+ θ C θ = : = θ = θ θ, = θ θ = θ θ θ+ θ + θ = : = =, = = θ θ+ θ + = : = θ = θ θ, = + θ θ = + θ θ θ

28 7 θ + θ = : = =, = = θ + A A + A A, θ, + A +, θ, + + = A, θ, θ θ + A +, θ, { + θ θ } = + A θ +, θ, A θ, θ, θ A θ θ = A θ A + A A, θ, + A, θ + θ, θ+ θ θ θ θ+ θ = A, θ, + A, θ + θ, 7. A A = A = lim = A, θ + θ, A, θ, θ θ A θ θ = A θ C A = [ A θ A ] θ 7.3c 9 B = A = / / / = A B =, B = A, B = A B = A = µ I π A = µ I ln + C C π A = A = µ I π ln + C φ = f φ = f 4πR R = 7.3 A = A x x + A y y + A = µ J 4π R = µ J x x + J y y + J 4π R µ J x µ J y µ J = 4πR x + 4πR y + 4πR A x = µ J x µ J y 4πR, A y = 4πR, A = A x = µ J x, A y = µ J y, A = µ J µ J 4πR

29 8 B. A = A x x + A y y + A = µ J x x + µ J y y + µ J = µ J x x + J y y + J = µ J B.3 A = A A 7.33 A = H = µ B = µ A = µ { A A } = µ { µ J } = J 8 F = B m t = B m x t = y B B y, m y t = B x x B, m t = x B y y B x x B = B x B > m x t m y t m t = P.8. = B P.8. = y B P.8.3 t = B = B x < R R y x =, y =, =, x = y = = x > P.8. x =, x = y P.8. t P.8.3 y t + B y = P.8.4 m P.8.4 y = y t = cos ω c t y = ω c sin ω c t P.8.5 P.8.6 ω c ω c = B m P.8.7

30 9 P.8.5 P.8. = t = sin ω c t = ω c cos ω c t P.8.8 P.8.9 >, < P.8.6, P.8.9 y + ± R = R P.8. R R = ω c = m B P.8. P.8.6, P.8.9, P.8. ω c, R ω c, R P.8.6, P.8.9 >, < e e E B m t = ee + B B x E O y =, V x E = E = V m x t = P.8. m y t m t = e B = e V + e yb P.8.3 P.8.4 t = x = y = =, x = y = = P.8. x =, x = y P.8.4 t P.8.3 t + ω c = P.8.5 ω c ω c = eb m P.8.6

31 3 P.8.5 t = = = C sin ω c t C P.8.4 y = m eb t V B = C cos ω ct V B t = y = C = V/B = ev/ω c m y, y = y t = = t = ev ω c m cos ω ct ev ω c m sin ω ct P.8.7 P.8.8 t = y = = y = ev ω cm sin ω ct ω c t = ev ω cm cos ω ct P.8.9 P.8. mx = ev/ω cm mx = H c H c = mv µ e P.8.9, P.8. 3 P I H = I π + cos x I P = y + cos y + sin = + cos y + sin = sin y + cos O I I P, y, φ y O ' F = I µ H = I sin y + cos = µ I I π cos y + sin + cos C.7 F = µ I I π = µ I I π = µ I I π π π cos + cos y µ I I π + cos π I I > π y + µ I I π π y = µ I I µ I π + cos x sin + cos [ ln + cos ] π y

32 3 4 B I F = F + F = I y B = B y F = F = IL B = I x B y = IB O I = I = I x F = I B = I B T = F = I B = I B = I [ B B] = I B B = B x x + B y y + B cos x + sin y = B x cos + B y sin T = I B x cos + B y sin sin x + cos y = I B x cos sin B y sin x + I B x cos + B y sin cos y T = =π = T π π = I B x cos sin B y sin x + I B x cos + B y sin cos y = I π B y x + B x y = Iπ B = I B = m B n [tuns/m] B = µ ni n Λ = nφ = n B = µ n I = µ n I π L = Λ I = nφ I = µ n π B = µni π Φ Φ = B = µni π = µni π

33 3 =, = + cos, = Φ = µni π = µni π = µni π π [ π + cos + cos ] π = µni O ' ' φ ' + ' cosφ ' ] [ = µni = µni C.7 N Λ = NΦ L = Λ I = NΦ I = µn 8 l B = µ N I /l Φ = B n = µ N I n = µ N I cos θ π l l N Λ = N Φ M = Λ I = N Φ I = µ π N N cos θ l θ n 9 M = µ l 4π = µ 4π = µ 4π = µ 4π = µ 4π = µ 4π l l l l l + ln [ + + ] l {ln [ l + ] [ ]} + l ln + + ln l + l ln + { [ ] ln + + ln [ l + ] } + l { [ ln [ + ] ] l + + } = = R = + P.8. [ l ln [ l + + l ] + l ] l

34 33 = = µ π l ln + l + l /l M = µ l π ln l + + l + + l + l + l µ l π ln l P.8. Int. = ln [ l + ] + l = l ln [ l + ] + l = l ln [ l + ] + l l + l/ + l l + + l l + l = l ln [ l + + l ] + l I P B = µ I π + cos x Λ = B x = µ I π = µ I π π = µ I π + cos = µ I I O P φ O' [ ] = µ I C y C.7 M = Λ I = µ 9 Λ = NΦ = NΦ sin ωt V e V e = Λ t = NΦ ω cos ωt y B = µ H y H > t = y t n C B = µ H y ω n = cos ωt x + sin ωt y y t Φ C Φ = B n = µ H y cos ωt x + sin ωt y x ω t n

35 34 = µ H sin ωt = µ H sin ωt N Λ = NΦ = Nµ H sin ωt V e = Λ t = Nµ Hω cos ωt 3 xy O B = B OA = = ω B = B ω E = B = ω B = ωb OA O A' A l y V e = O E = ωb = ωb A l l x = ωb l 4 B E = C t P.9. C xy B E = E E P.9. E = C π E + + = π : P.9. B π t = ωb cos ωt = ωb cos ωt P.9. = ωb cos ωt π = ωb cos ωt π E π = ωb cos ωt π E = E = ωb cos ωt π E = E = E π > : P.9. > B/ t = B π t = ωb cos ωt = ωb cos ωt = ωb cos ωt π = ωb cos ωt π π π

36 35 P.9. E π = ωb cos ωt π E = E = ωb cos ωt 5 = + B = µ H = µ H W m = B H B Hπ = µ H π * 7.6 I W m = µ H π = I c I c µ π + µ π π + µ π π π c = µ I 4π µ I 4π = µ I 6π + µ I 4π ln + µ I 4π [ + µ I 4πc c c 4 c ln c 3c 4c c ] L = W m = µ I 8π + µ π ln + µ [ c 4 π c ln c ] 3c 4c 6 L L M W m = L I + L I + MI I L L F = W m = M I I y y 8 M = µ F = [ µ ] I I y = µ I I y 7 H = J + D t = J + H = D t x, y, / t D = J = t D = t * = + = π + π π

37 36 8 E = µ H t, H = ε E t, E =, H = E = E E E = E E = E = E = µ H = µ t t H = µ t E = µε E t = ±/ µε ε E = µε E t t h 9.57 E E E t w 9.57 C B t 5.5 C t n = s, = = w h s w h h B t = B t B t B t B t = w h B t + B s t 9.57 E E t w = B.4 E E t = E E n s = s { n E E } h 9.57 H H H t w J J s s w C D C t t n = s, = = w h s w h h D t = D t D t + + D t D t = w h D t + D s t 9.57 H H t w = J s s w

38 37 W e = T = T = 8T = T T T W m = P s = T = T = 4T = T T [ ] ε E E t = T [ ε T Re [ Ẽe jωt] Re [ ] Ẽe jωt] t ε Ẽe jωt + Ẽ e jωt Ẽejωt + Ẽ e jωt t [ ] εẽ Ẽ + Ẽ Ẽe jωt + Ẽ Ẽ e jωt t [ ε T ] Ẽ Ẽ + Ẽ Ẽe jωt + Ẽ Ẽ e jωt ε t = 8 T 4 Ẽ Ẽ T 4 µ 4 H H, P l = [ E J Ẽe jωt + Ẽ e jωt [ [ T T ] t = T T σ Ẽ Ẽ [ Re [ Ẽe jωt] Re [ J ] e jωt] t J e jωt + J e jωt t Ẽ J + Ẽ J + Ẽ J e jωt + Ẽ J e jωt ] Ẽ J + Ẽ J + Ẽ J e jωt + Ẽ J e jωt t = ] t Re [ Ẽ J ] Ẽ = jωµ H H = J + σẽ + jωεẽ P.. P.. p = Ẽ H / p = Ẽ H = [ H Ẽ Ẽ H ] P..3 P.. H = J + σẽ jωεẽ P..4 P..3 P.. P..4 p = [ H jωµ H Ẽ J + σẽ jωεẽ ] [ = jω 4 µ H H 4 εẽ Ẽ ] σẽ Ẽ Ẽ J [ p = jω 4 µ H H ] 4 εẽ Ẽ σẽ Ẽ Ẽ J

39 38 3 Ẽ = Ẽ Ẽ, k = k k e jk = e jk jk = jke jk Ẽ = E e jk = E e jk = E jke jk = jk E e jk Ẽ = { jk E e jk } = jk E e jk = jk E jke jk = k E ke jk Ẽ = E e jk = e jk E = jke jk E = je ke jk Ẽ = {je ke jk } = j e jk E k = j jke jk E k = k E ke jk = {k ke k E k}e jk = {k E k E k}e jk Ẽ + k Ẽ = k E ke jk {k E k E k}e jk + k E e jk = = Ẽ = jk E e jk = jk Ẽ k Ẽ = H = jωµ Ẽ = jωµ je ke jk = ωµ k E e jk = ωµ k Ẽ 4 Ẽ = E e γ x H = E Z w e γ y p = Ẽ H = E e γ E x e γ y = E e γ Z w Z w e γ = e α e jβ e γ = e α p = E Z e α 5 x y Ẽ = / x / y / = Ẽ x y = jk E e jk Γe jk y Ẽ x = jωµ H = jωµ H e jk Γe jk y k E = ωµ H P..5 x y H = / x / y / H y = H y x = jk H e jk + Γe jk x = jωε Ẽ = jωε E e jk + Γe jk x k H = ωε E P..6

40 39 P..5 P..6 k = ω µ ε P..5 / P..6 E µ = H ε [ E H = Re Ẽ H ] [ ] = Re E e jk + Γe jk x H e jk Γ e jk y [ E H = Re Γ + Γe jk Γ e ] jk = E H Γ

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