I I

I

~.J:S0 1 J ~~ ~ (.5 l~~ -' lS~L:;..-, ~p I (.5 ~ 01 ~ ~L¢.. ~ ~jg J-,..w; )~ o);J) ~ IJ U i l..j u 1 .J~ -' t!~ l~ T ~0 1 J..:~ ~ I ~ .J; C~ t.:.. ~ -' ~ L:;.. J

:as ~~ ~ -' ~) IJ..J0 ~o L. j u I.,r.-:;Ai' as ~.Yo 01. 1~ vP } J r:=' .J~Jo

o~ ~ (,S'" JL. ~.r>J I ) ~ ' 0 S'" L. ~.rSJ I 0 1~ oX )JT~~J ,,-! J.. l~-....u ~ I..S'" ~ ~.J:5J I 0~..f:'" 'wSL, u-:1 t:M 0 1~ o..lJ°) -,T.') ~ -, 4! ~~ ­

(.5 1~ I) 6. J0.,,~ wS'" t... ~ L:~-'J L, u~1..J:5J I(.5 ~01 ~ as~ ~~ ~..A J

...l:.:-~.1 J-! .J" ~~ 0 l... j ~ ~ (.5 t~ 01~ J-' ...l.J°.J~ J.~j l JA:-... )\..bJ ..I.J°)I..I.J° r~ ~

W1. I) .') .,s' , ..lJ0Y ~ l~ I r~ j I Ji:-... ..1.:"0'.,,; cs....J J c-- I (.5J'5v. ~ ~~-' J~ J:3 ~ ~~ ~ y:--' -'

.ss.;! ~ J l.Ji .w \.h.. ~J Y' J.,a;

~~T ~f.i J~La w'1~~ 3 ~r-lw ~l:buf~ v-r q V· D = p r) V·B = 0 D = fE, B = J.lH

(v- \ )

y)VXE =o tt)V x H= J V·J= o, J = aE

~~l z.,~ft" JL. ~L:;.,. .jl~~y &~ ~?J IJ~ 'JL,~.J:SJI .jl~

••.U/~~ ~..

J\.J~j\~'Y~l....~LJIY~~~I ~ ,",r"n.JJ.>~~ <.$~L,a; .s..~)~ IJ'Yl~ o}'"L.,.

.~..,...; J~ J.;

~.D. ds== ~P'dV==Q. ~.E.dl== (v-y)0

~.B.dS= 0 ~.H.dl=~.J ·ds==I

o~f..)l9 w~L; V-f

~ y .:, ~~Lf.,1 •.J,~~ l.SS:~ y5:H z., ~~ .jJ.AT~.)~ J 4.~ c:»~ ~ u.:..C: j!~" ~'l:::­

~.>j ~ 0s't.... ~t:A.. LJI~ 4.-.S" c.;J(,S'" Jl~:.il \-u ,J.S"u-'" ~L. ~L: ... LJI~A

-.T-juJ.>.,pd.! ~lAjT•.:dJt; ~;!I l;..Lt \~;I uAt>v u~L.jT,.J,;) u~.?J1 LJ~~

.J.Su~.J:sJI0~~~..,j ...t.."'.J;u" 0L.j ~~ u~l:;..~IJ.=-, -6"~b ~t..~..j ~ ~I.) \~)'I

<.$J~;:; J ~~ IJ ~ s o..l.:~~ ~T~ 4 <.$JJ IJ ~~)~ o;:;IJl; - uJI

LJ~~ ,~~l ~ J~ .jl!~~) J & ~ ~~.J4J' .&>-~AJ ~.J) J.,pJ c...JLQ.. 4"-! IJ

·;:;YifJl}~ \J~ ~ r="",J') ~~~ I

d.J>~r:"'" 4 ~~jjJ;:; ~fAT 4}'1 ~;:;.J)0-.Ul~,,~...Alo~IJl; - ~

.s..:~ ~~r:-'" ~! } I ~ s ;:;Y-c.5" J l.JoJ! ~rsJ I LJ ~~ ~~r:"'" J;:; ~.J~ 0"1,,

. .)y~ JI} oJ! ~?J I ~~.J~ z.,T J') j~ .J.ScS f~' JL. ~l;;... ':'1~A ~ J.)

"':~ J lJ..a I!l! ~ u~ L:i.. <.$ )1; .Jg- I :.s..-) ~.J A.~ }' ~ ~ lAj!).) j I 0;:;1 J \j :~

~ l;:.. .:,TJ IJ.A.. tS;:; Yif to tAJ I ~ IJ... z.,T J;:; S.J l:l) ,n ~j z., L.j~ c.-:... j 0;:; J)Chi IJ

.J5(..$" J ~ J l...t... j I ",s'e-I c..s-:b l:A.. <.$..,1; c.J l..j u I~~j l!

:? w~Hi V-~-\

;:;Y')~ JIJ."J;:; .s..)dlAl\~.r>J ILJ~~ tS .) oJ!~ ~ L. jl<.$J..... ~! t~ 'A r" J L. J.) .;1

J~ J ..l.:S'u-'" c.AJ t;- e- I oJ.~ LJ T~ I.AJ I ~~ .s..)~ l;M <.>.)1; u I~;u ~ ~ TL>"

.e-I J!j ':;"J .).,p~ LJ T~ l:J

dq,v=-­ (v-r)

dt

1 1

l..S~~1 ~I~ ..;...J.J, ~ JI J~':;I ,CJI.. j ~ J i<:" t5G0f~.. ~ <.>~~~.. .)~ c.:r.'J~~ ~ ,,:-;j ~ ws'L. <.>~LJIJ.:," J:" (~>- ~! .)~ ll--W. • tAl I jl:.l.J) 4:_~ ~ 4 ($JJ

. ..1.:)If Chi I.) .:.A1>- d.s' c......,.1 LJ lAj d.1 G.~.-; l..S~~ L:A.. ($ -,1; ~ f If

(V-Y)

~ E· dl == J(VX E) . ds == - JaB . ds'f'c at$ I

J IJ~i1 ..r. j ..;....) ~~ ts:_! ~ I.1J ,~I ~.).:l ~ 1y.J.:l e:h... JJll .s IJ1 )' ~ .u s L.... LJ.J~ J

:~ .~~ J1 1..r. ~ ~

aBvxE== - ­at (V-~ )

:l~ 45'r""!-~ is" ~::; )'~ ~f.) j/

.~.J~ I 'JL tsS:!.?J101~0)\>..r. LJlAj~ J:-W ~.;5J10I..l:-o _ UJ I

.J..:)~ ..l.:JY l..S~J':s:J J 01.J.:A '0 lAj ~ ~~ l;M 0/..l:-o _ ~

J ~~ ts~l.:.iA 01~.. J~ (V-Y) ~,"/..k:....... .)l-L. :y_\ Jl;.o

v::::: - d<p ::::: - ~fB .ds ::::: i R dt dt ·

<1>= fB· ds=B/ 'ab

dri. . B osab S . '¥ B , li t b --"-- .- ::::: s ea -,..- 1 ::::: - edt Ra

y

b.....- _

Z(t\ &

Y-l J!:.A V-It( ~

li L T.1.: j:i lJ~A r~4.J;) .~.JI~ ~ .;>J C---'l uS'"L. .JIJ.A ~ f"!)'?d'.;9 }' l ~ .J )

to> .,1; ' 0 L..J ~ pi<:" ~ l:A.. 0 1...1.::.. I!l! .)~ .J l...lo cSJ> ; I .r. 4,) ;).;) .) .J..t2j ~ IYLSA

• ~ .J;' (..SA j l:J J ,.l~ I .) I..LA .);) 6.=-;...:::'; .J;) J ..\:. L ; ~~ ...t:5'l,S" (:1:; I.) .) I.J... 6,) ~::k L:M

.~) <.s" J..~.r..J 0.).J.p~! ~T~4!1.) ~~.JJTc.. .... ;)6,! LS I.;!

"

I .. ~ • • ~I X ~r

~III h

~Lu c.J1~ .)::> ~~ ~~.rOI) u.. V_ ~~

u-::k l:;.. 0 1-1.:,4 ct ~ J ~ d,)C J I...I. A.!J; ~~ j I 4)L5~ l.:;,. cS..,1; 0 1.):0': . ;' r~ Iy-:~

4 .j :l L..i lG ""' .J ..r. -'-'J (.5-" C b d, ~ C (1 j I d t 0 L.j J "' s ...t:S"" if J J >- B( t ) 4) r..,;J~

ot, j l! i'-:;T(.5~b L:.u LJ 1-1.:-- d,)'~,4 ,)s U ~~ .r"~ C ~ cS-' ,) P J~ 4) I..,;.J ~ ~i1,1

~ LA dl ~IJ~~~ J.,k~ -, ..t:.5'u .. ~.r- ~ L..J. ts" ~ 0 t$:.. ~ r JL

ds' == dl X udt

v == - dep == - '[J Bit+dt) . ds - J B (t) . dSJ == ~ E .di dt dt ' b 'a a ~

,h B·ds == == J Bb(t+dt).ds-J Ba(t+dt).ds+ ~, 0

$6 (1,

!. ,B(t + dt) -ds' (v- z)

(v- v)

dep J Jas p- == - V x (u x B) . ds-]­ - . ds == - E· dl== dt s s at ~

(V-A)

}------+-­---- Y f

v-rJ~ V-f ~

--y .-g

=-1.. (v XE) -ds

1.,B,(t+dt).dS-1., B,(t).ds-J[ (l~ (B•. ds)]at+

+pB(t+dt). (dl x u)dt=0

-aB . vxE;::: +vx(uXB)at

..:­

I.J .)1J._,A .)~ J lA.l J .J l;j -' . -L:.)cs" ~).r": Y C.i~"> ~ (..:-~ t;) u 0 ~f' ~ f g ('"Z"" .J

.J.:.SL;.J L>.

v= - dep == -J aB -ds-]- ~(UXB)'dl dt at 'Y

v == -J, B.Se"dxdy+ J: uoBJ"dx

6 t Stu zz: - B S aye -u B Q ae

o 0

J¢'CT~Jf...\..o w.s-j(s ~SlwJ(j V-tJ , ..1..:)(.5" ~ f5J I iJ l~ J.:l __~ iJL. j ~ J:!':"" (.5~ l:;.,. iJl~ ,,-_)..l.! ~ .? '&:'-)1." 'Y ~ .J~

.--4~ ~l:.v 01~~.i .:d iJL..j ~ J~ ~J:.SJI iJl~.. ".-) ~-'.Jif ..>Lb:n l..i.l

iJ~.r:- u-~l:M iJl~ ~J-,_j C~.:.. L5"" ~ ~S' '0)L, <.S~01~.. 4~ j,yy c.:>ot~ .)~

:~ ~~~ ~.;5J1

l-..>l; iJl ..j l~ J~" <.Sl~ 0 1J.:" LSI~ 0"';[; 0!' ~ t~.:l iJ~ ~1.J>if 0y.)1 .e-I

.~c.)lol 1.)0T~.J~ J e-I

S , c:h..,J~ c\ "':_~ ~" ,(":.:.)(.5" 01~ J-<":' ~ lb.. RC c~l-..>1J...4 ~ U~ LS ..> IJ... ~\y·l; l..i.l , ..I..;.) if ..> .J:;' ~ l;. ~:>vj I ":;}.)S'I & AS'c-.o I 4";.,;.f J~.J::. I..> S'I J

: S, e:1.... LSI~ ~y.<.s'" C:k....J~ ~I LSI~ I..> ~T

(v-\o)

R

I

5 ,

Sf

AS ' ,-;--:J..) L):....J.1 r ~ l c ...J.:-. j ~ L:. i &!..l:.~ ~.;.~ I .) .,) I jj ( r :. ..J I ...l ; :> ljT I1 1:. .J~ U:. l" »s 0 .:=:)

lSI.;! w.l:.>v. ~ 1..5~ -'.:l (V- \ 0) -' (v..«) ~.)f ~ L.v U )~

~H.dl

, L·J,.! J ~? 0 j l>. J>-I~)~ --4~ JG (:.;) lSI.;! 0-.:..-,... 1 0~A ';=? .J.Sr:~)-, Tc...,..~ 4\ !

c.~ b r~ 1-,-> r:~ ~ 11 t.=.; G ~ I) 0 ~.;~ Lr- I .;-c; lor:. .l ~~ .lb')~ LS~~ ~ 0 l:. .;~

(~cJb.)~)

(v-\ \)

()p d ( )V ·G == -==- V. D (v-v r)dt ()t

(v-\r)

(v-\r)

If;.i.J J J.j..; .To,) J ,-> 0 j l>. J-~~ c:h.u ~~ .u-~~ l;.w I L>,)~.b I,) S \ ek~ :J f~"'"

.)~~ I,) ;J l~ ~ ~ l ll " .J I j:!. e:h-.. 0 ! ' J .)y,)J ~J.:~ .:l ~L:..; ' JJ~ J~';~ I,; 01jl u=-..;

.J.) 1.1; ;).,~ J u.,a; l: j l"~ ~

J}'J.:..., I .J ~.>j ~ "s~~ L>.)J Lo L> l ~ ..:.J t>- j 1 ~ ~lb.. 0! I :S" ...L...Jis" );;~

.~I o~ ~~ l.. j l L>I J~ o l )~ ~::"'.J ..l;l o.1:-,,) 01 4\~ ~A

J~~4- 0 ~J~.J L, L>JLll ~ .)J 0 ~ J~ ~...s~J 0t~.j V-f J>:";' »s :v-r Jl~

.J.; J~ 1~ ~ t, 0 j l>. ,)J I d

',)- ­

'---------{ "-' ;-----_......J

d v I ==C -==JwcV

C dt

aD Ae dV Id==JnA== - A == -- - - == J wcV

dt d dt

.J I es 14:""1 J .sJ s l"", «..T.- I ~ ..r~ J I.J~· I .J I 0 1-, i LS" I.) (V_ , \') J.l.) ~A LS11.J~:iI 0.).J.,cJ

. ~ .) JT L->')~ LS::>-I .)~ lY"') .,,':""' 1 ~;

~ H· dl == J(J+ aD ) . ds ~c , at (v-, D)

L~ 0J~ . ...t.:.5'1.5" 0l:1 I j 0Tl»~1 tf'" ~ 01 ..lz-0Tu ~ 4~ l j £0 1-l:,:"" 4 (,J ••jJ j J 'y" ~

~J .J~i4.i c.A;A'>.).) .~ l! '-5" v' B == a OJ I-, ...~ if~ t: .) I_l; ~;;.~ (~b Lv) ~) ) l(...,1

ok .>b.> 'LS-~ l:. .. 0 l ...l~... .1-,k>. ~~ ...l,~.)~i 0 L..:.; I.) 1.5~ ~'" ) I! .).J~ J v=-~ 1....JT4 ; J

4 .)-' IJ <\) lS-:b LuA .s-,1; J ~.) ..:.> j ~~~ L~ ~ ..l,; -'~~; t :>' .s>~ "': J ...l.:.:_ ~ t5 1".:- :

..)-' ~ Cj l>. 0 T.J I J.: l! .)-'~ is" "-=-: ~

(v-, f)

.?-~.) -'.) ~ ~ ~ I .J~ L-.... I ( / i ~ ) 1~ <\J.) L.... JS"r ::;')L-; .) JS" ~.:__.d~ ..ri ~ ~

: JS'r~ ~ I.) 0 L:..; ~t:.. ...l,;'')J ...l...p ..:.> \) .) l.v

-aB v x E == - ­at

-av'(vx E)== -(v·B)== 0at

V·B==K

-aBvxE== ~ E·dl== -J aB -dsat ':Yc • at

~,D.dS = J.PdV (v-\ v)

a v XH := J+ - Dat ~H.dl ==J J·ds+ J~ D ·dsj-' • ja t

0v· B == ~,B'dS= 0

F== q(E+u x B)

-.J ..;:S:::l l [. 1-,..1 0 )1 ~ k. ..J. ~ l: ,~ l : d,,~ 1~ ~ -' ::;) ..h;::>.:.. ,) ~ 0,) L. t y . ~! ,,>1 ..;:~ 4,)u:;)

•..J.':"': I: \ -,.L.... .k ~ I..;"":' (,,51 ,) I~ ~ t: ~ ..> .r' ,),) LSJ-' s-,.4J' J>- l~0T (,,51..;1 <\J. t?I..J.::; I,) U""'~ L: ~,..

0.) k .... I t: I,) J -,.5 I.. ~)0 )1 ~ ~.. (,,51..;; ~l: >... ..h~ ..,) .) U ~1 !.l.J::...... C ..;1:......J .) ~>- ..b: I..;~

•~ .J:~: ) iJ' »s !) ~l:>.... .k:>v-'.) J-~ ~; Lb.. .r~ .J .J T(,S'" c.....,.) "': 0)'.) k. ~ I}~:J· I \) ..> I

H(t H E (t )

/

~ E·dl== -~J B·ds'f' at IS

.~ '-;-' t->o 0 T($I.J! I,)

~~ ~ ..... J I.1~:j 1 JS'~!~ ~ ;).1) '-;-' t~.:.; I I!.l.~ JS ,)~ 0 1Y is" I,; h 0 ~

J!t; E cr" k.,. «J j _ A ,-;-:>.r. \-=:- ~...., uk> J 1.1"S.::.i I -' X ) J ~ .1~ e.--.,.. 4~ ...:,.......1,)

.c.......1 "'~ ~

(v- \ A)

LS l ;> I,; 6 h or)~ '-! L:> I,) 01J 0 J ; 6h J 6/ ;) t"-! I&.: ~ J ) '; ~ .Gl:> l51.1! I,)

,; U ':A D .) ~ I) ...:....... I.) ~), P;) LS~...J J I.1~ :'; 1 0.)J...o u! J .) ~ 0;) .1) '-;-' l;.,:,"I ~J )

~~ I;) K LS~ b ...., 0 ~ .? "') J ,;J ...o ,; s u J J I u =--L J 1.15:..:.J·' J ) ....0 .r. 1.1! (..e. L cs:J l lt..

: <.J'"' ~ .;) J"':'- u" K!11 .;! I..;! r-=';' l!

(v-\~)

0 ,

~.-

t. l; j.J I~ "-=-!~ <.5 1J~ l.J if~ s= ify l; :~..rS:J I 01~ <.5)~ d. ~ J j A 1,.r- (C

0r-:':') \-SA 4.:-..... ~A As thu c:b.... J h

s.)~ <.5 C .J l..> <l.j I..,:..... 1 ~ ..... .J I A-S L.-.» I ~~ .?J I 15 ~.t; ~~ U _,1, \-S:><h.... J IJ5::.;I

~ J~ IJ! ' )J :-~ c.Jl>- LS:-j~ e:b..... j l <I.) ual l>- 15.,1 6 ) 1) 0~' 0 1.Jjif ~ )L~

~ ~ I J! IJ! J s I ....:,)" u~ I.f. ~ ( ) .J~ LS'" C.J t_>- ) -,:-LS'" ) .J IJ d.s-".J I~ 0 l~) e...- I

LS>cb ...."'l~ J~I J~ ..\.:.5'"" l5'" ~ J ~..p <.5 -' .... ~ h c.?J 4.J)~A \J) 0 J 1, -' (D ... - D\n)!1 s n :~ (~ ~ d.:~ b ~ J ::J ~ I) ..\~ l~ ~A .!J J:':'.. j J A <.5 J.J

(v-r 0)

(v-r,)

E~qEo J a~ 0 J Jl~Jl o 0L..a~ ~ c )l.. cl ~ L;a-' <y<a ~ :V-f Jlio ll.>c;...p J) 0~ <.51.,a; ..J~ J~ I o..\~ J"'t5' <.5 ) ~ Y ~ a - , J Y == Q 0l~ J ..\~ l~ ~

LSS:: ~ ";-<JI 0 1~ <.5) ~

E~ Eo cos (wt - {3z)ay

aB -aE.., X E == - --~ a ~ -E Bsin (wt- 0z)a v at az % 0 . fJ s:

:~

f3B~ - E ow cos (wt-f3z)a z

K == (0 -H) X a == E of3 cos (wt -{3z)a ~a- \ .." y wJ1.o

-E f3K I ==(o-H)x(-ay) == cos (wt-f3z)a

z17-a w~ 0

o

-::= qcoEo CO S (wt-f3z)Ps ) ' = 0- \

P, = - qcoE COS (wt -f3z)o )' ~ o

z

E-a.

Y-f J~ V-~ JQ

t

r-

I.) o" 6: t5 L~~ I> .1~ 'J.) ,~~ u,o ~,,t~. I.) 1..5"j4;:' e-J b-.) ~ c.S j.r .1: I J~ ) r ~ .1~ ' J.)

° rU J T1..5" J:j .)~

J•01~,o -' ;..l..:5"" cSJ-> t5~ljT A~ .J..·, -,ju4 .) ~ 0\.)~ A) c.. ...1 (.S4_~ ' J"'~ 0: l~ U:.,;";

r j l (.S4)'l~J -,S::L LS~;,o .) ~ J ~.) I! AS' ::Jj":-LS'" c..;:.l! ,~t> O:t~ J>.I.:l »s ~.rs::11 : .~ L~ j f c.S J.) •r lj 1..5" -I.::A.. .) ~ I.) l~ ...>l! u: I 4S' (J. J' -'~ l5" 0 ~ .J )\~ ~ J-,5:1.) .J..'-,':' I~ ~ ' .."

~ u 4Jo 0.) b.) I} 0 t..~-,>. 0JJ:~ jl ~ 1)::',0) J.';' ,,;I .}..J! ~ I j \ u~ 0 ~..J~) u 5:': .,;;5J I.) ~

.J.: \ LSA.)::J-.J! j CJ.) -'~ ~ ..b! IJ.) u: I.,;! ~ '( r-~ l!

(v-y r)

~ H ~ rA l1 E if r., 0 l~ .w j A LJ.;:~J r~ ~ D ~ i~ t, B L5~ "'4~ 0 ~w y ~

•...l:.:-!l. J! I.r. ~

JolS"'.9 ~,> lSllblS~llb lS'-.r. lSjyo ~f~ V-A-y

.) ~ ~!~ cl~ u~ I ' i !Jf l5"" p"):J J",t;l>;) ~ I) ~ _--> <.5 L~ L5 ;) ~ ':J ",-+1l.'" L. ~ .))

:J ~ j ~ c.! l~ ~~.1"'; 0 1 )1~ ~ J-.. <.5); 0~ <.5.)L~ 0.,,=;- c,......1 ~y>-

(0== 7' X, oV s/m)

.~~L>".1i.o .1! I.1~ D ~. )~ J E LSS::!.1:5J1 0 1~A ~ls' l> .)~ )~ .s:ril.)L$'" .~~L5"

.s : b 0 ~ ? u-J"ls' J9 J..! LS~ L5 .)l~.J') 0 l!~ c! j ",j 0 ..J'><.J0 ~ L5-~ k.. 0 1-,-=A .).J..J...J.) LSJ ~

C:k.....,~ 0l~.1~ ')..J':" ~l~j u-ils'.1; J..~fl u~~I-,>- C-.z~..p .).Jyu!I).) I~ -s:0).."k~

o~ .1 =:- .1i.P ~ ~.rJ t;.1;)) ~~ .11 J ~ l!L>" JJ~j 0l!.1~ 0~ ~ J>-I) .J~ -' ~ Tif c,S.)~

01..r.J; '-:'..» 0 L~15 ~ lA 0.) .1" ..k!I~ ",S--c.......l ,j ':J liJ ' .)~LS" C!.)..'j ":">-I.".:~)~

·i:-!-'~ <l.J·~ I ~ LSi t.. j ~ 0l!~J ( LS J" l..j ul..r0 0J.J.!) r:A:-" 0~J=:-

n., X (H, -H,,) == (v-rr)0

. j! ) I..t; us-L cJ ~ ) ~ ~.... 0 ~ ~ i:';~ as" 0 L:::;- 0J::;­

:L5 j l.. j ~ l5~01-l:'"

"\'\' ·D, == Ps ",,\,.(B,-B'I')==o D,,\, X E, == 0 D,,\,XH,==K (v-Y r)

(v-,,~)

0.J~ j-:J 0l..j ~ ~ (.5~ iJl~.):J .~)~(.£.;I-iSrti <.s-:Ll.:.;... J=-J.~ .)1:J .r. I.; A J

~v (.5lJliJl~ (.5 1J ! ~ J .:J J)u,!..;Ai iJl.Ji loS'" I.; 4 ..... 1.., C.:-Su-!I r)~... V. B =: 0

..:.-i JlA! I 0 L.j l! ~ ~.rsJ I 0 1..l:-- 0-,~ E =: -\HI ~.J; iJ l .Ji~· 0L.j ~

.~l1 U .. VX E ~ - (aB/ at) 4.-<::11

.~ .JJ' 0 1.Ji <.s" .u:J t..... 0! IJ ) (v-r c) 4 11) (.£.) 1~ l::- ~

aAvxE=-VX ­ at

(v-rr-)

aAE+ -~ - \7vat (v-rv)

aAE::= - vv- - ­at

(VXA) a ( aA) VX ~J+E - - \7v- -JL at at

(v-r x)

J).J~ Jb J 1 0IJ.;5'J u-i1jJ.J!) ·<.s:-!~)Y u..a>C~ ~ ... t).)I)J!~ O:~1 (.£1.J1 r~'I)l5"

.,J)lA.A.») C.;) ~4 'r~~!/i ~I y":' .).J1J"~ I.) v -A r :; I.J;u'" l..u ~~ ua>C.=...

' )Yl5" ~Y A ~J1 .bA; .,J)t..... i~ '-;"'l>w" I..r- j U .) -'~ ~ IJ01..?1 r:':~ L5" , y ~

(v- rv)

(V-t' \)

~ .r: ~ A .J V <.S~~s- ~ ~~~ LJ ~' . J.:.:.....AI c.J--'I ~':l~~ ,~}'~lA .. ~I -,1~.J!.J~~> lj ('s~J:5J1 J=_jl=; ~ ..i 4! A .J ·v t5lAl~.J.~~S- (,SA CoS-~ \/VIU

•J..:.. li~ <..> J:> lj <.s-:b tM J:-i l::

§L ~t.:.;.,. LJI~ ~ .J' ~.J>- is:J~ .J.J~ J~ a t.~~ is); ~, ~!

.~~.J u-. :Jt~1 "-=-! .JI.,L.~! J~ o~ lk...J .J.>.~(.S--" w lSl~JIj c.&-.r" ~ B

•J.J LJ TLJ 4fi'" .J .) l...v .)~ oJ...:, ~~ I d$"j»''' c.>J~,. ,~ -;.J ~

~IR

LJJ~ ~! .J:J W ~.r" ~ J!j J~ ~ lh. S ~~ J~ ~.r-" (.5)9 4.4b- 4 .r .~~L> J.J ~b..J:J oJ...:, :J~I AS'"rvlSJ..d ...\>-J~'-S'" ~~J §L. ~l.:.M

--t~_ B s

,o..l~ o~,j .J-'~ IJb J5:..:. (,,51 o.)! b <t:> IJo ,» ) J>j, ~ Ih.. B (t) ~ l: c.s-:1 L:..v cJ I~0

BoU) .~ ~L> I.J (.S~.?JI cJ'..\.::" •.:ub ~.Y':"-'

t

' 0 t. L..~~ 15 1 0 .J ~ I ~

0\) ),) I~ ;)J~ ) R t: L..~~ 0 ~ I~ (5) ,) A~ I: ~ l~ I! LSb>. ,) ~ 4 JS:~ ~! l1:.. •f

B 0 ~! lJ ) ~) L., LS- : b 14~ cJ I~ a t l~ "'! CI.J: b J>- b 4~ L- .J ~ ...l>..J~! ...1..; 1Y ~

.J! s : I) (,,5 1",b>.J ,» ) 1.:..:S ~~ L:>- ~.J~ c::k; B 0 1..t:... .Js= I •( a<R) s.: b.J I"'; 0

! +.. I

. 1.> cJ I.J! ~.> I) (,,5 14!-)lj ~ JS'-' o\ib.

B0 (JS--.s10\: ) Ij ~A == RA7Ta'"B0 : ~ 1~ )

DE d l

A

I ~)b (.Sb:. 0 1: ..1:>;- c1 ~ j I R c...) ~) S <1.1.,0 I;4: S ~~ J~~!.).. 4",1:>- 4 .~

•..J.! ~ ~Jb t5'.;: j ,.:.u.J4' 4! I cJ 1:..1:>;- .)s= 1 .~,) I~ .)I.J .): j J~ J! lh..

(\ -at)] I (t)=

o t>-1

a

•..J.:)"~ ,) ..r.~ ~1 >- (,,5),) ~o ~ jl ~(.S~.r>J I.>~ JS',~~L.>

• f

s ,....-A-..,.W} s s,

~

V c:» .r: W ~ ~ J C--! ~ Po J ~~ ~..,:SJ IJ ~ 4J.. '1 4. ..r-! j J5:..:. tY. lb

...u ~ is" V 0 J.jk)JJ.jT~ J=-i ~ 0)1.;.>.1 •.J.:S" ~ cS.r": ,-;",a'1 ~ .J.i ts""J...liT~

~ 0-1. 1J ,) LJ~~ ~~ .~,-;-,t_ IJ 4:>ti ...... J:J c.s:~~ iJ~.J~ c.sJ~

•.J.::5""tj.r i J ~J.To IJ "-:> L­

•.:U b ,).P:'J .J1. j ..;.JJy.o ~ ~~ I iJ1..1:-- 'fe0 J P.0 ..;.J L..a~~ c.s~ J:J

.~

• V

E =aE sin \o\o(t- ~) ~ 0 v

.IJ E / H e-~. .J H J V :..1.::\~L...>-

' L

'( 't V

1. Jordan E. C. , and Balma i n .K vfl, «Electromagncf ic Waves and Radi

ating t ys tern s-, Mc Craw-Hill, N.Y. 19 .

2. Coll in , R-E ., <Fou ndati nn for M icrow a ve Engi neeri ng) M e Craw­

H ill, N .Y. , 1966.

3. W ai t. J. R., «E lectromagnetic W ave Theory », Joh n Wi ley 1987 .

4. Ma rsha ll , S. V . , and Sk i te k, C . C, « El ectroma gnetic Con cep ts and

A ppli cat ions », 3rd. Ed. , Prenti ce - hall , 1990 .

5. Criffi th s , D. J. , «in troduction t o Electrody nam ics», pren tice - Hal l,

1981.

1. Kraus, J.D, «Electromagnetics», 3rd-ed ., f..1cGraw-Hill, N.Y. 1984.

2. Lorrai n.P . and Corson, D., (Electromagnetic fields and Waves»,2nd

ed., Freeman, 1970.

3. Plonsey, R. and Collin, R. E ., «Pr incip les and Application of Elec

tromag netic Fields», 2nd ed .. McGraw - Hill. N.Y. 1982.

4. Ramo, S; Whinnery. [ vr.: and Van Duzer, T.; «Fields and Wa'l,.'2S in

Communications Electronics , \!\Tiley, N.Y., 1984 .

5. Zahn, M., «Electrom agnetic Fields theor-y», Wiley , N.Y., 1979.

B. Chenj, D. K., Field and Wave Eleclromagnetics, Addison Wesley,

1989.

7. Marsha ll . S. V. , and Skitek, G. G., «Electromagnetic Concepts and

Applications», 2rd Eg , Prentice - Hall. 1990.

8. Hayt, \ !\T. H ., (Engineering Electromag nctics-. Mc Graw _Hill, N.Y.,

1981.

9. [ohnk, C. T . A., Engineering Electromagnetic Fields and Waves,

John Wiley, 1975.

10. Planus, M.A., (App li ed Electrorn agne tics >, Mcflraw.Hill, N.Y. 1978

11. Reitz, Millford, (Foundation of Electromagnetic Theory»,

12. Jordan, E.C. and Balmain, K.G., «Electromagnei tc V'Javes and Radi

ating Systems, McGraw Hill , N.O., 19

13. D.M. Pozar-, Microwave Engineering, Addison - Wesley, 1990.

14. C.A. Balanis, Advanced Engineering Electromagnetics, John wiley,

1689.

15. R.E. Collin , Foundation for Microwave Engineering McGraw Hill N.,1966.

16. Paris, D. T. , and Hurd , F K., (Basic Electromagnetic Theory», Mc

Graw - Hill, N .Y ., 1969.

17. 'W atson , J.K ., (Ap pli ca t ions of Magne t i sm ~ , John Wi ley & Sons, inc, N.Y ., 1980.

18. Panofsky. W . K· H. a nd Phil i ps , l\1. , «C lass ical Ee lectrici ty >

Magnetism, Add iso n - Wes ley P ub. 1962

19. Stratton, «E lectro m agne fic theoy» l\1cGra w -Hi ll , N .Y .,1941.

20. Schelkunoff , S. A ., «E lectr ornag netic W aves », Van Nostrand, N.Y ., 1943.

21. Smythe, \IV. R , (Static and dynamic Electr ic ity », 3 rd Edition, Mc Graw- Hill, N. Y., 1968.

22. Wait, J.R. , (E lectroma gnet ic Wave theory John Wi ley. 1987.

(A)

Amplitude

Angle

Angular

Angular velocity

Associative law

Average

Axis

Anisotropic medium

Absorber

Anisotropic

(B)

Bessel function

Boudary condition

Breakdown voltage - '/;' ;'L:J~.J )

(C)

Capacitance

Capacitor

Cartesian

Charge conservation

Charge density

Charge density, surface

Charge density, volume

Circular

Circular cylinder

Coaxial cable

Coil

Commutative law

Component

Component vector

Conductance

Conductivity

Conduction current

Cone

Conical

Conservation of charge

Conservative field

Constant

Continuity

Continuous

Convection current

Conversion ta bIe

Coordinate sys tern

~\,; '~.Jt) .)

.;L l> ~

.J~~~

~.;~~~

~.J~~~

(J~I.,.() .J~ r wkt)

~r

'~ l>-') "\jl5 '" y

"

~-'.rV

.J~ l>~

~~ I')I~

lLC.:.; I .) L cs: _f:

J: ~ I"J-,~

Coplanar vectors

Cross product

Cross section

Current

Current density

Current sheet

Cylindrical coordinates

Cha rge

Curl

Closed surface

Closed line

Coulomb law

Charge distribution

Coefficien t

Conductor

Density

Derivative

Dipole

Discontinuous

Distribution

Distribution, cha rge

Dot product

Double integral

~~ <.Su,).)-r.

l..?".J1,;.:. <...;J~l>-

~.rC:W

LJ ~~

j~~~~

LJ~? ~".I

is I .G Iy I Co I.....a.::.:v

(D) ,..;;

~I.),~~

~

~J.)

C:.JY

L ' ­.J • l:!- .JY

C..~_t,:. I.) ,<s I~ ~~l>-

....;LfJ .) JI~ 1

1- :

Dual

Duality

Direction

Divergence

Distributive law

Differential

Diamagnetic

Dielectric

Dielectric constant

Dimension

Displacement

Displacement current

Efficiency

Electric conduction

Electric displacement

Electric fI ux

Electric field

Electric flu x density

Electric susceptibility

Element

Equation

Equipotentia I

Equipotentia l surface

,.,

(E)

~.?0I~ i~

~.?01 ~~l.:

~.?0 I.JL.;

~.?01 0 1~0~

~.?0 1 .J t.;, ~~

~.?01 ~L.- ~.rR

~l.:; ~

~L:;~ c:-L

Equivalent circuit

Expansion

Experiment

Experimental law

Exponential

Exponentia l decay

Expression U.JW- - .:> L-. .

Expand

(F)

Factor ~ls:

Field .:>1.Le

Flux lines .J G b # Flux tube .J G ~..,J

Fundamental concepts lP~ ~ LU

Ferrite ~..;J

Ferromagnetic ~LA..J)

I Free space .)Ij I <.S L..aj

I Frequency .lA~-~lf.; !

(G)

Ground ~.J

Gradient ~ ,':>4.)1.;f

Gauss's law If.t .:>y lj

Hemisphere

Horizental

HelmHoltz equation

Homogenous

Ideal dielectric

Isotrope

Intensity

Irrotational field

Isotropic

Kineticenergy

Leakage flux

Linear

Loop

Laplace equation

Law of conservation of charge

Law of conservation of energy

Loss

(H)

o.}" ~

- ' I ~

;;~ ~.bLv.

(I)

~L...JI ~.r5:J1 <5.)

(y-,~-,~I) 0~'y ~

J.}" 0-,~ 01~

...s:....., - . I - ..-'f-'.f..

(K)

(L)

V'"~:J ~.b Lv.

~.r5J1..J4 ~~ 0 y u

(M)

Magentic circuit

Magnetomotive force

Magnitude

Medium, media

Mobility

Moment

Moment, dipole

Magnetic field

Magnetic flux

Magnetic moment dipole

Magnetic material

Maxwell equations

Microwave

Null

Nonpolar

Origin

Orthogonal

~~J l...v

~~ ..s.rv <.»~

ojl...l.il

~

~ J') .J J t..:..:..)

~~ 01~

~~<.> ~

~~~),)01~

~ l.:..;v ,)1.>-"

J.".s L. .:»'j .) La....

. C'L.Cy J!.J- ~))/'-!

(N)

- . ~,~

(O) . . \...:.:.... -I.w

Parallel-plate capacitor

Path

Perfect

Perfect conductor

Perfect dielectric

Periodic

Permeability

Permittivity

Permittivity, relative

Perpendicular

Phase angle

Point charge

Polar

Polarization

Position vector

Projection

Property

Polarization vector

Paramagnetic

Partial derivative

Poynting vector

Quadripole

(P)

; .. ..:.-L \j ~ -.

I~ Lis .J.

, . -.. :. ~..r:~

~ I.,)- _'>::.J -r.

(Q)

Quantum mechanics

Quantity

Rule

Ra dial

Radial plane

Ratio

Rectangular

Rectilinear

Relation

Root

Rough

Reciprocal

Scalar

Scalar product

Scale

Shield

Solenoid

Solution

Space

Spherical coordinates

Spheroid

-

·"1 «: ~L(.,. ~y •

~' <"> ..l.:..>--- -:

(R)

hll • 4- " I ­

~l..)

(8)

)K....I .<..>.)..\$­

<S .)..\$- ~~ l>-

LUcr ­

j;~ 'JSJ.J ,0'j,j.

<..>1 "-.i l.,,:-I ~ r J~ ,4..1.)\..... ~ I~ , j>­

L..;j

<SJ..? w~

Static fields

Superposition principle

Surface

Surface current

Suceptibility

Symmetry

Saturate

Separation of variable method

Table

Tangent

Tangential component

Tangential field

Theory

Toroid

Torque

Transient

Transmmission-line

Transmitted wave

Transverse

Undefined

Uniform

t~1

U,~ i.S.J L... I ~ d'J.J

(T)

JJ~

if\........

LS-'L-. Wy

LS-'w 01~

~~

o~

",.;

J~ -.JJ I.:...:S

I.J£

J t£..; I h.;..

O;)"?.JY C-'"'"

(U)

Unit vector

Unity

Unshielded

I· I I

Valence band

Value

Vector

Vector analysis

Vector geometry

Vector mult iplica tion

Vector product

Vertical

Volume cha rge

Volume resistivity

Velocity

(V) ,

~'jIJ ~ ~

.;I..LQ..... ' <J-.i)

.;I'>..r.

<s.;I '>..r. ..r.J L; I

<S.;I .)..r. L..l;.;b

1S.;I .)..Yo '-:"~

l5.;1 .)..Yo '-:"~ l>­

' L;r-'

~J~

~~~~JLU

':::'->-r

Wa velength

(W)

Cy J.,b

Zero reference

(Z)

b