?ueqz
#w
#g
1t s{t, cl.'{,&a^ f\'r 4",
a,4
.
^'*i
l.E'=
rT,z=-\-
zotb
9\lve,(
"t--
L;nivry
C: SrlJ
uo
e+
htrrtr.*
p1L4
= 2trx ro'o
a^*!
eo
*
/-r
I
-
T^
{
tAj
@7'o'S4*
=
4rr*t$' 3*lg[ro,ii
= 24'lfL. lO''
zo
to .lo--16
t
Z+e x lo'o
4xlo'
r^14 > R.tq
fre-e-Co
l^t
,[Tq"
Rx
-
E= !
I,{61=
|
tcG
A *d'A *f, 7,^
fl-uL -F^",L>^ of
x lo
i)
r
C(r
l}t(r r;)
= t/^
,.uo*d uroA4 '*'I/,
^'.rvttod,turL
i\ta,rs;Q r&*t^^y- o--t
b @')-= T,<(O'd
(lt*'h"* 1- F6,4- i.\ tq oOo)
u"r^t"(
r
.
p)
3nu20t6
Skin depth of water ahdar{etals I Physics pages
Physics pages
Notes on topics in science
Skin depth of water and metals
References: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd
Edition; Pearson Education
- Chapter
9, Post 19a-b,
Electromagnetic waves in a conductor (where there is free current but no free
charge) can be written as
S{+1*I
- &4!F =*i]]
where the wave vector is complex:
For a poor conductot, the conductivity s is small, so for large enough
frequencies s €:er,,r and we can approximate
:
m
by
.t*i
Since the imaginary part of S governs the attenuation of the wave as it
penetrates the material, the skin depth for a poor conductor is
http://www.physicspages.com/2014/09/
l3lskin-depth-of-water-and-metals/
3nU20t6
Skin depth of
wat"r#.r,d,
For pure (deionized) water is,=,$;$,,:g.19*sgr
;l
I Physics pages
and {'l=ffirla* (at.g#.€) (we can
take I*,,F'6 ) so the skin depth of water is
d,;..'$xitlilil,,;., ,
Because the skin depth is so large, water is transparent.
For a good conducto{,
ffl:p,f;,{"s
and we can approximate
so the skin depth is
where * is the wavelength within the material. For a typical metal, *1*.tgf*#*.*
and In,:es.::::#r so the skin depth at visible frequencies $ ffi}"$,ffi;l is
*fr
,,ru{".3$.,*..l$=$ffi
With a skin depth this small, even
a
, :,,,
:t
thin film of metal is effectively impervious
to any penetration by visible light.
Share this:
.
g srrare
;---...--...
i
.J
Like this:
.
* tite
!1
@
Be the first to like this.
http://www.physicspages.com/2014/09/
l3/skin-depth-of-water-and-metals/
2t3
3nlt20t6
Electromagnetic waves in conductors: phases and amplitudes I Physics
pages
s)
Physics pages
Notes on topics in science
Electromagnetic waves in conductors: phases and
amplitudes
References: Griffiths, David
l. (2007), Introduction to Electrodynamics, 3rd
Edition; Pearson Education
- Problem 9.19c.
Electromagnetic waves in a conductor (where there is free current but no free
charge) can be written as
: ffi;*ttr=4i,;rit1r.r,ffi
g:ge'r} :
fli*e ili'l,{*l
rt{--=*]
where the wave vector is complex:
l*_
Fl!+
&,{**fi}
: fus' b}{*'*'t1 (+i
B{";*J
:
''r,.{sl
By applying Maxwell's equations in a conductor we can get a few more
properties of these waves. The equations are
http://www.physicspages.com/20 14/091 13lelectromagnetic-waves-in-conductors-phases-and-amplitudes/
u5
3^U20t6
Electromagnetic waves in conductors: phases and amplitudes I Physics pages
V,rS :
6'm,'-f$)
;Wril
:
mi'.irffi
vxE
: -#
{sl
il.:
Using the same techniques as Ln analyzing waves in vacuum. Both ffi;:t -=,€
urd €=;.3 -- 0 from which we get
:
V',,.,'fr :
V:.;ft
f,+'
f-*€xl.,.&#
Since this must be true for all e, w€ must have
That is, the wave has only
a
m
and
components, so it must be a transverse wave:
H
wave that oscillates in a plane perpendicular to the direction of propagation.
If we orient the axes so that g is polarized in the m direction then
iil1[Is)
Applying 8 to this gives
.V."x,,,E
:
, i:
r\fr,
,
http://www.physicspages.com/2014109/l3leleclromagnetic-waves-in-conductors-phases-and-amplitudes/
3il1t2016
6)
Electromagnetic waves in conductors: phases and amplitudes I Physics pages
As in vacuum, E and B are perpendicular and transverse to the direction of
propagation. Unlike in the vacuum, howeveq, the two components of the wave
may not be in phase, due to the presence of the complex variable
equation for ff. If we write
gl
S
in the
in modulus-phase form we have
Kl.+'wffil
,t,,..{1S}
where
Then the complex amplitudes of the two components can be written as
ffi :
ffik{s6.:{riil*tffi,1
and the ratio of the real amplitudes is
Example For a good conductor,
dffirence between B and n
ls
from 3 k,**,x so from 22 the phase
ffi. The ratia of amplitudes is
ff,.,,#: ew so
http://www.physicspages.com/20l4109l13lelectromagnetic-waves-in-conductors-phases-and-amplitudes/
3t5
3ltv20t6
Electromagnetic waves in conductors: phases and amplitudes I Physics pages
For a typical good conductor
trl p,,,,,.f$f$
g:l
*
I
lffiff" -r and'Ea,w;l1s* and at uisible freque ncies
SO
Share this:
.|.. .'
,-*,,,"".,..,-."." ..1
i €.snare
L
-.
...
_ .".................."..........
.........
,
l
..
"
Like this:
t
r*Like,
li
Be the first to like this.
Related
Klein-Gordon equation: plane
wave solutions
Thu,3 December 20L5
In "Physics"
Klein-Gordon solutions from
harmonic oscillator
Moru 29 February 201.6
In "Physics"
Klein-Gordon equation:
continuous solutions
Tue, L5 December 2015
[n "Physics"
This entry was posted in Electrodynamics, Physics and tagged conductors, electromagnetic waves on
Sat, 1 3 September 2014 [http://muw.physicspages.com/2014/09/13/electromagnetic-waves-in-
conductors-phases-a nd-a m pl itudes/l
.
2 thoughts on "Electromagnetic waves in conductors: phases and amplitudes"
Senor Puto
Tue, 7 October 2014 at 04:46 GMT
What exactly do the units mean in this problem? I got the same answer as you but I didn't
http://www.physicspages.com/20l4109l13lelectromagnetic-waves-in-conductors-phases-and-amplitudes/
\
311112016
Electromaen\tic waves in conductors: energy density and intensity I Physics pages
Physics
pages
I
I
Notes on topics in science
Electromagnetic waves in conductors: energy
density and intensity
References: Griffiths, David I. (2007), Introduction to Electrodynamics, 3rd
Edition; Pearson Education
- Problem 9.20.
We can write the electromagnetic wave inside a conductor as (if we orient the
axes so that ry is polarized
in the o direction)
ffiW:
w*w
where
The actual fields are the real parts of these equationt so
ffi*.
http://www.physicspages.com/2014/09/
l3lelechomagnetic-waves-in-oonductoF-encrgydensity-and-intensity/
IB
3nu20t6
Elecromagnetic waves in conductors: energy density and intensity I Physics pages
ffi*
o
The energy density in the wave is
Taking the time average (over one cycle) of this we have (since the average of
W
over one cycle
ffiisff):
For a good conductor,
ffiffi
so
sSfr
.t6
From 1O we see that the magnetic contribution (*{W) is much larger than the
electric contribution (x) for a good conductor.
We can express this in terms of the wave vector x by using 5 for a good
conductor.
u*ffi
:ffi
m*ffi
ffiffit
The intensity is the energy crossing a unit area in unit time, which is the energy
htp://www.physicspages.com/20l4l09l13lelectomagnetic-waves-in-conductors-energydensity-and-intensity/
!nnorc
Eecbomagnetic waves in conductors: energy density and intensity I Physics pagcs
density times the volume crossing
a
unit area per unit time, which is
where u is the speed of the wave, which is
ffi
so
Share this:
lcil;l
Like this:
$I*l
Ele
th€ first to like this.
Related
Klein-Gordon equation :
orthonormality of solutions
Sat,5 Decernber 2015
In "Ph5mics"
Klein-Gordon equation : plane
wave solutions
Thu, 3 December 2015
In "Physics"
Electromagnetic field tensor:
four-potential
Wed,27 March2013
In "Physics"
This entry was posted in Electrodynamics, Physics and tagged conductors, electromagnetic waves on
Sat, 13 September 201a [http://www.physicspages.com/2014109/13/electromagnetic-waves-in-
conductors-energy-density-and-i ntensity/l
.
hgp://www.physicspages.com/2014t09.l13lelecFomagnetic-waves-in-conductors-cnergy-dcnsity-and-intcnsity/
3B