7
4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie o &, Tn(an- n',n-, -lZAun,^ , ffi/ o'^7 ,64,,* /'t - u^^,0( ( rl^'r1ib,,;"<^ ) Jrt- r. 1uoka / . io'fut 3 eLe KrR o f,zz+ Tt t< '/''-"{ ,- tt" B *6r',Vu-{.R- i44'1--cr2- I fo46neruJm+/K o &>g*/, hnd->.-, a& a&L4e\r+,11 /*lrrryofuisut- Wun,,-.d EdLfr-,^(^/ u #_, wTh: ,rt; /tert rUd*4u oh,&k {g):o ab; g<dr/^L Q, =>d +{ (} >NeY- J./*'t'"o*'oor Gou*R,Y+'nc.,{ ) rf' -l-L,T Te/e( --> r xt &*e P,7E S bP4^one,.f + s&wd/^+d-p*; E/4 4.1 Elektrostatik in Materie: Dipol-Polarisation . fr>.*eRrE J, Por-?orAR-r funo xt ( h.- \t Av t, * 1 ta't"'- \ I ANr^ , 2o^/&- ot..- J-'y&- &&;) ; P*-lr{'.rv\e*, Av 'DFw'uB /IL - : AN; 7- 41{ d;: 1ir) aqr --> A#G;F',) : r-> { + >f4,*o,^,'t dh ;- k- **^t/A'bI;0' 4,1;tf6'?, UN^owoaf,; P^:/e/f A/", Lur<-,o/,s--o( rrt6r4 Uo(:, * ul o &{, + o /eo t D+ryz7P-GoA uu -/ qZvs(t^-"pt- AV o-. $l'Ut * aqelle /Ptd'oxvq ?el /L' *t t o ?"{t^{t^( A6 CF.T') d,,c u+! p(<4-1-e-wr \ -2 1 r Z +t;CF) <1> L VC')Gi') AV - 24 -

MAGNETISCHE FELDER - TUM · 4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie 4 '3e-EL €UTR| SCU? '--d b+Cp .Y1 tCAe E j€{< ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

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Page 1: MAGNETISCHE FELDER - TUM · 4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie 4 '3e-EL €UTR| SCU? '--d b+Cp .Y1 tCAe E j€{< ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

4. ELEKTRISCHE und MAGNETISCHE FELDERin polarisierbarer Materie

4'3e-

EL€UTR| SCU? '--d b+Cp€.Y1 tCAe E j€{<ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

o &, Tn(an- n',n-, -lZAun,^ , ffi/ o'^7 ,64,,*

/'t -

u^^,0( ( rl^'r1ib,,;"<^ ) Jrt- r. 1uoka/

. io'fut 3 eLe KrR o f,zz+ Tt t< '/''-"{,-tt" B *6r',Vu-{.R- i44'1--cr2-

I

fo46neruJm+/K

4, r' ELEkTRotfaT//< rl^ LL/+ER:E 7

J r?ou - ?orl? t ' .P+r to M

o &>g*/, hnd->.-, a& a&L4e\r+,11 /*lrrryofuisut-Wun,,-.d EdLfr-,^(^/ u

#_,wTh:

,rt; /tert rUd*4u oh,&k{g):o ab; g<dr/^L

Q, =>d

+{ (}

>NeY- J./*'t'"o*'oorGou*R,Y+'nc.,{ ) rf'

-l-L,T Te/e( -->

r xt &*e P,7E S bP4^one,.f+ s&wd/^+d-p*; E/4

4'3e-

EL€UTR| SCU? '--d b+Cp€.Y1 tCAe E j€{<

ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

o &, Tn(an- n',n-, -lZAun,^ , ffi/ o'^7 ,64,,*

/'t -

u^^,0( ( rl^'r1ib,,;"<^ ) Jrt- r. 1uoka/

. io'fut 3 eLe KrR o f,zz+ Tt t< '/''-"{,-tt" B *6r',Vu-{.R- i44'1--cr2-

I

fo46neruJm+/K

4, r' ELEkTRotfaT//< rl^ LL/+ER:E 7

J r?ou - ?orl? t ' .P+r to M

o &>g*/, hnd->.-, a& a&L4e\r+,11 /*lrrryofuisut-Wun,,-.d EdLfr-,^(^/ u

#_,wTh:

,rt; /tert rUd*4u oh,&k{g):o ab; g<dr/^L

Q, =>d

+{ (}

>NeY- J./*'t'"o*'oorGou*R,Y+'nc.,{ ) rf'

-l-L,T Te/e(-->

r xt &*e P,7E S bP4^one,.f+ s&wd/^+d-p*; E/4

4.1 Elektrostatik in Materie: Dipol-Polarisation

. fr>.*eRrE J, Por-?orAR-r funo xt

( h.-\ t

Av t, * 1ta't" ' -

\

-3+-

IANr^ , 2o^/&- ot..- J-'y&-

&&;) ; P*-lr{'.rv\e*, Av

'DFw'uB /IL - : AN;7- 41{

d; :

1ir)

aqr-->

A#G;F',) :r->

{ +

>f4,*o,^,'t dh ;- k- **^t/A'bI;0'4,1;tf6'?, UN^owoaf,; P^:/e/f A/",

Lur<-,o/,s--o( rrt6r4 Uo(:, *ul

o &{,+

o /eotD+ryz7P-GoAuu

-/ qZvs(t^-"pt- AV o-.

$l'Ut * aqelle /Ptd'oxvq ?el

/L'

*tt

o ?"{t^{t^( A6 CF.T') d,,c u+! p(<4-1-e-wr

\

-2 1

r

Z +t;CF) <1>L

VC')Gi') AV

- 24 -

Page 2: MAGNETISCHE FELDER - TUM · 4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie 4 '3e-EL €UTR| SCU? '--d b+Cp .Y1 tCAe E j€{< ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

- sd-

4,> J, ELekr&r S:HL lfee,fct-rr e&auCo T\r<*V- ,6*. 6o-za'."*voUht. .

(/

C3r

t^_ ^ f pr ;y Zcy.( ; - ; ,1),D Qrq: /o"'l#f ffi/j, -PGl - e,'Froy

l'-t + Il r - r t

(,",-.2- p't/r"/A, Tg,-Yot '^tu:4'a"nAT '

4 dr,- W{"* P u.^il? yc{e.c"

Qa.*( o&- Tfufs-a r*L'*r/.

tr> ea. ?"/-^{V t(t d-u R,f/-a r-eL

(,r'* b*c "\* **9 { %Y o4o,= - ) Mry 44 kf r*=eF a

io >/, ) r€L€krQttcue -l7eR,lc*tegux,6+ -=; , i

J: F + 4zrP

4> d-au-, 714'

i-+G) : - 4r [f G)-+'Ee]

iG):4op\-+->I V*f :ogt-Ql'urrt\g1n n&

4.2 Dielektrische Verschiebung

7l-

4.3 D te L E k-/ e"/ 'fchfe ."fu-s*tfn Etu,lifr

+(- ?,L^"!a6\c- F L-.-L--^(r( 'P':tlqxv/'*#

A s-1-t^>no4o f-Q'- E - \ t42- eA[*t \u[-e4'@ *6;(;#t xn_

_>'' '' q a ,(e 1)+{n E .(,(,u1-"-e du4 ,9 1)+{4

r'U' *;s a,\^ ,1p 7wf2-2

--Jq.--L'1,1-t4 7t{

L4-^9(

ocLrr

F.

qrQ - j E

.{ (E) t' " i )7,-J /-

oL"-s / <-u--'l-xr

Tt : F-J

: ( t* 4rK )E

, ?*Ur" dq.l1<c4 - 7\ ae<^'v* a( IL\

-a-r .Zq--lcXg-S

4n

T-e-(.

c> frJ E>-L,

J<'/- oC\^v.- 2

.y 'e €: /+4zrY-

/-c47b4ry-+AeV-E: ?E+-e

><d+ 3\ar f-*(r---*&*

zz,L1

4.3 Elektrische Suszeptibilität

- 25 -

Page 3: MAGNETISCHE FELDER - TUM · 4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie 4 '3e-EL €UTR| SCU? '--d b+Cp .Y1 tCAe E j€{< ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

- c(o -

4.+. ?*tt &earuGuNG€p a*, €**zZ4e.H€+)

@/*fyO, &H zN<Wye (*-a/a'"{{)

UIh.gie.,, ae D'rQnt il- >' h'A kn,,.-='/*,-/r-- €-r€.,

ts*"-n* dt''J'- a\,-o-- eeg,"LT.te'.He:

-ffQn' '1t/^,* 4d4

d,z C,"t-*/6'U,- e.l^'r&1vr44,t)g6*k;d*_ F:

t)Aiw^^&'-w'kfu{*'dQk

"&l-- dAr

->/ ,o Qv'a-. /Ss.-orr,a) t

nKJa/f> :

Ir', v'52V

PG

o !nr+*.4,/? a'L/-.-h a-,LL s&-86p--- 6Je&^e,i ttu' f G:^3re&,

tz---t

ftL ew&

/Jn k1-U

E a*f,_, r

6."*>kA"/*I

,uS?Uwrlu]

:

1r:4

w-> 4nAa

IIIt

=rc- /o4,'qn#*u "V( /u__To&^-,*,* T

T<r>,a "4 6' wY &* {-d fr -/"*

1/oA,^4 -

4.4 Randbedingungen an Grenzflächen

- qt-

Ar :4nZAtr€ >e -q )-d+ da*, h({;

_>,/ /^ i . -+A + ---!)- q1-t-f

GV/r.trt> itr

A,L e-L^: CSERQicPtEu - Lroqnqldlc?r=-AQ' ae'' d'r a"^TheLT : Zf

(/tr- .-.,.r I

c[; 9-a-'auL41 4,, / /0

/(t u-.po t &-.-1- {a* dutI

7-ettil^,-ful ,*Ln'r5,t

oLw -lvDRhetEN -

--i -->

o kq* f* F:o fu6+ dT de" ' -t - / d/

,-F" KEg'J,n*

f --r --t ->I df- V*E:

J/

a Ldg

l,/ |

dz *E,v Ge u77 * L- l'fu n^(oh u{4

.? ---> r -?( E_E \xryt_:6)\-- t uz '

' -E rdE-

., 2-

1= - (+, +")

(E -q )- i : 4zt

2

dsIo

+4

^->4 dg-E: oJ

brtrP #- d-,zwpk*Y h-d',^ L'fu

fr b --', r-L

J. dE Eo: J*ot '

+ 3e4;nq44 1:*_/ / (\ \-/

de- f - T"ker:

- 26 -

Page 4: MAGNETISCHE FELDER - TUM · 4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie 4 '3e-EL €UTR| SCU? '--d b+Cp .Y1 tCAe E j€{< ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

4.s 3a>h4,/-

- . t2_

) r e.LEk rR r-g,C/iE J<" Ce-r-

r

€, F*x-f**fuU*(o, crq ) '/

o

o

,rt o(h 2f-^4uP,#rcal : f Ae rn q G*<e) G=n)

rD AJz

-

JQ"c;t : 7 [=n-t* e,{e-"_] Q6rn1

G=-B)o@,JZ-fu= (u7E=-Fh)

4? -ze:-rE aao' z-*trp B-.3- Eo 2 ^I/"- Bz:o nA- 4+t

?t"-f U-A-',j t(-/ / 7 --5E*c#,^i- sLAsn-ttE:

J-c/-U -,E:-vf F--I-W*+ T"o

Rao/,'cu R. ,

2/t-a;/54'e /=ru Eo:I

?t {- *V t-: 7,'.rr*-llrz o<-taa- d-v- z - A o[-4-U

A.ry -?'z*t^ Fa'fZ

o f lhue*, e

lr=*"A70QQ;| :_-L7e lr=R T

+J"; *=R. i

4.5 Beispiel: Dielektrische Kugel

-42 -

l\zoRh+LEN ^ .9.&'

-€

-2t-

2+t ' o

-++- lb:eE:

: ?6"1?r lr= B

: +K3Eot+2

t,%7r

4> A>zdyr^rnn -Sfnd Qtot dW

'D+a *'-/( 1&-neudeh:

o)Ar: -Eo "* ; t ) €,1 : -4- #(ry4'o1-oA7)q> 2G€,*. fr AL, C, kd--y,

A,:-v-L

47 TzTTNT:AL:

d,G;- 3 EoretO2+L

z:-- L--

-E+2 co ^

E^ R3 cvt oItaD

ruf^Ca4--Eorcpso+#

r> ELekrQ,txcuel Ez = E:-V

' a""* - ' Er: #Eodz (lE..l. g...->

le ; ft':")a

3qs C e-:^4-*3

- 27 -

Page 5: MAGNETISCHE FELDER - TUM · 4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie 4 '3e-EL €UTR| SCU? '--d b+Cp .Y1 tCAe E j€{< ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

c &-/\*rIJ< a\ Vo&^t.-4 a) alu.t-U'^d/tz

1>dr-:tre57e-

-> -+c>L- : - ef

t

AtJ_>tc

+v t-{

6crz" -Et= :tr --> :?

I dsr v"TUV

- 1_- r Pr*1a ,,

n: + df -E: AFE-?J

AF : - 7!F 8- 'P

A .V{ ' ,n-aoL ih,nen," f "A** :

Qr*=-71

7a^h/0,-

->J-o

+ 0

l7

h. >F

17rz-v;et<1,r (ru-?7futre\ A7:6V f

. )"dnuq(+:

c n r Aap* : e--E: + *+ Eo @xo"pJ Zf

'r 4r €+2

(-f" t>')

-4s -

-+o+v7) .z

(r"l--tf= T"7--+

t

-4F+O

*

\FI-o /

o

: 4 --t)T€,+t t tw"t E: E -.t

+)+)

!,\

d.p- E&b .e" )v',-,

V5: ; :e-cE*n/")

o .vr-> d.azL -\d-q3'q^ t-- b'ta+Z n48F@J{-

I

-+d : # E"vQ iz

/4r, Eo: Eou/

o ?"Lr+R1^y4r/ON ( .\ab^z; et-{e- D-'1 s/"L"J''k )

aLoht<r rf€) * . 7:X. d,lL.

._3t+2

fF

-e

.a --+( n\ l*"H*^P 1tu4)s/

4 :#

T^qe-a but<"/. o(s J<y->. /

47 foraRr C<r/CA/J - Aac{&-qj *.L/a. Jc l--- ' -U

' '-?->r- .4f

ol : 3 (s-r \=1f 4tr \ s6/ E'

7,^a{l.a4% /-*r>"].b'*' {UA

J-t'lDDD!a,

G(-

(:

__t2, 1v -7---+ ,+V"E : -4zr 4Tfp*e

- 28 -

Page 6: MAGNETISCHE FELDER - TUM · 4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie 4 '3e-EL €UTR| SCU? '--d b+Cp .Y1 tCAe E j€{< ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

-q3-

4. 6 FLE krRo'li71n Cc tte EI-€RG (E

tru:q< 4,.&r- L"/-*f 'qr€7 3/:w: (* [o'. rE t- ) I .[u" 7Gt #c;t

fu-br"A *oo1 c''('v ?'tl-"'snHo'^-' - 'Loe(

/'&r '\t

",/-l-

-r- t,W Va'k-t-c'ta t'u' '

er-? : +v 'D ,) 4-T

I [at,&tY' t

/) ^ r .(- rH fup; /ae-oLuno /-r" 4\- Jnu'ug? w r-{ I

ffS) + : -#, [,r3. t-A4

1^T =2ias, 5 ;w -fr/ '-/'

fo1* lEl-J

"[ot^ /i/-

l^l

8rr

L(zr I

4.6 Elektrostatische Energie im polarisierbaren Medium

-4v -

+.7 h-ActuE-rD{fu ,"*L/rtil L-" PScfu*.t'tnozs^,^

o h-t- \-/

lz.K,q. Ue o-.y-r*.\o4e- J|"*e-

J ^ u4l-.Ov-a4+''o-? Jc

-_.)

W, jl-o.14:_i-J

--->

,yl (F) : oL(F) <^7>)'.2t"

&'V-6'^-o 't4: {

rp

nC;) : Z rh"- ri ) {a^>1

1''4*f2^_o--(,c o(

/"--{""1 -r\^-nA*{-*-,'

{-q-, (^t* }1e-r-(t..u-,I

-.>

)*(F') ): c

ris.'--- f*k, X C;l

--->t | -+V * JL(€'t | / ) |: - - IAcfc-J

)

jc;'t * 7rG'tI A r l rIT-T I

l'41vtn-gu-wfte-u,- (el+

- 1 [arr,[Acl : c l ( lJ -t l ,lY-- Y I

)(j

rL- haez-v,-i.'

: T [J'+ ei-fr-) ,

4.7 Magnetostatik im makroskopischen polarisierbaren Medium

- 29 -

Page 7: MAGNETISCHE FELDER - TUM · 4. ELEKTRISCHE und MAGNETISCHE FELDER in polarisierbarer Materie 4 '3e-EL €UTR| SCU? '--d b+Cp .Y1 tCAe E j€{< ir, Ru< Rl { r ER 8n ReP JLlE-Jr"Fru

4.8 Magnetische Induktion- ' t6 -

et@viPtlA

---D.jJ0

-=)

fu-J$t f >1- ' fr f*'-tu *' d(^rL*'"/e-us D; tl,k in" h-'a-ccctuq '-'"A{-e-- {og

ov^ e- P"'"* /q-J --'-)--)c 4:ry9 -t t ,uqf-& ( +- &/rL a,-\ 'P<

I

( "\" "t ^9'<t{< t1-4w-'o-( A</*^

du,n ilf"-* tU-"-//--(4 n--+772

l"<L 2(

n-1 <- tt'.^

,/, Etg-Q 6-^-,5<-- v

:Z-/*zr

4.9 Magnetisierbare Kugel im äußeren Magnetfeld

- 30 --.rg -

+f /14C lvEt- tcf-re .DYJ u'tkJ(crt ' t

c Jrf.^-'nt" U-ut(

( rpl - -v&reu'J*

_> -5 ->

H: B-znrf l-5=5 : f +zrnT )

9--"ett^rzr^-srn ^T

-__> /__f-7?= -RJ

(fr;oZ c*e prt E rtr T7t r X. .u-tL-

qLc ,'>" 6opa[/-t ^

-.-a

-k l - x*H

Lt {**-*n/

s wf*a'*A- T<*"^&LY;t,<).€+E: tt+ ) f '= y'+ +uK"U {**.+{-er {we(

o Vr-tttry-z-z<sr/z -['7-4-F('iq <--€r' j

W""4 dca*/4

p o.-q ,L^eq/ -v ^n4>"4 :

^n dx "-1 :

T:-- , , . AA^ .- / . \^ / -o / '1^/<^ '= 4 ' -e-*

t>r<

4r:" -J

(,{ .

' Z^'-Zlrrr

'-f '-'

,^:? V-D : 4n F ,

rs lLd;-&y*\-/

VxE:o

ja+e x, ET t 'Pc He

yr&{"-^,

n--"'.-4rf lUo*--