Phys math help.pdf


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Monochromatic wave

with ~k =

~ = Re[E~0 eiωt−i~k.~x ]
E

(45)

~ = Re[B
~0 eiωt−i~k.~x ]
B

(46)

~= 1E
~ ×B
~ = ~n.cW
S
µ0

(47)

1 1 ~2 1 ~2
B + 0 E
2 µ0
2

(48)

~

c

Poynting vector

Energy
W =

−J.E =
Snell law

with n =

∂w ~ ~
+ ∇.S
∂t

(49)

n
sinβ
=
0
n
sinα

(50)

c
v

Brewster angle
cos2 α =

6

n02
n2

1
+1

(51)

Emission of electromagnetic waves
1 ∂2
ρ
− ∇2 ]ϕ =
2
2
c ∂t
0

(52)

1 ∂2
~ = µ0 J~
− ∇2 ]A
c2 ∂t2

(53)

[
[
Potentiels retard´
es

ϕ(~x, t) =

1
4π 0

~ x, t) = µ0
A(~

Larmor formule
I=

~0

Z
dV

Z
dV

ρ(t − |x c−~x| , ~x)
|x~0 − ~x|

~ − |x~0 −~x| , ~x)
J(t
c
|x~0 − ~x|

µ0 e2 ~a2 − ( ~vc × ~a)2
6πc (1 − vc32 )3

5

(54)

(55)

(56)