, , − , . , ,
.
() , . , , .
: ( ); ( ); ( ). , , , . , , .
: ( ). ()
. .
.
, , , . .
:
Q = q [ Q ], (1.11.1)
Q, q , , ; [ Q ] .
, , .
:
(), , :
; .;
(), - , . , , ,
,
. . ,
() : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 . , , , , 8, 9 ;
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, , : ; ; ; ; ,
;
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.
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, . .
.
XVIII − XIX .. . , . , , , . , .
.
:
, , ( 1881 .).
: , -, ( XIX .).
: , , , (1901 .).
SI , , XI 1960 1971 . . System International of Unites SI. 8.417 81 , 1 1982 . SI, .
, . XX . . XX XXI .. , . .
SI ( 1.1), ( 1.2), ( 1.3 1.5),
, SI ( 1.6), ( 1.7).
SI : , , , .
|
|
SI 2.1.
1.1. 2.1.
, | , | ||||
, m m | , (299792458)--1. | L | , m | ||
, kg | M M | , kg | |||
, s | -133 | T | |||
− | , | (273,16) 1 | Ө | ||
, mol | , -12 0,012 | N | |||
, A | , - , 1 , 1 , 210-7 | I | |||
, cd | , 540 1012 , 1/(683) /. | J |
1. ( , m, L) , , 1/(299792458) ;
2. (, kg, ) , ;
3. (, s, ) , 9192631770 , -133.
4. (, , Θ) 1/(273,16)
5. (, mol, N) , , , -12 0,012 .
6. (, , I) , , , 1 , 1 , 210 (, N).
7. (, cd, J) , , 540 1012 , 1/(683) / SI, . 1.2:
1.2.
, | |||||
, rad | , . 2 π | ||||
, sr | , , , |
|
|
(, rad) − , , . 2π .
(, sr) − , , , , .
SI . SI . , .
, - , . 1.3. ( , 25).
) ()
) - ()
) 1.3.
, |
f | f =1/ 1/ | -1 | (, Hz) | ||
F | F = ma / c 2 | LMT-2 | (,N) | ||
, | p, σ | p = F/s /2 σ = F/s /2 | L-1MT-2 | (, Pa) | |
, , | A | A = FL ͷ | L2MT-2 | (, J) | |
, | P | P= A/T ͷ/c | L2MT-3 | (, W) |
-, -,
, | U | U= P/I /A | L2MT-3I-1 | (, V) | |
, | Q | Q= IT A c | IT | (, ) | |
- | r | r = U/I B/A | L2MT-3I-2 | (, Ω) | |
- | g | g = 1/ r | L-2M-1T3I2 | (, S) | |
- | Q/ U / | L-2M-1T4I2 | (,F) | ||
H | H = nI/l, A/, : n 1 l | I/L | |||
, | = Q r | L2MT-2I-1 | (, Wb) | ||
, | = / S | MT-2I-1 | (, ) | ||
, | L | L = /I / | () | ||
−1 | T-1 | (, Bq) | |||
2−2 | L2T-2 | (, Gy) | |||
2−2 | L2T-2 | (,Sv) |
, . 1.4.
1.4. ..
, , , . . .. .: , 1987. 1600 ., [108; , , 39].
|
|
, | |||||
υ | , . υ = J d Ω, d Ω | ∙ | , () | ||
υ | υ = J d Ω/(d Acosθ) d A , ( ); θ | ∙∙ -2 | , () | ||
L υ | L υ = J /(d Acosθ) | / 2 | |||
e | , ; , | , () | |||
I e | I e . I e = d e/ d Ω | / | |||
e | e = d e/(d Acosθ), | / 2 | |||
L e | L e = d 2e/(d Ω d Acosθ) = dΙ e/(d Acosθ) = d e/(d Ωcosθ). | ∙ -1 -2 |
( e) ( υ) (. . .), 0.00146 / λ ≈ 555 . , . . ., .
(, ) .. () , , .
, , 2 6 . 1.4 , : 2 , 6 . e, υ , .
() : I υ, ( , ), υ (, , ∙), υ (, , ∙∙-2), L υ ( , /2, ∙-2).
υ, , e, .
e , ; , . ().
( e) ( υ) (...), 0.00146 / λ ≈ 555 . , ..., . e, υ ,
.
Le , d, d2e d2G = dΩ∙dA∙cosθ:
Le = d2e/(dΩdAcosθ) = dΙe/(dAcosθ) = de/(dΩcosθ). (3.14)
dΩ , dA , ( ), θ . ∙-1-2. dΙe , , de , , , , , (3.14).
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|
Ie . , , ; /.
e , , . /2.
, .
3.
: 1) , 2) , 2.1.
2.1 __________________________________________________________________
1 2 3 4 5 6 __________________________________________________________________
1) ,
1. = 1 d / dℓ L1 1
.
2. r r = 1 d r / dℓ L1 1
r = 2π r (θ)sinθ d θ
3. (φ, θ) (φ, θ) = 4π r (φ, θ)/ r .
1/2 x (θ)sinθ d θ = 1
4. μ μ = 1 d μ/ dℓ L1 1
μ = + r
5. Λ Λ = r /μ = r /( + r) .
6. r (θ,φ) r (θ) = n d (θ)/ d V L1-1 11
7. δ δ = 2π r (θ)sinθ d θ L1 1
8. β β = 2π r (θ)sinθ d θ L1
9. = δ/β .
10. g g = (½)x(θ)cosθ sinθ d θ .
2)
11. s s = μ(x) d x .
12. τ τ = (ℓ)/(0) = es .
13. ρ ρ = ρ/(0) .
14. αα = α/(0) .
15. σ σ = σ/(0) .
16. ε ε = ε/ε0 .
2.1 : , d V, dℓ; d , d r, d μ , , , d V; (0), (ℓ), ρ, σ, α , ℓ, , ; θ
( ); d (θ) , d V θ; E n (), d V,
; ε, ε0 ,
; x(θ) ( θ).
. 2.1 , 4 14, , − , .
, , 12 . 2.1, , .. , (, ). , , . .
2.1 λ , d λ. .
, r, μ . . , dℓ. , d , dℓ:
d = dℓ.
.
, :
d e = L e d G,
(
e r
, = /r2, . 1604 .). d e , d G = d Ω d Acosθ , L e .
L (ℓ) , ℓ, 2.1
L (ℓ) = L (0)τ= L (0) es = L (0)eμ*ℓ = L (0)10μ10 l,
μ* = ℓ 1μ (x)dx ℓ;
μ10 = μ*, = lg e ≈ 0.4343 , . 10 r 10.
.
d V = dℓ E n = /, , dℓ . dΙ, d V θ,
dΙ = r (θ)En d V. (2.1)
r (θ) θ.
, d V d r = ∫ dΙdω, .2.1 d r = r dℓ. (2.1)
4π
d r
r = r (θ) dω = dφ r (θ)sinθ d θ = 2π r (θ)sinθ d θ. (2.2)
(2.2) :
[ r (θ)/ r ] dω = (θ) dω /4π = 1,
(θ) = 4π r (θ)/ r , θ.
(1/2) (θ)sinθdθ = 1.
r dV λ : 1) r λ, 2) r ≈ λ, 3) r λ.
:
( ,
σ , σ = 8π/3r02= 6.651025 2, r0 = e2/mc2 <<λ , e m ); (σ ~ λ4, ω ω0 , ω = ω0 , λ2~1010 2); ( , , , , 103106 .. ).
, . r λn , . r ∆ : σ~λn 4r6∆2 (. . , 1871 .). r r ≈ λ (2r = mλn, m =1, 2, 3, ; . , 1908.). 6πr2; , ; . , , ~ 1000 . 16 [14,32]. , ( ), , , . ( 10 ) ( 10 ) [32].
, (, ) : , ( ), , .
. . : (γ) = const. :
(1/2)constsinθ d θ = 1. ,
SI, . 1.5
1.5.
SI | ||||||||
, min ,h ,d | 1 = 60 1 = 60 = 3600 1 = 24 = 86400 | |||||||
,t | 1 = 103 | |||||||
º,º ´,´ ´´,´´ | 1º = (π/180) 1´ = (1/60)º=(π/10800) 1´´=(1/60)´=(π/648000) | |||||||
, L | 1 = 13 = 10-33 | |||||||
( ) | , Np B, | 1 = 1 1 = (1/2)ln 10 1 = lg(P2/P1) P2 = 10 P1. 1 =2lg(F2/F1) F2 = F1. | ||||||
(- ) | Q | Q = IU sin φ φ I U | ||||||
- | S | S = IU | ||||||
SI, ..1.6
1.6
, | , | ||
1024 | , yotta | ,Y | |
1021 | , zetta | , Z | |
1018 | , exa | , | |
1015 | , peta | , P | |
1012 | , tera | , T | |
109 | , giga | , G | |
106 | , mega | , M | |
103 | , kilo | , k | |
101 | , deca | , da | |
10-1 | , deci | , d | |
10-2 | , centi | , | |
10-3 | , milli | , m | |
10-6 | , micro | , μ | |
10-9 | , nano | , n | |
10-12 | , pico | , p | |
10-15 | , femto | , f | |
10-18 | , atto | , a | |
10-21 | , zepto | , z | |
10-24 | , yocto | , y |
:
,
,
0,11000.
. ,
().
.
, : -, : - ..
, , - (-), (/2).
:
-, - .
,
, 10.05 0.01 .
- . : , : %.
. , , : (0,3048 ), (0, 45359237 ), , , (ºRa = 5/9 ), .
(1 .. = 735,499 ), . ; (1,852 ) (0,514 /) ; ; . .