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2 . 6. S =3ˆ+4ŷ +5ẑ â = ˆ+ ŷ + ẑ () S â () â ˆb.,b,c,d O A, B, C, D b =(d c) (3) â, ˆb AD BC P AD BC 3.,b,c b θ c = +b ccosθ O A, B, C, D O A, B, C, D A,B,C,D () AB BC A B = B C () AB A B (3),b,c,d A + bb + cc + dd = = b = c = d (4) A B θ cosθ 5. ABC l BC, CA, AB D, E, F AF BDCE FBDC EA = ĉ (4) S S = S â+s bˆb+sc ĉ (5) S (,,,b,c) 7. =ˆ 3ŷ+ẑ, b =3ŷ 4ẑ () b ( = + ) (), b c. 8.. C C P, S 9.. C C P ( )

3 C S.: C P P C O.: C..3, S ( ) 6 ( ) 4 d.3:.5: ( ) c.4: 6 S O 5.6: S 3..7 ( ) 4.7: ( ) 4..8 ( )V 5..9 ( )V 3 V π/6.8: V 4 V 4.9: V 6. φ = π 6 ˆρ, ˆφ ˆ,ŷ 7. r,, A(r)=A(,,)=ˆ+ŷ+ ẑ r = ˆ+ŷ + 6ẑ A A(r ) () A(r ) () r ˆρ, ˆφ ˆρ = ρ ˆ+ρ ŷ, ˆφ = φ ˆ+φ ŷ ( ρ,ρ,φ φ ) (3) r r = ρ ˆρ+φ ˆφ+ ẑ ρ,φ, r (4) A(r ) A(r )= A ρˆρ + A φ ˆφ + A ẑ A ρ,a φ,a r (5) r r (6) A(r ) r.3 8. r = ˆ + ŷ + ẑ, r = ˆ+ ŷ+ ẑ R = r r R ( ) R 9. A(s)= sˆ+ s s +ŷ+ s 3ẑ ˆ A(s)ds

4 ..,. dr. = Cˆ (.) A(r)=ˆ A dr + + (+ ). = C ( + ) A(r)= ˆ+ 3 ŷ+ ẑ A dr C.: = = O C π/4.: = C.: C 3. r = ˆ+ŷ +ẑ A(r)= r = (> ) + r 3 ˆ C A dr C 4. r = ŷ φ = 35 ˆ+ ˆ C A dr C 5..3 C( = =log ) ˆ A(r)=ˆ A dr C ˆ eˆ+ŷ C O e.3: C 6. S r(u,v)=uˆ + vŷ + ẑ,( u, v ) A(r)=ˆ + ŷ + ẑ A(r) ds ds + 7. S A(r)=ˆ A ds ds ( ) 8. A(r)=ˆ+ŷ+ẑ S A ds ds 9..4 S( ) A(r) = ˆ + ŷ + ẑ A ds ds +,+,+ ( ) S ds S.4: 3. r(ρ,φ)=ρcosφˆ+ρsinφŷ+ẑ ( ρ, φ π ) S A(r)=ˆ+ŷ +ẑ S A(r) ds ds + S 3. r = ˆ+ŷ+ẑ φ(r)=3 r V φ(r)dv 3..5 V( ) V S S 3

5 φ(r)=++ V V φ(r)dv.5: V 33. A(r)=ˆ+ŷ +ẑ V dv A.4 V 34. () e = (5 ) f e () () 3 ( 3 ) e.,e. ( ) (3) sin = (5 ) f sin () (4) f()=cos = (5 ) f cos () (5) e jθ =cosθ + jsinθ 5 f e (jθ)= f cos (θ)+jf sin (θ) 35. () f()= = (+) () f()= =8 (+) 36. log e = 4 log e. 37. f()= = (+)(+) f(,)=sin() r = π ˆ+ŷ ( ) r = ˆ+ŷ+ẑ ϕ(r)= r () ϕ () r = ˆ+ŷ ϕ(r) + (3) r = ˆ+ŷ ϕ(r) (4) r = ˆ+ŷ ϕ(r) 4. f(,) f () f(,) ( F(,) ) () F(,) (3) C : r()=ˆ+ ŷ, ( ) ( r = r = ˆ+ ŷ ) F(,) (4) F(r ) F(r ) ( ) 4. f(r)= r = ˆ+ŷ+ẑ V = lim f(r)dv V V V 4. f(r) =sin(k) r = ˆ+ŷ+ẑ V = V f(r )dv k,, : lim V V V f(r )dv 43. A(r) =ˆ + ŷ + 3sin(k) ẑ 4

6 r = ˆ + ŷ + ẑ V = S lim A ds ds V V S 44. A(r)=ˆ+ ŷ +sin(k)ẑ (k ) r = ˆ+ŷ +ẑ V = S S A(r ) ds ds V,, : lim V V S A(r ) ds 45. A(r)=ˆ+ŷ +ẑ r = ˆ + ŷ + ẑ S = ( ) C( + ) lim A dr S S C 46. A(r)=ˆ+ŷ +ẑ V S A V () AdV V () A ds ds V S 5

7 .. λ [C/m] r = ˆ+ŷ +ẑ E(r) [V/m].. [m] Q [C] [m] 3.. [m] σ [C/m ] [m] σ [C/m ].:.: 4..3 [m] h [m] Q [C] [m] h / h/.3: 5. [m] Q [C] ẑ [m] ( ). 6. Q [C] [m] h [m] V 7. ẑ Q [C] ( ) [m] S E ds S 8. E(r) E(r) ( ) (= ) 3 E(r) 4 ) E(r) E(r) r θ,φ ( ρ, φ ) 3 E(r) θ,φ 4 () [m] E(r) () E(r) (3) E(r) 6

8 (4) [m] E(r) (5) [m] E(r) (6) E(r) (7) [m] E(r) (8) [m] h [m] E(r) (9) [m] E(r) ( ) 9. ρ(r)[c/m 3 ] E(r) [V/m] r = r r E(r)= 4r ε r> E(r)= 43 r ε r3 ρ(r). λ [C/m] ρ [m] E(ρ) [V/m]. ( [m] ) σ [C/m ] ρ [m] E(ρ) [V/m]..4 (, ) () Q [C] () Q [C].4: 3..5 r [m] r Q [C] b<r c Q [C] <r b r>c E(r) [V/m] +Q Q c b.5: 4. ρ(r) ρ(r)= r = r { 3( r) π 4 Q, r,, r>, (.) () r [m] r E r (r) () E(r) (3) E(r) ρ(r)=ε E(r) (4) ( ) E(r)= 5. E(r) [V/m] λ [C/m] r = ŷ [m] Q [C] ( [m]) ρ [C/m 3 ] ( b [m]) d [m] (d+b<).6 ρ.6: ( ) d b 7

9 .3 6. Q [C] (.7 C ) ˆ C W [J] 7..7 C ˆ C W [J] Q C C.7: C,C 8. r = ˆ+ ŷ + ẑ Q [C] r = ˆ + ŷ + ẑ φ(r) [V] φ(r)= Q 4πε r r φ(r) 9. r = ˆ+ŷ +ẑ r = r ρ(r)=ρ [C/m 3 ] r> ρ(r)=[c/m 3 ] (ρ ) () E(r) [V/m] ( : ) () E(r) E = (3) ϕ(r) [V] ( r< ) (4) ϕ(r) E(r) (5) ϕ. [m] Q [C] r [m] ϕ(r) [V]. Q [C] r r ( ) Q ϕ(r)= 4πǫ r r r d = ˆ d +Q [C] r = Q [C] ˆ r = ˆ +ŷ ϕ(r) r = r r d d r d r. ϕ(r)= p r 4πε r 3 E(r) 3. [m] Q [C] r [m] E(r) [V/m] 8

10 3. ( S [m ] d [m] ) ±Q [C] () CV (). 3. ( [m] [m]) +Q [C] Q [C] () CV () W (3) ( ) ( ) C [F/m] : V λ C = λ/v memo: C [F/m] ( 3.b) b () (b) 3.: 4. [m] ( C V) Q [C] W [J] V 3.: 3. ( [m]) b [m] ( 3. ) ( A) ( B) bˆ V [V] A λ [C/m] B λ [C/m] b ( ) () q [C] v [V] () dq [C] dw [J] (3) C Q [C] (4) C =4πε 5. [m], b [m] (A, B) d [m](,b) r A = ˆ r B = dˆ ( 9

11 ) C [F] [m] ( ) d [m] ( ) (d> ) () p,p () Q [C] i Q OK p ij = p ji 3.3: d

12 4. 4. > ε =5ε ( ) < ε =3ε ( ) = + E =ŷ+3ŷ [V/m] = + D [C/m ] = E [V/m] D [C/m ]. E, E [V/m] E, E [V/m] θ,θ ε,ε [F/m] θ,θ ( [] ) ε =5ε ε = ε r = ˆ E =ˆ 3ŷ [V/m] r = ˆ D [C/m ] r = +ˆ E [V/m] D [C/m ] m ε ε ε ε () V [V] [m] V() [V] V ( [] ) L [m] [m] L [m] c [m] b [m] ( ρ<b) (b ρ<c) ε,ε [F/m] +Q [C] Q [C] L c ( 9/4 8/9 [] ) () ρ < b,b ρ<c () ρ < b,b ρ<c (3) C [F] (4) σ p [C/m ] 4.: = 4.: 4. ( d [m]) t [m] (d t)[m] 4.3 c b ε ε t d V 4.3: () C [F/m ] 4.4: L 6. [m] b [m] 4.5 L [m] ( [] )

13 () V [V] Q [C] () ε r (<L)[m] V() [V] (3) V [V] Q [C] Q (4) U [J] U F [N] lim (5) σ p [C/m ] (6) V [V] σ [C/m ] C [F] 8. ( S [m ] d [m]) 3 ε r =5 ( ) V [V] V [V] () E [V/m] D [C/m ] E [V/m] D [C/m ] () σ [C/m ] σ [C/m ] (3) C [F] b 4.5: ( S [m ]) 4d [m] 3d [m] ε r = V [V] E = ŷ [V/m] 3d εr= 4.6: () D [C/m ] () D [C/m ] (3) E [V/m] (4) P [C/m ] d L 9. S [m ] d [m] ε r ( S [m ] d/[m]).8 ε r. 4.7 [m] ( ε r ) E = E ẑ [V/m] P [C/m ] ±q [C] N [m 3 ] + d, d () ±ρ [C/m 3 ] d ρ () P

14 (3) E p [V/m] ±ρ r E p E p P E E E p E E E ε r (4) d r E p E E E p E E 4.7: D = ε rε E = ε E +P P =(ε r )ε E E E 3

15 Ì μ μ 5 5. =. I [A] + ρ = ˆ+ŷ B [T] B(ρ) ( ρ φ) (ρ,φ,) ( : ρ ˆρ =cosφˆ+sinφŷ φ ˆφ = sinφˆ +cosφŷ ). = [m] I [A] (+ ) r = ẑ B [T] [m] I [A] r = ˆ B()[T] = I [A] B [T] O I 5.: = I π/4 5.: I [A] B [T] = 4 I [A] = B [T] I 5.4: 5.3: [m] I ( ) I [A] () S () S J S [A/m] (3) B()[T] Js 5.5:

16 B(r)= µ I( ˆ+ŷ) π( + ) () 5.6() R r () dr (3) B(r) dr C (4) 5.6(b) θ = π B(r) dr 4 R R I R r R R C R I R θ b [m] ( ) I [A] ρ [m] B(ρ) ( [3] ) I [A] I [A] ρ [m] B(ρ)[T] r Ri RO 5.8: ρ 5.6: = + B(r)= µ I( ˆ+ŷ) π( + ) C,C B dr > () C :P Q R S P C = I [A] d [m] (I [A] [m] [m]) I B [T] B = µ I ( ˆ+ŷ) π( + ( ( ) )5 [4] ) () C :P T U S P Q I P 3 T () = ( ) () R S 5.7:. [m] + I [A] U F [N] B [T] B(r)= µ I( ˆ+ŷ) π( + ) 5

17 I d I d 5.9: 5.: ψ [m] I h B(r)=B ŷ [T] (B ) I [A] ψ B ŷ 5.: d B = Bˆ [T] B = ± ( m [kg] q [C]) v = v ŷ [m/s] t =s E = V/m (ε [F/m] µ [H/m]) ( ( )[4]5 ) () t(> ) [s] d v(t)[m/s] r(t)[m] () = d (3) (b) = d (4) (b) = d I b I B = B ẑ [T] E = E ŷ [V/m] t =s ( q [C] m [kg]) r() = [m] v() = v ˆ [m/s] t> v(t) v q O B d 5.: 5.3: t = B(r) =B ẑ [T] [m] S [m ] + ω [rd/s] ±ρ [C/m 3 ] () ρ [m] v [m/s] () E [V/m] ρ [m] dρ [m] ( ρ [C/m 3 ]) v(ρ)= v φ (ρ)ˆφ E(ρ)=E ρˆρ (3) E v V [V] B = B ŷ [T] (B > ) t =s ( q [C] m [kg]) r() = ˆ + ŷ [m] v() = v ˆ + v 3 ẑ = v [m/s] t> v(t) r(t) R [m] ω [rd/s] ω ω B E 6

18 B 5.4: 5.5: t = 9. CRT(Cthode R Tube; ) ( ) ( ) ( m e [kg]) ( B = B ŷ, ( d), B [T] ) 5.6(b) t =s t = v() = v ˆ (v [m/s] ) e [C] (e>) >d[m] ± ± ( = d ) t [s] () <t<t F = ev(t) B [N] v(t)=v (t)ˆ+v (t)ŷ +v (t)ẑ,, B v () v() = v ˆ <t<t v(t) (3) r(t)=(t)ˆ+(t)ŷ+(t)ẑ dr(t) = v(t) dt r() = <t<t r(t) (4) B B (5) (4) t [s] r(t ) v(t ) (6) =d [m] P Anode Cthode P [m] N S P () CRT P (b) B d P d 5.6: CRT ( P ) 7

19 6. q [C] [m] ω [rd/s] (ω = ωẑ) m [A m ] c. [m] σ [C/m ] ω [rd/s] (ω = ωẑ) m [A m ] I [A] [m] b [m] µ r = ρ [m](<ρ<b) B [T] H [A/m] [m] b [m] µ r = I ρ C ρ 6.: () l =5mm A 6.3(b) A l g =.5mm B Φ[Wb] 6.3(b) I B A I A [A] N µ r = ( H4 ) ➀I B I A [A] ➁I B I A [A] ➂I B 5I A [A] ➃I B I A [A] ➄I B 5I A [A] 6.: 4. [m] b [m] c [m] µ r ( ; 6. ) N () I [A] ρ [m] ( : ρ [m] ) () Φ[Wb] 6.3: µ [H/m] b Φ[Wb] S [m ] (b, cd, ef, c, e, bd, bf) l [m] C N C I [A] 8

20 ( H5 ) ➀Φ= N Iµl ➁Φ= N IµS ➂Φ= NIµS S 5l l ➃Φ= NIµl S ➄Φ= NIµS 5l / ) ) (3) B i,m B M θ : [m] ( µ [H/m]) ( B [T]) M [A/m] ➀ B i [T] ➁ B m = 4π3 M [A m] 3 B m [T] : B = B +B m (B m ) B i M 6.5 B = B ẑ,m = Mẑ,B i = B i ẑ ( []H6 ) () r = B, B i, B m ˆr, ˆθ, ˆφ µ m 6.5: ( µ r,µ r l,l [m]) δ [m] N I [A] S [m ], H, H [A/m] H [A/m] () C H dr = NI NI = () l + (b) l + (c) δ () (c) () Φ[Wb] H,H,H Φ (3) Φ ( : φ (.8)-(.) ) () B i M ( : r,θ (= 6.6: 9

21 7. 7. B = B ŷ [T] ( [m] b [m]) θ () () θ(t)=ω t B b θ θ ➀ Φ/ t ➁Blv ➂d c b ➃Blv ➄B ➅ Φ t ➆ ➇b c d ➈Blv ➉A 7.: 7.:. 7. D v [m/s] B [T] D l [m] ( ) b pq H 7 ) ( D e [V] D t [s] Φ [Wb] e = [V] dc pp q q t b pp q q t D e = [V] e D D [V] D : ( :A, B) t =s [m] b [m], ( ) U [V] ( [3]H7 3 ) () B = B cosω tẑ [T] U [V] () B = B ˆ [T] ω [rd/sec] U [V] (3) B = B cosω tˆ [T] ω [rd/sec] U [V]

22 R [Ω] U 7.4: [m] d [m] (d ) I [A] ( ) l [m] (i) L i [H] [m] l [m] () [J] L ii L i = (b) [H] (ii) r = ẑ ( H() [A/m] ( ) H()= (c) Φ[Wb] Φ= ˆ l ˆ d µ H ds = (d) dd = (e) S = = L e [H] Φ=L e I L e = (f) L [H] L =L i +L e = (g) d O 7.5: ( [m] N [m ] ) I [A] ( B ŷ [T]) S [m ] ( ) ( ) I I b () B () ˆn ŷ θ (ˆn ŷ =cosθ) Φ[Wb] θ (3) M [H] (4) ω [rd/s] I(t) [A] t = θ = (5) ( ω ) R Q [J] n θ Coil 7.6: ( µ [H/m] S [m ] l [m]) ( N ) ( N ) () I [A] Φ [Wb] () N Φ L [H] W m [J] w m [J/m 3 ] (3), M [H] (4) (V [V]) Φ[Wb] V [V] V, V Φ Φ V V R

23 ( µ) N N l 7.7: ( ) M [H] M [H] h b+s b b d +s 7.8: 7.9:

24 8 Mwell. + : E (,t)=f( c t), H (,t)= Z f( c t) f(u) (ε,µ ) c = ε µ =3. 8 [m/s] (σ =) f(u)=h( u),,(ζ>) H(ζ)=,(ζ<) () t =s t =. 9 s E =m =m E ( ) E t = E E = E t E t = 9 E () S(,t)[W/m ] E = E (3) 8. m m m=m 3 V( S) () <t</c S t (E H) ds [W] ds V (b) <t</c V : w e dv V w m dv [J] V (c) = S(E H) ds d (w e +w m )dv dt V V 8.:. + : E (,t)=f( c t), H (,t)= Z f( c t) f(u) c = [m/s] ε µ () f(u)=e cos( k u) E,H k = ω c [rd/m] ω [rd/s] () S(r,t) (3) 8. = b [m ] T = π [s] W [J] ω ˆ T ˆ b ˆ W S(,,,t) ẑdddt (4) t = π ω b = = c T V t = π ω 3

25 V V c T b 8.: 4

26 ( ). AD, BC, t,s ( t, s ) +t(d ), c+s(b c) 3 s,t 3 +t(d )=c+s(b c) 3 sb ( t) td+( s)c = b d+c = s = t = t = s t = 3, s= 3. A, B, C A,B,C = B A,b = C B,c = A C, =,b= b,c= c c = b c = c c =( b) ( b)= +b + b = +b +bcosθ 3. A, B, C A,B,C = B A,b = C B,c = A C A, B, C m,b m,c m c m r c A r c = +l ( +b ), l b m r b A ( r b = +m b+ c ) = +m {b } ( b) m +l ( +b ) = +m ( + b ), ( = +m + b ) ( + l ) ( +lb = m ) + m b l = 3,m= b 3 m m r A r = n n n = b 3 4. () AB B A BC C B B A =(B A) (B A)= B + A B A = A B = C B =(C B) (C B)= C + B B C = B C () B A = A B A B (3) A B = B C = C D = A C = A C = B D p ( + b A,B +(b+c+d)p =, b+(c+d+)p = ( b)+(b )p =( b)( p)= p = b b = c, c = d (4) 3 A +(b+c+d)p = (+3p)= p = A B =cosθ = 3 5. AB = A, BC = B, CA= C A+B +C = AF = γa, BD = αb, CE = βc α,β,γ AE = ( β)c = κaf +( κ) AD κaf +( κ) AD = κγa+( κ){a+αb} = κγa+( κ){a+α( C A)} = {κγ +( κ)( α)}a ( κ)αc = ( β)c κγ +( κ)( α)= κ = α γ +α ), 5

27 6. β = γα γ +α, AF BDCE FBDC EA = γ γ α α γ +α+γα β= = ( α)( γ) γ +α γ +α β β = γ γ α ( α)( γ) = α γα () S â = () ˆ â = ŷ + ẑ ˆb = ˆ â ˆ â = ŷ + ẑ (3) ĉ = â ˆb ĉ = ˆ ŷ ẑ (4) S b = S ˆb,S c = S ĉ S b =,S c = 3 9 ( 3 S = + 9 ) â+ ( 3 9 ) ĉ ˆb+ (5),, S = =5,b,c { ( } 3 S = + ) 9 ( ) ( ) =5 7. ( ) b b () = b b =( b) b b = 3 5 (3ŷ 4ẑ), = =ˆ 36 5ŷ 7 5ẑ () b =9ˆ+8ŷ +6ẑ 8. r(θ)=ŷ + ˆ+ (sinθˆ+cosθẑ), π θ π 9. 4 () r(θ)=cosθˆ+sinθŷ+ŷ, π θ π () r(θ)=cosθˆ+sinθŷ+ˆ+ŷ, π θ π (3) r(θ)=cosθˆ+sinθŷ+ˆ, π θ π (4) r(θ)=cosθˆ+sinθŷ, θ π..3 r = ŷ +ẑ, d, <<.4 r = ˆ+ẑ,, c c. r(,)=ˆ+( +)ŷ +ẑ,,. r(s,θ)=3scosθˆ+ssinθŷ +ˆ+4ŷ, s, θ<π 3. r = ˆ+ŷ +( )ẑ,, r(ρ,φ,)=ρcosφˆ+ρsinφŷ +ẑ, 3, ρ 3, φ<π 5. r(ρ,φ,)=ŷ +ρcosφˆ+ρsinφŷ +ẑ, ρ, φ π, 4 6. ˆ =cos π 6 ˆρ sin π ˆφ,ŷ 6 =sin π 6 ˆρ+cosπˆφ 6 7. () A(r o )=ˆ+ŷ +6ẑ () ˆρ =cosφˆ+sinφŷ, ˆφ = sinφˆ+cosφŷ ˆρ = ˆ+ ŷ, ˆφ = ˆ+ ŷ 6

28 (3) ˆ =cosφˆρ sinφˆφ = ˆρ ˆφ, ŷ =sinφˆρ+cosφˆφ = ˆρ+ ˆφ r = ˆ+ŷ + ( 6ẑ = ˆρ (4) A(r )=ˆ+ŷ +6ẑ = ˆρ+6ẑ (5) r =,r = ˆr ) ˆφ ( + ˆρ+ ) ˆφ + 6ẑ = ˆρ+ 6ẑ ˆ =sinθcosφˆr +cosθcosφˆθ sinφˆφ, ŷ =sinθsinφˆr +cosθsinφˆθ +cosφˆφ, ẑ =cosθˆr sinθˆθ θ =tn 6 =tn 3 = π 6, φ = π 4, ˆ = 3 + ˆr ( r = ˆr + ( ) 3 6 ˆθ = ˆr ( (6) A(r )= ˆr + ( ) 6 3 ˆθ ˆθ 3 θ ˆφ 3 ˆφ, ŷ = + ˆr ) ( 3 + ˆr + ) ( 3 θ ˆφ + ˆr + ˆθ + ˆφ, ẑ = 3 ) ˆθ + ˆφ R = {( ) +( ) +( ) } R = R, ˆ ˆr ˆθ ( ) ( 3 ˆr ˆφ = + 3 ) ˆr+ ) ( ) ( ) ˆθ + 3 ˆφ +6 ˆr = ˆθ +3 3 ˆr+ 9. Ads = 3ˆ+log 5 ŷ + 3 4ẑ..: r(s)=s ˆ+sŷ, <s<, dr =(sˆ+ŷ)ds.: r(φ)=cosφˆ+sinφŷ, π 4 φ 7 4π, dr = ( sinφˆ+cosφŷ)dφ r = ˆ+sŷ, s, dr = dsŷ ( ) = d ( ) R R dr R = R 3. r = cosφˆ + sinφŷ, φ π dr = ( sinφˆ +cosφŷ)dφ A = cosφˆ ˆ A dr = sinφcosφdφ A dr =. C r = ˆρ = (cosφˆ+sinφŷ), φ π dr = dφ( sinφˆ+ cosφŷ) A = ˆ + 3 ŷ + ẑ = 3 sinφcos φˆ + 3 cos 3 φŷ + cos φẑ C A dr = ˆ π ˆ π ( 3 sinφcos φˆ+ 3 cos 3 φŷ + cos φẑ) ( sinφˆ+cosφŷ)dφ = ( 3 sin φcos φ+ 3 cos 4 φ)dφ= π4 3. r C = ˆ, < dr C = dˆ A(r C )= 3 ˆ = ˆ ˆ ˆ dˆ = d = = 4. r(s)= sˆ+sŷ, s< dr =( ˆ+ŷ)ds A(r) A(r(s)) = sˆ+sŷ = ˆ+ŷ s 3 ds A dr = s5 s ˆ ˆ ds A dr = s = [ ] = s ˆ [ ] 7

29 5. r () = ˆ+logŷ, e dr =(ˆ+ ˆ ŷ)d e (log)ˆ (ˆ+ =ˆ e ŷ)d (log)d = r()=e ˆ+ŷ, ˆ dr =(e ˆ+ŷ)d ˆ (e ˆ+ŷ)d = e d = 6. ds = r u r dudv = ẑdudv A = ˆ +uŷ +vẑ A ds = vdudv v ˆ ˆ ˆ A ds = vdudv= 3 7. r(θ,φ)=sinθcosφˆ+sinθsinφŷ +cosθẑ, θ π, φ π ds = r r dθ θ φ dφ = sinθ(sinθcosφˆ+sinθsinφŷ+cosθẑ)dθdφ A(r) A(r(θ,φ)) = sinθcosφˆ A ds = 3 sin 3 θcos φdθdφ ˆ π ˆ π A ds = 3 sin 3 θcos φdθdφ= 4π3 3 r(θ,φ)= ˆr(θ,φ), θ π, φ<π r θ = ˆr r = ˆθ, θ φ = ˆr φ = sinθ ˆr sinθ φ = sinθˆφ ds = r θ r φ dθdφ = sinθ ˆθ ˆφdθdφ = sinθdθdφˆr A A = ˆ = sinθcosφ(sinθcosφˆr+cosθcosφˆθ sinφˆφ) A ds = 3 sin 3 θcos φdθdφ 8. r(θ,φ)=sinθcosφˆ+sinθsinφŷ +cosφẑ = ˆr, θ π, φ<π ds = r θ r φ dθdφ = sinθdθdφ(sinθcosφˆ+sinθsinφŷ + cosθẑ)= sinθdθdφˆr A = r(θ,φ)=ˆr ˆ π ˆ 3ˆ π π ˆ π A ds = ˆr ˆr sinθdθdφ= dφ sinθdθ=4π 3 9. r(,)=ˆ+ŷ+( )ẑ,, ds = r r d d =(ẑ +ŷ + ˆ)dd ˆ ˆ ˆ ˆ = ˆ A(r(,)) ds = ˆ ˆ { + +( ) }dd = [ 3 +( ) +( ) ] d = { ˆ+ ŷ +( ) ẑ} (ˆ+ŷ +ẑ)dd ˆ ˆ ˆ {3 +( ) +( )}dd = ( 3+ )d = 6 3. ρ,φ ρ r =(cosφˆ+sinφŷ)dρ = ˆρdρ, φ r = ρ( sinφˆ+ cosφŷ)dφ = ρdφˆφ ds = ρ r φ r = ρdρdφẑ ˆ πˆ ˆ ˆ π (ρsinφˆ+ρcosφŷ +ρ sinφcosφẑ) ẑρdρdφ= ρ 3 dρ sinφdφ= 3. V r(r,θ,φ) =rˆr(θ,φ), r, θ π, φ π dv = r sinθdrdθdφ φ =3 + + =3r ˆ π ˆ π ˆ φ(r)dv = 3rr sinθdrdθdφ=48π V 3. V r = ρcosφˆ+ρsinφŷ+ẑ, ρ, φ<π, ρ r = ˆρdρ, φ r = ρˆφdφ, r = dẑ dv = ρ r φ r r = ρdρdφd ˆ ˆ π ˆ (ρcosφ+ρsinφ+)ρdρdφd= 8

30 ˆ ˆ ˆ [ ] ρ ˆ π ρdρd =π dρ = π ( ) d = π 33. V r(r,θ,φ)=rsinθcosφˆ+rsinθsinφŷ+rcosθẑ ( = rˆr, r, r θ π, φ<π dv = r r ) r θ φ drdθdφ = r sinθdrdθdφ A = r ˆ π ˆ π ˆ ˆ V A dv = ˆ π ˆ π r r sinθdrdθdφ= rdr sinθdθ dφ =π 34. () e () e =.57 (e ) e =.9483 (e ) (3) sin = (4) cos = (5) e jθ =+(jθ)+ (jθ) + 6 (jθ)3 + 4 (jθ)4 + (jθ)5 =+jθ θ j 6 θ3 + 4 θ4 +j ( θ5 = θ + ) 4 θ4 =cosθ+jsinθ 35. () () 3 54 ( 8) ( +j θ 6 θ3 + ) θ5 36. log e ( ) ( ) + 3 ( )3 4 ( )4 log e = f() r f f (r)= π 39. () ϕ(r)= r =( + + ) f (r)=, (r), f f ( π ), (r)=, (r)= f(r) + { ( π ) ( π ) ( ) π( π )( )} ϕ = ϕ ϕ ˆ+ ŷ + ϕ ẑ = ( + + r ) 3 (ˆ+ŷ +ẑ)= r 3 () ( ϕ)(r ) ˆ = 5 5 (3) ( ϕ)(r ) (ˆ+ŷ)= 3 5 9

31 (4) ( ϕ)(r ) ( ϕ)(r ) ( ϕ)(r ) = ( ϕ)(r ) ( ϕ)(r ) 4. = ( ϕ)(r ) = 5 ( ϕ)(r ) ( ϕ)(r ) = ˆ+ŷ 5 () f(,) f()+ f f ()+ () + f () + f () + f () F(,) { } { } f f () F = ()+ f f ()+ () ˆ+ ()+ f ()+ f () ŷ (3) dr =(ˆ+ŷ)d ˆ ˆ [{ } f f F dr = C ()+ f ()+ () ˆ { } ] f + ()+ f ()+ f () ŷ (ˆ+ŷ)d ˆ [ { f } ] = ()+ f f ()+ () +3 f () + f ()3 d = f () + f () + f () + f ()3 + f ()4 (4) F(r ) F(r ) = f()+ f () + f () + f () + f () + f ()4 f() = f () + f () + f () + f ()3 + f () lim V V = lim V = V S ˆ = V V [ ] + fdv= lim V A ds V ˆ + f(r)dv = lim V ˆ + ˆ + ˆ + ˆ + ˆ + [ V ] + ˆ + fdv= V [ ˆ + ˆ + ] + lim,, = lim ˆ + = lim V ˆ + d d d = sink d d d k sink sin = k { } sin k k A(+,, ) ˆd d + sink = sink sinksin k k A(,, ) ( ˆ)d d { } A(,+, ) A(,, ) ŷd d { A(,,+ ) A(,, {(+ ) ( ) }d d + + {3sin(k{ + }) 3sin(k{ }) } d d = [ ] + {+ + }+ [ ] + 3 )} ẑd d {( + ) ( ) }d d { }

32 = C + + [ 3] + { sin(k{ + }) sin(k{ })} = +4 + ( lim V S V lim V V A dr = ˆ + ˆ + lim S A ds = A ds = +4+3 lim = +4+3 kcosk S ˆ + = ˆ ˆ + ˆ + ˆ + ˆ + ˆ + ˆ ˆ + ˆ + ˆ + ˆ + ˆ + ){sin(k{ + }) sin(k{ })} {sin(k{ + }) sin(k{ }) { A (+,, ) A (,, ) } d d { } A (,+, ) A (,, ) d d { A (,,+ ) A (,, )} d d { (+ ) ( ) } d d { ( + ) ( ) } d d { sink( + ) sink( ) } d d = + + cosk sink A ds = ++ sink kcosk = ++kcosk = A k ˆ + A(,, ) ŷd + A(, +, ) ẑd + ˆ + { ( ) ( + )} d + A dr = S C A(,,+ ) ( ŷ)d A(,, ) ( ẑ)d ˆ + ( )d = ˆ + d = 46. () A =3 AdV =3 4π3 =4π 3 V 3 () r(θ,φ)=ˆr, θ π, φ<π ds = ˆ sinθdθdφˆr A A = ˆr π ˆ π A ds = ˆr ˆr sinθdθdφ=4π 3 S. r = ẑ, < < dr = d ẑ, dr = d λ d r = ˆ+ŷ+ẑ de de = λ d {ˆ+ŷ +( )ẑ} 4πε { + +( ) } 3 3

33 ˆ E = [ ˆ d ˆ +ẑ de = λ (ˆ+ŷ) d 4πε { + +( ) } 3 { + +( ) } 3 ] E = λ (ˆ+ŷ) πε ( + ). r (φ )=cosφ ŷ + sinφ ẑ, φ π dr = ( sinφ ŷ+cosφ ẑ)dφ dr = dφ r = ˆ,r r = ˆ cosφ ŷ sinφ ẑ r r =( + ) E = ˆ π Q π dφ ˆ (ˆ cosφ ŷ sinφ ẑ) Q π = (ˆ cosφ 4πε ( + ) 3 4π ε ( + ) 3 ŷ sinφ ẑ)dφ Q = (ˆ[φ 4π ε ( + ) 3 ] π +ẑ[cosφ ] π Q )= (πˆ ẑ) 4π ε ( + ) 3 3. r = r cosφ ˆ+r sinφ ŷ, r, φ < π r r =(cosφ ˆ+sinφ ŷ)dr, φ r = r ( sinφ ˆ+cosφ ŷ)dφ ds = r r φ r = r dr dφ ẑ ds = r dr dφ σds r = ẑ de de = σr dr dφ (ẑ r cosφ ˆ r sinφ ŷ) (r + ) 3 ˆ ˆ π ˆ σr (ẑ r cosφ ˆ r sinφ ŷ) E = de = dr 4πε (r + ) 3 dφ = σẑ ˆ r dr = σẑ ( ) ε (r + ) 3 ε + 4. r (φ, )=cosφ ˆ+sinφ ŷ+ ẑ = ˆρ(φ )+ ẑ, φ < π, h h φr =( sinφ ˆ+cosφ ŷ)dφ = ˆφ(φ )dφ r = d ẑ ds = φ r r = ˆφ(φ ) ẑdφ d = ˆρ(φ )dφ d ds = ds = dφ d r = ẑ, r r = ˆρ(φ )+( )ẑ, r r = { +( ) } E = ˆ hˆ π Q πh dφ d { ρ(φ )+( )ẑ} = Q ˆ h d 4πε h { +( ) } 3 4πε hẑ h { +( ) } 3 = Qẑ 4πε h +( h ) +( + h ) 5. r (θ,φ )=sinθ cosφ ˆ+sinθ sinφ ŷ +cosθ ẑ = ˆr(θ,φ ), θ π, φ < π r = ẑ ds = ds = θ r φ r = sinθ dθ dφ r r = sinθ cosφ ˆ sinθ sinφ ŷ +( cosθ )ẑ r r =( + cosθ ) E = ˆ π ˆ π Q 4π sinθ dθ dφ { sinθ cosφ ˆ sinθ sinφ ŷ +( cosθ )ẑ} 4πε ( + cosθ ) 3 = Q ˆ π sinθ ( cosθ ) ẑ = Q 8πε ( + cosθ ) 3 4πε ẑ φ, + cosθ = t Q(ˆ+ŷ +ẑ) 6. E = 4πε ( + + ) 3 r(φ,)=cosφˆ + sinφŷ + ẑ = ˆρ + ẑ, φ<π, h h r ds = φ r dφd = φ ẑdφd = ˆρdφd 3

34 ˆ h h ˆ π Q ˆρ+ẑ 4πε ( + ) 3 ˆρdφd= ˆ h h ˆ π Q dφd 4πε ( + ) 3 ˆ h = Q d = Q h ε h ( + ) 3 ε h +4 h = ρˆρ+ ẑ, φ<π, ρ r(ρ,φ)=ρcosφˆ+ρsinφŷ + h ẑ ds = r ρ r φ dρdφ = ˆρ ρˆφdρdφ = ẑρdρdφ ˆ π ˆ Q ρˆρ+ h ˆ π ˆ ẑ Q h ρdρdφ ẑρdρdφ= = Qh ˆ ρdρ = Q ( ) h 4πε (ρ + h 4 )3 4πε (ρ + h 4 )3 4ε (ρ + h 4 )3 ε 4 +h E ds = Q { ( )} h S ε h +4 + h = Q 4 +h ε 7. r =ẑ r = {sinθ(cosφˆ+sinφŷ)+cosθẑ}, θ π, φ<π r r = {sinθ(cosφˆ+sinφŷ)+(cosθ )ẑ}, r r = {sin θ+cos θ 4cosθ+4) = (5 4cosθ) ds = sinθdθdφˆr E = Q r r 4πε r r 3 E ds = Q ˆ π ˆ π {sinθ(cosφˆ+sinφŷ)+(cosθ )ẑ} ˆr sinθdθdφ S 4πε 3 (5 4cosθ) 3 = Q ˆ π ˆ π sin θcos φ+sin θsin φ+cos θ cosθ sinθdθdφ= Q ˆ π cosθ sinθdθ= 4πε (5 4cosθ) 3 ε (5 4cosθ) 3 8. () [m] E(r) r θ,φ (ρ, φ ) 3θ,φ 4 () E(r) ρ φ, (r φ, ) 3φ, 4 (3) E(r) 3φ 4 (4) [m] E(r) 3φ 4 (5) [m] E(r) 3φ 4 (6) E(r) ρ, φ (r,θ φ ) ρ, φ (r,θ φ ) ρ, φ (r,θ φ ), ( ) ( ρ,φ )(r,θ φ ) 3, (ρ,φ ) 4 = (7) [m] E(r) (,, ) 3 4 (8) [m] h [m] E(r) 3φ 4 ρ, φ (r,θ φ ) 33

35 (9) [m] E(r) ( ) ) 3φ 4 r,θ φ (ρ, φ 9. r E = = ρ = ε ε ε ε r E = 4 3 ε r ε r ( ε r 3 = 43 3 ε r 3 + r 3 + r 3 + ) ( ) ( ) r 3 = 43 3 ε r 3 3 r 5 3 r 5 3 r 5 = 43 3 ε r 3 3r r 5 = ρ =. l ρ πρle(ρ)= λl, E(ρ)= λ ε πε ρ. l ρ πρle(ρ)= ε πσl, E(ρ)= λ πε ρ, (ρ ) πρle(ρ)=, E(ρ)= (ρ<). () Q Q Q E(r)=, r< E(r)= Q 4πε r ˆr, r< E(r)=, r< E(r)= Q 4πε r ˆr, r () Q E(r)=, r< E(r)= Q 4πε r ˆr, r 3. r r 4πr E = Q 4πr 3 = r3 Qr ε 4π 3 3 ε 3 3Q E = 4πε 3 <r b 4πr E = Q E = Q ε 4πε r b<r c 4πr E = ( Q 4πr 3 )+ 4πb3 Qε = Qε c 3 r 3 Q c 3 r 3 ε 4πc 3 3 4πb3 3 3 c 3 E = b3 4πε 3 r c 3 b 3 r>c 4πr E = E = 4. () r r 4πr E r = ρdv = ε 4π ˆ r 3Q V ε π 4( r )r dr = Qr3 ε 4(4 3r) E r = Qr 4πε 4(4 3r) r> 4πr E r = Q ε 4 E r = Q 4πε r 34 ˆ ( r )r dr = Q ε

36 () r E = E rˆr = Qr 4πε 4(4 3r)ˆr = Q 4πε 4(4 3r)r Q r> 4πε r ˆr = Q 4πε r 3r (3) r =3, rr =4r, r = r3 r ε E = Q 4π4 (4r 3rr)=3Q( r) π 4 r> ε E = Q 4π r { r 3 = (4) rˆr =, r ˆr (r) = (r) } { (r) ˆ+ (r) } { (r) ŷ+ (r) } ( ẑ = r ) r ˆ+ ( ) = E = Q 4πε 4(4 rˆr 3 rˆr)= ˆr Q = E = ˆr r 4πε r = 5. E = λ πε ρ ˆρ = λ (ˆ+ŷ) πε ( + E = ) Q{ˆ+( )ŷ +ẑ} E = λ (ˆ+ŷ) Q{ˆ+( )ŷ +ẑ} 4πε { +( ) + } 3 πε ( + + ) 4πε { +( ) + } 3 A) ρ B) dˆ b ρ A) ρ E ρ = πρ ρ = ρ ρ = ρ ρ πρε ε ε E = ρ ( + ) ˆ+ŷ = ρ (ˆ+ŷ) ε ( + ) ε ρ> E ρ = π ρ πε ρ = ρ ε ρ ˆ+ŷ E = ρ ε ( + ) ( + ) = ρ (ˆ+ŷ) ε ( + ) B) dˆ ρ ρ <b E ρ = πρ ρ πε ρ = ρ ρ ε E = ρ {( d) + } ( d)ˆ+ŷ = ρ {( d)ˆ+ŷ} ε {( d) + } ε ρ >b E ρ = πb ρ πε ρ = b ρ ε ρ E = ρ ρ b ε ρ = ρ {( d)ˆ+ŷ} b ε {( d) + } ( d) + b E = ρ dˆ ( d) + >b + ε E = ρ [ ˆ+ŷ b ( d)ˆ+ŷ ] ε ( d) + + > E = ρ { ˆ+ŷ b( d)ˆ+ŷ } ε + ( d) + 6. r = ˆ, < dr = d ˆ E = Q(ˆ+ ŷ + ẑ) E(r)= Q ˆ < { } 4πε { + + } 3 4πε { } 3 = E(r)= Q ˆ 4πε 3 = Q ˆ 4πε W = ˆ E dr = Q 4πε ˆ Q ˆ ( d ˆ)= 4πε ˆ d = Q 4πε 35

37 7. r = ŷ +ˆ, < dr = dŷ ˆ W = E(r) dr = Q ˆ ŷ +ˆ dŷ = Q ˆ d = Q 4πε ( + ) 3 4πε ( + ) 3 4πε 8. φ = Q { ( ) ˆ+ ( ) ŷ + ( ) } ẑ 4πε r r r r r r r r = { ( ) +( ) +( ) } = { ( ) +( ) +( ) } 3 ( )= r r 3, φ = Q 4πε 9. () r> 4π3 3 ρ E = { ( )ˆ+( )ŷ +( )ẑ r r 3 4π 3 4πε r 3 ρ = ρ 3 3ε r r 4πr E = ε 4π 3 () r r> E = ρ 3 {( 3ε = ρ 3 3ε ρ r 3ε E = ˆr, (r ) ρ 3 3ε r ˆr, (r>) } 3 ρ E = = Q 4πε r r r r 3 4πr 3 4πε r 3 ρ = ρ r 3ε E = ρ {( 3ε ) ( ˆ+ ) ( ŷ + ) } ẑ = r 3 {( 3 r r 5 ) r 3 ) ˆ+ ( ˆ+ r 3 ( 3 r r 5 ) r 3 ) ŷ + ( ŷ + r 3 ) } r 3 ẑ ) } ẑ = ( 3 r r 5 (3) r> r = ssinθcosφˆ ssinθsinφŷ scosθẑ = sˆr, <s r ˆ dr = ˆ ˆrds r ρ 3 ˆ r ρ 3 ds ϕ(r)= E dr = ˆr ( ˆr)ds = 3ε s 3ε s = ρ 3 3ε r r r =( s)ˆr, s r r ˆ dr = ˆrds ˆ r ρ ϕ(r)= E dr +ϕ(ˆr)= ( s)ˆr ( ˆr)ds+ ρ 3 ˆ 3ε 3ε r ρ = ( s)ds+ ρ = ρ ) (3 r 3ε 3ε 6ε (4) r> ϕ = ρ 3 3ε ϕ = ρ 3 3ε r ˆr r ϕ = ρ ϕ = ρ r 3ε ˆr ( ) = ρ 3 ( r 3ε r 3 ˆ r 3ŷ ) r 3ẑ = ρ 3 ( r ) 3ε r 3 = ρ 3 3ε r ˆr r = ρ ( r ) 6ε 6ε r ˆ+r rŷ +r rẑ 36 = ρ 3ε ˆr = ρ r 3ε ˆr

38 (5) r> ϕ = ( ϕ)= ( ρ 3 ( r ϕ = ρ ) r ˆr = ρ 3ε 3ε ) 3ε r ˆr = ρ 3 ( 3ε r 3 + ( + + ) = ρ ε r 3 + ) = Qr. r > E = 4πε r 3 r E = Q 4πr 3 r 4πε r 4π 3 3 r = 3 Qr 4πε 3 r = sr, <s r r = r = s = s dr = dsˆr ˆ r> ˆ r ˆ Q sr r φ(r )= E dr = 4πε s 3 ( dsˆr)= Q ds 4πε s = Q r 4πε r ˆ ˆ r Q φ(r )= E dr = φ()+ 4πε 3( sˆr) ( dsˆr)= Q ˆ r 4πε Q 3Q 4πε 3sds= 8πε Qr 8πε 3. r r =( d )ˆ+ŷ,r r =(+ d )ˆ+ŷ Q Q ϕ(r)= { ( ) { d (+ ) 4πε + } d 4πε + } { ( d ) } ) ) + = ( + d+ d = (r d+ d 4 4 { = ( ) } d d [ { r r r + ( ) }] d d r r r r + r r + d r 3 { ( + d ) } + r d r3 ϕ Q 4πε {( r + d r 3 ) ( r d r 3 )} = (Qd) 4πε r 3. p = p ˆ + p ŷ + p ẑ,r = ˆ + ŷ + ẑ r =( + + ) ϕ(r)= p r 4πε r 3 = p +p +p 4πε ( + + ) 3 { } ϕ = p 3 p r = 4πε ( + + ) 3 ( + + ) 5,, E = ϕ = { 4πε r 3 p ˆ+p ŷ +p ẑ 3 (p r) r (ˆ+ŷ +ẑ) r 3 { 4πε r 3 p 3 (p r) } r } = { 4πε r 3 p+3 (p r)r } r ( ϕ(r)= pcosθ 4πε r ( ϕ ϕ = r ˆr + ) ϕ r θ ˆθ = pcosθ psinθ πε r3ˆr + 4πε r ˆθ 3 = prcosθrˆr p(cosθˆr ẑ) πε r 5 + 4πε r 3 = pẑ (p r)r +(p r)r + 4πε r3 4πε r 5 3. r E = Qr Q r> E = 4πε 3 4πε r w [J/m3 ] w = ε E r w = Q r 3π ε 6 r> w = Q 3π ε r4 ˆ Q r 3π ε 64πr dr + ˆ Q 3π ε r 44πr dr = 3Q πε 37

39 3. C = ε S d () CV = Q C = Q d ε S () E E = Q ε S ε E ε E V = ε Q Q d ε SSd= ε S. E = Q 4πε rˆr r ˆr () C = 4πε (, CV = Q C = Q ) 8πε () E = Q 4πε r w = ε Q ˆ E = 3π ε r 4,W = Q ( wdv = 3π ε r 44πr dr = Q ) 8πε (3) d = C = 4πε = 4πε = 4πε ( +d) = 4πε d S =4π C εs d (+ d ) 4πε d 3. A + > πe A = λ E A = λ B ε πε <b π(b )E B = λ λ E B = E <<b ε πε (b ) E =(E A +E B )ˆ = λ ( πε + ) ˆ ( b ) r =(b t)ˆ,( t b ), dr = dtˆ ˆ b ( λ V = πε b t + ) ˆ ( dtˆ)= λ ˆ b ( t πε b t + ) dt = λ log b ( λ log b ) ( ) t πε πε 4. C = λ V = πε log b () v = q 4πε () dw = vdq= q4πε dq ˆ (3) W = dw = 4πε πε log b ˆ Q qdq= Q 8πε (4) C =4πε W = Q C = Q 8πε 5. A +Q B Q Q r = ˆ,(<<d b) E = 4πε ˆ + Q ˆ 4πε (d ) 38

40 V = ˆ A B 4πε + b d E dr = Q ( 4πε d d b + ) b C = Q V = 4πε ) A, B Q, Q V A = Q 4πε V B = Q 4πε b + Q 4πε (d b) Q 4πε C = = V A V B d d b + b Q 4πε (d ), d d b + b ) A, B Q A,Q B V A,V B Q B = V A = Q A 4πε,V B = Q B 4πε (d b), Q A = [ V A V B ] = [ 4πε 4πε (d b) 4πε (d ) 4πε b ] [ ] Q A Q 4πε Q A = Q,Q B = Q V A,V B C = = V A V B d d b + b 6., V,V [ ] [ Q,Q ] [ ] V p p Q = V p p () Q V = Q 4πε = p Q,V = Q 4πε d = p Q p = 4πε,p = 4πε d p = p p = 4πε d () V = Q = Q = 4πε Q + Q 4πε d Q Q = d Q Q Q B 4. D =5ε E = ε (ŷ+5ẑ) E = E ŷ+e ẑ, D = D ŷ+d ẑ E = E =, D = D =5ε D =3ε E =6ε, E = D =5 E =ŷ +5ẑ, 3ε D = ε (6ŷ +5ẑ). E = E,E = E E sinθ = E sinθ ε E cosθ = ε E cosθ tnθ = tnθ ε ε 3. D = ε E =ε ˆ 3ε ŷ ˆt = ˆ+ŷ ˆn = ˆt ẑ = ˆ ŷ ε E D E t = E ˆt =,D n = D ˆn = 5 ε ε E D E = E nˆn+e tˆt,d = D nˆn+d tˆt D n = D n,e t = D t E n = D n /ε,d t = ε E t 5 5 ˆ ŷ 5 ˆ+ŷ D = ε ˆn+5ε E tˆt = ε ε = 5ε ŷ V A = Q 4πε Q 4πε d E = D n 5ε ˆn ˆt = ˆ ŷ ˆ+ŷ = ŷ 39

41 4. () V Q D = Q S,E = Q ε S,E = Q V = ( ε S t E t+e (d t)= + d t ) Q ε ε S C = Q ( t V = S + d t ) ε ε C C = C ( t S = + d t ) ε ε = ε ε ε t+ε (d t) () t V()=E = Q ε S = CV ε S = V ε V C = ε ε t+ε (d t) 5. t< d V()=V(t)+E ( t)=v(t)+ CV ε S ( t)= ε V ε t+ε (d t) t+ ε V ε t+ε (d t) ( t)= ε t+ε ( t) ε t+ε (d t) V () L D πρd = Q L D = Q πρl () E ρ<b E = D ε = (3) V V = πl ε log b + ε log c b ˆ b Edρ+ ˆ c b Q πε ρl b ρ<c E = D ε = Q πε ρl Edρ= Q πε L log b + Q πε L log c b C = Q V = ε ε πρl ε b ρ<c P P = Q ε ε πρl ε P ds = σ p ds σ p =( P +P ) ρ=b = Q ( ε ε + ε ) ε = Q ( ε ε ) πbl ε ε πbl ε ε (4) ρ<b P P = D ε E = Q πρl ε Q πε ρl = Q 6. () Q E = Q πρε L V V = Q ˆ b dρ πε L ρ = Q πε L log b Q = πε L log b V () σ σ d D πρd (L )=πσ (L ) D = σ ρ D d D d = σ d ρ E E d E = σ ε ρ = E d = σ d ε r ε ρ σ = σ d ε r Q π(l )σ +π(ε r σ )=Q σ = ˆ b σ dρ V V = ε ρ = σ log b ε = Q logb πε {L+(ε r )} = L L+(ε r ) V Q logb (3) V = πε {L+(ε r )} C = Q V = πε {L+(ε r )} log b () V = Q πε L log b Q = CV = L+(ε r ) Q L 4 Q π{l+(ε r )}

42 (4) C = πε {L+(ε r )} log b 7. U + U U + U = V U = V () D = ε E = ε ŷ πε {L+(ε r ) } log b U U = CV = V πε {L+(ε r )} log b πε {L+(ε r )(+ )} log b F = V πε (ε r ) log b () D = D = ε ŷ (3) E = D =ŷ ε (4) D = ε E +P P = D ε E =9ε ŷ (5) P ds = σ P S,σ P = ±9ε (6) D ds = σds σ = ε Q = σs = ε S V = 8. d+ 3d = 3d C = Q V = ε S 3d = 4 3 () E = V d = E,D = ε E = ε V d,d V = ε ε r d =5ε V d () σ = D = ε V d,σ = D =5 ε V d ε S 4d (3) Q Q = S 3 σ + S e σ = 5 3 C = Q V = 7 ε S 3 d 4 3 ε V d S+ ε V 3 d S = 7 ε V S 3 d 9. Q D D = Q S E = Q ε S E d = Q ε r ε S V = E d + E d d = Qd ε S + Qd ε r ε S = ( Qd + ) C = Q ε S ε R V = ε ( S d + ) C.8 ε S ε r d ( + ).8 ε r 9 ε r. () ρ = Nq () P = Nqd (3) Nq d r E p + d E p + = (4π r 3 3 ρ)(r d ) 4πε r d E 3 p d Ep = (4π r+ 3 3 ρ)(r + d ) 4πε r + d E p 3 E p = ρ d = P 3ε 3ε 4

43 E = E +E p = E P = E (ε r )ε E 3ε 3ε E = 3 ε r + E = E (ε r )E 3 (4) 4π3 ρ d p 3 p = 4π3 4π3 ρd = 3 3 P P =(ε r )ε E =3 ε r ε r + ε E p = 4π 3ε r ε r + ε E E p = E = E +E p = E ẑ + { ẑ +3 r 4πε r 3 } εr r ε r + { p+ 3(p r)r r 3 r 3E } = { ẑ +3 r } εr r ε r + 3 r 3E 5. r = ẑ, < < dr = d ẑ r = ˆ+ŷ db = µ Idr (r r ) 4π r r 3 = µ Id ẑ (ˆ+ŷ + ẑ) 4π ( + + )3 B = µ ˆ I 4π ( ˆ+ŷ) d ( + + )3 = µ I 4π = µ I( ˆ+ŷ) π( + ) ˆ+ŷ d ( + + )3 = ρcosφ, = ρsinφ + = ρ, ˆ+ŷ = ρ( sinφˆ+cosφŷ)=ρˆφ B = µ I πρ ˆφ. r = cosφ ˆ + sinφ ŷ = ˆρ, φ < π dr = dφ ( sinφ ˆ+cosφ ŷ)=dφ ˆφ r = ẑ ˆ r r = cosφ ˆ sinφ ŷ+ẑ = ˆρ+ẑ r r =( + ) µ Idr (r r ) = B = 4π r r 3 = µ ˆ π ˆ I dφ ˆφ ( ˆρ+ẑ) µ I π µ I = (ẑ +ˆρ)dφ 4π ( + ) 3 4π( + ) 3 = ẑ ( + ) 3 3. r = ẑ, < < Idr = Id ẑ r = ˆ r r = ˆ ẑ, r r =( + ) = B = (ˆ ˆ ) (ˆ µ Id ẑ (ˆ ẑ) ˆ ) µ I + = + 4π ( + )3 4π ŷ d = µ ( ) I ( + )3 πŷ + r = cosφ ŷ+sinφ ẑ, π φ π Idr = Idφ ( sinφ ŷ+cosφ ẑ) r r = ˆ cosφ ŷ sinφ ẑ, r r = + = B = µ ˆ π Idφ ( sinφ ŷ +cosφ ẑ) (ˆ cosφ ŷ sinφ ẑ) = 4π π ( + ) 3 ˆ π µ I (sinφ 4π( + ) 3 ẑ +sin φ ˆ+cosφ ŷ +cos µ I φ ˆ)dφ = (πˆ +ŷ) π 4π( + ) 3 B +B 4. r = cosφˆ + sinφŷ = ˆρ, π 4 φ 7 4 π dr = dφ( sinφˆ+cosφŷ)=dφˆφ r = 4

44 r r = (cosφˆ+sinφŷ)= ˆρ = B = µ 4π µ I 4πẑ ˆ 7 4 π ˆ 7 4 π π 4 Idφφ ( ˆρ) 3 = dφ = 3µ I ẑ 4 π 8 r = ŷ, ˆ+ dr = d ŷ r r = ( ŷ r r = ˆ + B = µ ˆ = µ ˆ I ẑd = µ I 4π 4π πẑ d ŷ ( ˆ ŷ) ( + )3 B = 5. ( ) r = ( ( 3µ I 8 + µ I π ) ẑ = µ I + )3 ( π ) = r = ˆ +( )ŷ, dr =(ˆ + ŷ)d r r = ˆ ( )ŷ r r = { +( ) } = db = µ I(ˆ+ŷ)d { ˆ ( )ŷ} = µ I{ ( )+}ẑ µ Iẑ d = d 4π{ +( ) } 3 4π{ +( ) } 3 4π 3 {( ) + 4 }3 ˆ B B = db = µ ˆ Iẑ d = µ I 4π 3 {( ) + 4 }3 πẑ r = ˆρ, φ 3 π dr = ˆφdφ r r = ˆρ, r r = B B = µ I = dφˆφ (ˆρ) 4π 3 = µ I dφ = 3µ I 4πẑ 8 ẑ B = B +B 6. r = 4 ˆ + ŷ, < < ( ) ( dr = ˆ+ŷ d r = ˆ r r = ) 4 ˆ ŷ, r r = ) ( ) + = ( 4 7. B = µ I 4π = + 4 ˆ ( ˆ 3 π ˆ+ŷ) d {( ) 4 ˆ ŷ } ( ) 3 = µ I + 4 ˆ 4π ẑ ( + 4 ) ẑ ˆ 3 π ) d = µ I 4 ẑ () r = cosφ ŷ +sinφ ẑ + ˆ, < <, φ π () J s = πˆ I (3) ds = dφ d ˆ ˆ π µ B = πˆdφ I d ( cosφ ŷ sinφ ẑ ˆ) 4π ( + ) 3 = µ ˆ ˆ π I cosφ ẑ +sinφ ŷ 4π dφ ( + ) 3 d = µ ˆ I π d ( + ) 3 ŷ = µ I π ŷ 8. () r =(cosφˆ+sinφŷ)r, φ π () dr = R( sinφˆ+cosφŷ)dφ (3) B dr = µ ˆ π I sinφˆ+cosφŷ π R C R( sinφˆ+cosφŷ)dφ = µ I 43

45 (4) r = R ˆ+ŷ, R R dr = dŷ 9. C B dr = µ I π ˆ 7 4 π π 4 = 3µ I 4π + µ I 4π = µ I dφ+ µ I π ˆ R π ˆ+ R ŷ ŷd = 3µ I R R + 4π + µ I π R π R ˆ R d + R () C 4 P Q r = sˆ+ŷ, s dr ˆ = dsˆ B dr = µ I π P Q Q R ˆ ˆ sŷ s + ( ˆ)ds = µ ˆ I ds π s + = µ I 4 Q R ˆ r = ˆ sŷ, s dr = dsŷ B dr = µ ˆ I sˆ ŷ π +s ( ŷ)ds = µ ˆ I ds π s + = µ I 4 R S R S r = ˆ sˆ ŷ, s dr = dsˆ B dr = µ ˆ I ˆ+sŷ π s + ˆds = µ ˆ I ds π s + = µ I 4 S P r ˆ= ˆ+sŷ, s dr = dsŷ B dr = µ ˆ I sˆ+ŷ S P π +s ŷds = µ ˆ I ds π s + = µ I 4 B dr = µ I C () C 4 P T r = sˆ+ŷ, s 3 dr ˆ = dsˆ B dr = µ ˆ 3 I ˆ+sŷ P T π s + ˆds = µ I π α =tn 3 T U ˆ 3 ds ( s + = µ I α π ) π 4 T U ˆ r =3ˆ sŷ, s dr = dsŷ B dr = µ ˆ I sˆ+3ŷ π 9 +s ( ŷ)ds = µ ˆ I3 ds π s + = µ I π β U S β =tn 3 U S r = sˆ ŷ, 3 s dr = dsˆ ˆ B dr = µ ˆ ˆ I ˆ sŷ π s + ( ˆ)ds = µ I ds ( π s + = µ I α π ) π 4 S P 3 S P r ˆ= ˆ+sŷ, s dr = dsŷ B dr = µ ˆ I sˆ+ŷ π s + ŷds = µ ˆ I ds π s + = µ I 4 C B dr = µ ( I α π C π 4 α+β = π ) µ I π β µ I π 3 ( α π ) + µ I 4 4 = µ I π (α+β)+µ I =. ρ I µ πρ,ρ< π πρb(ρ)= µ I, ρ<b, ρ>b 44

46 B(ρ) ρ µ I, ρ π µ B(ρ)= I πρ, <ρ b, ρ>b. ρ + i(ρ) ρ ρ r i(ρ)= I πr πρ = ρ r I πρb(ρ)=µ i(ρ) B(ρ)= µ Iρ πr r <ρ R i i(ρ)=i B(ρ)= µ I πρ R i <ρ R i(ρ)=i ρ Ri R I = R ρ R i R R i ρ>r i(ρ)= B(ρ)=. I B(ρ)= µ I πρ R ρ R R i () r = ŷ ẑ, d d+ dr = dŷ df = Idŷ µ I ( ˆ) π = µ ˆ II dẑ F = df = µ ˆ d+ II d π π d ẑ = µ II d+ log ẑ π d () = d Idr = Idẑ B = µ I ˆ πd df = Idr B = µ I I πd ŷd F = µ I I ŷ πd = d + Idr = Idẑ B = µ I ( π(d+)ˆ df = Idẑ µ ) π(d+)ˆ I = µ I I π(d+)ŷd F = µ I I π(d+)ŷ F tot = µ ( I I ŷ π d ) = µ I I d+ πd(d+)ŷ 3. B = µ I ˆ π ➀ r = dŷ +(h + b)ẑ +(ŷ bẑ)s =(d + s)ŷ +(b + h sb)ẑ, s dr =(ŷ bẑ)ds df = Idr B = I(ŷ bẑ)ds µ I ˆ π(d+s) = µ I I(ẑ +bŷ) ds F = µ ˆ I I(ẑ bŷ) ds π(d+s) π d+s = µ I I(ẑ bŷ) d+ log π d ➁ r =(d+ s)ŷ, s dr = dsŷ µ I ˆ df = Idsŷ π(d+ s) = µ I Iẑ π(d+ s) ds F = µ ˆ I I ds ẑ π d+ s = µ I I π ẑlog d d+ = µ I I d+ ẑlog π d ➂ F 3 = Ibẑ µ I πd ˆ = µ I Ib πd ŷ F = µ ( I I b d+ log b ) ŷ π d d 4. r = cosαcosψˆ+cosαsinψŷ +sinαẑ, α<π dr = dα( sinαcosψˆ sinαsinψŷ +cosαẑ) 45

47 df = Idr B = Idα( sinαcosψˆ sinαsinψŷ ˆ +cosαẑ) B ŷ = B I(sinαcosψẑ +cosαˆ)dα F = df = dn = r df = (cosαcosψˆ+cosαsinψŷ +sinαẑ) ( B I)(sinαcosψẑ +cosαˆ)dα = B I {( sinαcosαcos ψ +sinαcosα)ŷ +sinαcosαsinψcosψˆ cos αsinψẑ}dα ˆ ˆ π N = dn = B I sinψẑ cos αdα= B Iπ sinψẑ 5. () m dv dt = qv(t) Bˆ = qb(v ŷ v ẑ) dv dt = ω c v, dv dt ω c v,v = ω c = qb m d v dt = ω c v v = Acosω c t Bsinω c t v () = A = v v v = dv = v sinω c t +cosω c t v () = B = ω c dt v(t)=v (cosω c tŷ sinω c tẑ) r(t) v r(t)= v (sinω c tŷ +Bcosω c tẑ)+r ω c r() = v ẑ + r = r = v ẑ r(t) = ω c ω c v {sinω c tŷ +(cosω c t )ẑ} ω c () v d ω c (3) v = v (4) t = sin ω cd ω c v 6. dv dt m dv dt = qv B + qe = qb ( v ŷ + v ˆ) qe ŷ = qb m v = ω c v, dv dt = qb m v = qe m = ω cv qe m d v dt = ω c dv dt = ω c v v = Acosω c t+bsinω c t v () = A = v = Bsinω c t v v = dv ω c dt E = Bcosω c t E v () = B E B B B = v ( ) ( B = v + E B v = v + E ) cosω c t E (, v = v + E ) sinω c t B B B 7. () v = ρω () ρ dρsv φ ˆφ B ẑ +ρ dρse ρˆρ = ρ dρsv φ B ˆρ+ρ dρse ρˆρ = ρ ρ dρsv φ B +ρ dρse ρ = E ρ = v φ B (3) E = v φ B ˆρ = ρωb ˆρ V = ˆ E ˆρdρ = ˆ ρωb dρ = ωb 8. r() = ˆ + ŷ, v = v ˆ + v 3 ẑ m dv dt = qv B = q(v ˆ(+v ŷ)+v ẑ) ( B )ŷ = qb ( v ẑ+v ˆ) m dv dt = qb v, m dv dt = qb v (m dv dt = v =) d v dt = ω dv c dt = ω c v ω c = qb m v = Acosω c t+bsinω c t 46 =

48 v () = A = v v v = dv = Asinω c t + Bcosω c t ω c dt v () = B = v 3 v =(v cosω c t+v 3 sinω c t)ˆ+( v sinω c t+v 3 cosω c t)ẑ V = v +v 3 v = V ( v V cosω c t+ v 3 V sinω c t ) ˆ+V ( v 3 V cosω c t v V sinω c t ) ẑ = V(cosαcosω c t+sinαsinω c t)ˆ+v(sinαcosω c t cosαsinω c t)ẑ = V cos(ω c t α)ˆ V sin(ω c t α)ẑ tnα = v 3 v r = ˆ t v(t )dt +r() = V ω c sin(ω c t α)ˆ+ V ω c {cos(ω c t α) cosα}ẑ + ˆ+ ŷ ω = ω c ŷ 9. dv () m e dt = ev ( B ŷ)=b e(v ẑ v ˆ) dv m e dt = eb dv v, m e dt =, m dv e dt = eb v () 3 d v dt = eb dv m e dt ( ) eb = v v = Acosω c t + Bsinω c t ω c = eb m e v () = A = v v v = dv ω c dt = Asinω ct Bcosω c t v () = B = v = v ˆ+v ẑ = v (cosω c tˆ+sinω c tẑ) ˆ t (3) v r = vdt+c = v {sinω c tˆ (cosω c t )ẑ} ω c (4) v >d B < m ev ω c ed (5) t = = d v sinω c t = d t = ( ) sin ωc d cosω c t = ω c ω c v v (ω c d) ( ) ωc d = r(t )=dˆ+ v ( cosω c t )ẑ = dˆ+ v (v ) d v v ω c ω c ω ẑ c v(t )=v (cosω c t ˆ+sinω c t ẑ)= v (ω cd) ˆ+ω c dẑ (6) t (d d) t t = 9d v (t ) = p = ()+v (t )t = v (v ) d ω 9ω c d + c v (ω c d) ω c m e 9d v (ω c d) 6. I = ω π q m = ω π π qẑ = ω q ẑ. θ dθ di di = dθ πsinθ σ ω π = σω sinθdθ dm dm = π(sinθ) diẑ = ˆ ˆ π σπω 4 sin 3 θdθẑ m = dm = σπω 4 ẑ sin 3 θdθ= 4 3 σπω4 ẑ 3. H dr =πρh φ = I H φ = I πρ ρ<,ρ>b B ρ = µ I πρ ρ b B ρ = µ I πρ 4. 47

49 () ρ πρh = NI H = NI πρ ˆ b () B = µ µ r H c Φ=c cµ µ r NI π logb µ µ r NI dρ = πρ 5. A H NI Hl= NI A A Φ=BS = µ µ r HS = µ µ r HS = µ µ A r l S B ( B ) H m, H NI B = H m (l l g )+H l g = B (l l g )+ B l g B = µ NI B µ r µ µ l l g Φ= µ NI B l l µ r +l g S g µ r +l g ( A, B I B = I A l g l + l ) } g l µ r = I A {+.5 3 ( ) I 5 3 A 6. b H b,φ b dc H dc,φ dc b bcd NI = H b l+h dc 3l = Φ µs l+φ dc 3l µs b Φ=Φ dc NI= Φ µs l+ Φ 3 µs l = Φ 5 µs l Φ= µnis 5 l 7. () ẑ =cosθˆr sinθˆθ B i = B i ẑ = B i cosθˆr B i sinθˆθ B = B ẑ = B cosθˆr B sinθˆθ B m = µ { 4πr 3 mẑ +3 = µ 4πr 3(mcosθˆr+msinθˆθ) } { (mẑ r)r r = µ 4πr 3 m(cosθˆr sinθˆθ)+3 m = 4π3 3 M B m = µ 3 M(cosθˆr +sinθˆθ) 3r3 } (m{cosθˆr sinθˆθ} rˆr)rˆr r () (r ) r = (B r= +B m r= ) ˆr = B i r= ˆr B cosθ + µ Mcosθ = B icosθ (θ ) r = (B r= +B m r= ) µ B i µ sinθ = B sinθ+ µ 3 M sinθ ˆθ = B i r= µ ˆθ (3) B i,m B i = B i ẑ = 3µ µ+µ B ẑ,m = Mẑ = B µ 3(µ µ ) µ+µ ẑ 8. () () H (b) H (c) H () H = Φ µ S,H = Φ µ S,H = Φ µ S (3) NI = ( l µ S + l µ S + δ µ S ) Φ Φ= NI l µ S + l µ S + δ µ S 48

50 7. () r = ˆ +scosθŷ +ssinθẑ,(, b sb ) ds = s r r =(sinθŷ cosθẑ)dds dφ b dφ=b ds = B sinθdds Φ= dφ=b sinθ b () Φ(t)=B bsinω t V = dφ dt = ω B bcosω t. : e = Φ t 3. : φ = Blv t e = Blv : b : : ➉ () Φ + Φ=bB cosω t U = dφ dt = ωb bsinωt dds = B bsinθ () Φ = B ˆ b(ẑcosω t ˆsinω t)= B bsinω t U = dφ dt = B ω bcosω t (3) Φ = B cosω tˆ b(ẑcosω t ˆsinω t)= B bcosω tsinω t U = ω B bcosω t 4. (i) ρ πρh = I π πρ H = Iρ π w w = µ H = µ I ρ 8π l 4 ˆ µ I ρ W = l 8π 4 πρdρ = µ I l = 6π () L ii L i = µ l 8π (b) (ii) = = d d H()= πˆ+ I π(d )ˆ I + ds = ˆdd (c) ˆ l ˆ d ( µ I π + ) dd = µ Il d log = L e I L e = µ l d log d π (e) π (f) (d) L =L i +L e = µ l 4π + µ l π 5. log d (g) () B = µ NI () Φ = BScosθ = µ NIScosθ (3) Φ = MI M = µ NScosθ (4) θ = ωt I = V R = dφ R dt = µ NIS R ωsinωt ˆ π ω (5) Q = RI dt = (µ NISω) ˆ π ω sin ωtdt = π(µ NIS) ω R R 6. () N I = Hl= B µ l = l µs Φ Φ = µs l N I 49

51 () L I = N Φ = µs l N I L = µs l N W m = L I = µn S I l ( ) Φ = µn I S l V = Sl w m V = w m = BH = µ B = µ µn S I l µs (3) MI = N Φ = N N I M = µsn N l l dφ (4) V N dt V dφ = N dt V = N dφ dt V = N N V 7. I B = µ I ( ˆ) π ds = ddˆ dφ= µ I π dd ˆ ˆ h+b ˆ d+ µ I Φ= dφ = h d π dd = µ I d+ blog π d M = µ d+ blog π d 8. I B = µ I Φ=MI πŷ r =(+t)ˆ+(b+u)ẑ,( t s, u t ds = t r u r = ŷdudt ˆ µ I dφ dφ=b ds = dudt Φ= dφ= ˆ π(+t) s ˆ t µ I π(+t) dudt = µ ˆ s I t π +t dt = µ ( I s log +s ) M = µ ( s log +s ) π π 8 Mwell. () E E E E.3 t /3 8 t t = t = 9 = () S = E H = E ˆ H ŷ = E H ẑ = f ( c t)ẑ = H (c t )ẑ { Z Z (3) (E H) ds = H (c t)+ } H (c t ) = ε = Z Z Z µ = (4) w e = ε H (c t ) W e W e = ˆ ˆ ε c t ε w e dv = H (c t )d = d = ε c t = t ε µ 5

52 (5). w m = µ w m dv = µ c t = t ε Z V (w e +w m )dv = dw e dt µ + dw m dt = { } H(c t ) W m W m = Z ε µ () E = E cos( k { c t})=e cos(k c t k )=E cos(ωt k ) H = E Z cos(ωt k ) () S = E H = E H ẑ = E cos (ωt k )ẑ Z (3) W = ˆ T ˆ b ˆ E Z cos (ωt k )ẑ ẑdddt = E Z b ˆ π ω cos ωtdt= E Z b π ω (4) t = π ω E = E cosk, H = E cosk Z E w e = ε E cos k,w m = µ Z = ε E cos k V ˆ π c ω wdv = b V cos k,= ε E cos k w = w e +w m ε E cos k d= ε E c π ω b = E π Z ω b 5

53 [] msters/detil 69.html(7 4 7 ) [] ( school/news/ pdf/7 H94.H89 sotei denkidenshi.pdf)(7 4 7 ) [3] web/dmission/pstem.html(7 4 7 ) [4] ) 5

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq 49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r

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128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds 127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds

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