ТЭД - Лекция 3 2019
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( E H
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, ,
q=q(t).
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r 2
ϕ =
A =
∂ |
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∂ϕ |
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∂ |
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ϕ |
# ϕ (r, t ) =ψ (r, t ) / r |
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r |
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− |
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= 0 |
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∂r |
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∂r |
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v |
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∂t |
q |
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ϕ =
4πε 0εr
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ϕ(r, t ) = |
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ψ + (t − r / v) |
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′ |
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r |
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1 |
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′ 2 |
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′ 2 |
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ρ(r ,t − R / v) |
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dV ,R = |
(x − x ) |
+ ( y − y ) |
+ (z − z ) |
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4πε0ε V∫ |
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R |
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− R / v) |
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µ0µ j (r , t |
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dV |
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4π V∫ |
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R |
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E( x, y, z, t ) = H ( x, y, z, t ) =
D( x, y, z, t ) =
B( x, y, z, t ) =
j ( x, y, z, t) =
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iωt
E0 ( x, y, z)e iωt
H 0 ( x, y, z)e
iωt
D0 ( x, y, z)e
iωt
B0 ( x, y, z)e
iωt
j0 ( x, y, z)e
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jσ = σE |
j |
= jσ + j |
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ε = ε − i |
σ |
= ε − i60λσ |
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× H = iωε 0εE + j |
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ωε0 |
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ε - ) #
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2π |
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ω = |
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µ0 |
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= 120π |
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λ ε0µ0 |
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ε0 |
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2 E x + k 2 E x = 0 |
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1 d 2 X 1 d 2Y 1 d 2 Z |
+ k 2 = 0 |
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E x ( x, y, z) = X ( x)Y ( y)Z ( z) |
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X d x 2 |
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Y |
d y 2 |
Z |
d z 2 |
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d 2 X |
+ k x 2 X = 0, |
d 2Y |
+ k |
2Y = 0, |
d 2 Z |
+ |
k z |
2 |
Z |
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d x 2 |
d y 2 |
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y |
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d z 2 |
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$ . % |
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! $ – ,
$!
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∂D |
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× H = |
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+ j |
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∂t |
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∂B |
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× E = − |
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∂t |
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−1 |
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µ |
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× |
ε |
× H |
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c 2 |
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ε |
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× (µ −1 × E ) + |
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c 2 |
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× (ε −1
× (µ −1
∂2 H = × ε −1 j
∂t 2
∂ 2 E |
= −µ 0 |
∂ j |
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∂t 2 |
∂t |
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×H ) = ε 0 ∂∂t ( × E ) + × ε −1 j ,
×E ) = −µ 0 ∂∂t ( × H )
1
ε0 µ0 = 2
%
$ . % 16
,
. .
( a ) = 0
B = 0
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1 |
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B = × A, A - |
H = |
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× A |
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µ 0µ |
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2
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∂A |
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∂A |
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× ( E + |
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E = − ϕ − |
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∂t |
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∂t |
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17
$ . % 17
! ( a ) = ( a ) − 2 a
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εµ ∂ |
2 |
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εµ ∂ϕ |
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2 A − |
A |
= |
+ A − µ |
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µ j |
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0 |
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c 2 ∂t 2 |
c 2 ∂t |
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", # #
$
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εµ ∂ϕ |
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A + |
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= 0 - % |
c |
2 |
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∂t |
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' ( ) |
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# & " ( & ") —
! . & "
$ ! ,
", , !
) -+. ! ! !
! * ! & " 1886—1888
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$ |
20 |
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% ! |
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j (r,θ ,ϕ, t − R / c)− > j (r,θ ,ϕ ) exp(−iωR / c) |
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m |
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k = ω εµ |
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= |
µ |
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j m |
(r,θ ,ϕ ) exp(−ikR) |
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A |
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dV |
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∫ |
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m |
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4π |
R |
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V |
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∫ jm dS = z0imcm
S
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µ icm |
l / 2 exp(−ikR) |
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dζ |
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A = z |
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m |
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m |
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0 |
4π |
∫ |
r |
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−l / 2 |
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R = |
r 2 + ζ 2 + 2rζ cosθ |
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r >> l |
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µ imcml |
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exp(−ikr) |
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Am |
= z0 Azm |
Azm |
= |
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4π |
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r |
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