lec16 sept10 maxwell eqns

6
L I e am vn a'n^} h - LV 6"N-e . --_-----V y !:!- l=^r *-*^J4 p"-h't"-t;t "1z"ln,^7'^'h',* h{.\ra.a - t-c''* f[,- 4 n"^in 7^"e T .L"hs,,,,-d.T.t* k-r\.E1,Ln t a.4 M n'n.r.)l l" Be.o-'a- fL r-y..} \- 2v'1 4tz"u e'a f r.l; 't;d (m',^c."lo d u; ltr ,X., ttv -a<t*d h..-.,1^a4d tr* +&Lt _e ("ra.^* W LLtt, lV."-,,-t",1 ,^J-Z-^R. t* u^ f'-f 5'6-..\ tA^ 'J l",r"J .--., *^l ,,,^f ., I o-J- - Ja,c, ).,.-p ". +".,.,.1 - l"--."* lE- P,n^! + i.*tlnn; e.,l , ULr.rz- -^- +Zrt-: diil-"^.J- ,*); "l M^*<o)lt1 at* -"-fzttu-""< Vo.uuv^ ,,^,<)lt,r <1V-l-7'" , !1".,-e- r,te",,"" 'vtc.a-+.-,nt <d k- fL l-;.+ ]; ^.,^2, ]1.-L. \ rt; e,*y";,". "^1- U1 "r-4 + a,{. Et'4 4 ^) t ^, ll t h 1'l r..L2rlr al -2 L:W

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Page 1: Lec16 Sept10 Maxwell Eqns

L I e am vn a'n^} h - LV 6"N-e .--_-----V

y !:!- l=^r *-*^J4 p"-h't"-t;t "1z"ln,^7'^'h',*h{.\ra.a - t-c''*

f[,- 4 n"^in 7^"e T

.L"hs,,,,-d.T.t*

k-r\.E1,Ln t a.4 M n'n.r.)l l"

Be.o-'a- fL r-y..} \- 2v'1 4tz"u e'a f

r.l; 't;d

(m',^c."lo d u; ltr ,X., ttv -a<t*d

h..-.,1^a4d tr* +&Lt _e

("ra.^* WLLtt, lV."-,,-t",1

,^J-Z-^R.

t* u^ f'-f 5'6-..\ tA^'J l",r"J .--., *^l ,,,^f ., I o-J- - Ja,c, ).,.-p ". +".,.,.1 -

l"--."* lE- P,n^! + i.*tlnn; e.,l , ULr.rz- -^- +Zrt-:

diil-"^.J- ,*); "l M^*<o)lt1 at* -"-fzttu-""<

Vo.uuv^

,,^,<)lt,r <1V-l-7'" , !1".,-e- r,te",,""

'vtc.a-+.-,nt <d k- fL l-;.+ ]; ^.,^2,

]1.-L.

\ rt;

e,*y";,". "^1- U1

"r-4 +a,{. Et'4

4 ^ ) t ^ ,

l lt h 1'l r..L2rlr al

-2L:W

Page 2: Lec16 Sept10 Maxwell Eqns

$1*rJL t"=

(voron').

:.11.*-J-iJ ,"1

-

Lsn

Da\'t 't'ob^-t,le q^,L4rL,^r-^4 .

Yu a; splaee 6,.r[ &.,-rn il- l.o,r-

3/- tu-o- Ln c--^',.. o-+ hL fur- taelsz^'tt 2a

(il aL.L NiA 1f^l; ," f*nn\ L<'.n Tk4r L

t} ./EJL

E- tu.

CA"".A,^2 +-n^a-,.-2.*'<-----v- v€ = - 4-9u.

cU-

i" $ e,c-a,'t-a<--

D.D'tf '[,-'...e-

t-

=

ts 'r'ro

:F , '

6 E.ea- =c los-J

6h,dn-- o'<: t l " , -4 S^l^et,

f r'a, =-)+;

VX IJ =f Hoe" eF

-_-< el

E* o1o.""rn1,,.."1-0.^'-;'-t lar,'1 ,

lb=

a*

.l;.td e-^z^n ilo"E)o l;-U ,

e'L a-"1 L,,

O . I J

i t"-"t. 9t

tr"-^aTs.l- a u u^V^trLa-2",,, b-J- ;f + L

Page 3: Lec16 Sept10 Maxwell Eqns

T^frc ^;tt h.,,*- ;t t k,vtd,^t'1 4, Ll"t-;^I

e"4

(,3) ut t'*

(o*nu4' a 'h"- Pn-e T " e.rc^;l-

bX ^ u-ok.,,\4'tl; a-^4 "^-V n; a,,*'J.6. atf nttn-'t;

hr:u 1-L ("- *O .:* I)Dft. il I /r4!d /"

,"*VO' o.t ft: 'l-",,'? A

(1.). YL. a-J;. Paq nt,,*^^t;a Z .\ s1-,!.-r,-,*-1CA "-re. a C-,to-.'. ..;'h u. t^ .no/.r-l., fi-41- 1

-

u( E .ft f- ", &D,--l p^.tL z" 7a-'o. tt- ^o.,ti;c

+:"r4 ry 4 "l*-f^J ^f. i.-<ah :CL_!::::::4!y. )t_ .1,f1._d.

7,u n y^A.

:

Cv

1.

( r-) J-.L I l+fL .lo-a lr. y7^ ^-l^-o-,.' ftr^ cLa^*^2 //4t-".| | -___0_ 0_

.rY.-^X4404'<_, l-'4d ._ A Tl." lZ

La,- Lz ;+^ b e,l-"oa-".*, 4,^r. "of

^"". rt*

FIdr' xtL;rr a.-,), *^1 *^^fl.4, tv:dr- L'fa"dv,,1,-a ) ; 6.1"^te.^ fL

-+,.,^ Pi",A ^^T ...^./t-

, _7z or'rL .

(() JvorE _ *^ ::@* ^A". - %4g '.'f.:"1- w

.wof fLu,,u ̂^' fr- l:S

nn^84

Page 4: Lec16 Sept10 Maxwell Eqns

!y!-it:@ ; 1v",tr14.

&LL tt^ .7"/,-*". l,rrl;"t' "nt

e'D fo Va'e L'tutn y'"-1'4

VL- P-,,o61 ,."-. L H znz L;- "'''^'Lo^-'^!

( = f,1 + f 6

t'L f 6r. .^-,a ! o.--d , lV o-"n ' Nt dn-"|' tr'n'o d ?1

61a^lal; tr- b"-'^dLtL"-^,'-.t'L

661"'-,,,e

, f v.E =

V . n^">t '.o ""V /-

,/ze H 3o a.n s'7,t-,- / 7- t"rt- la lr^^ /in'L

-t'.,,nn "l_ f,* **t ,*t n--t'v i-.

o-"11 . 1z)'" "t- '"L

- O V r F

V- ( e"

c;zt

[1P):frT

aoJ l+ ) b

a-. - o

+ 0,P = f,l

P / ;F I_ .J. f l - v ' r /

€a

---->.---.v

6 n- 'tn'-l--' t" '1^o"n

tqa; tf'z^ ; Y 1"t"'^ 'j f"*

,:A"-**. *J-l

V,o . fn,:r

qql.J

4)

v ' /5 ^v

VXL = * " - l r r

)^ fL +--*fA. oqfo-tr^o' n;- {;"'^il^'- 7'-sL)''"'^L,-tr^ fr-* -7 lr- tr #""o c"''il-'"""[ J L "'y'lrll-

k*r-^- "p

t"{t; cL Lo-., b^- "-"*rh

ry,^-a-a'o-"-,-.-td -

Page 5: Lec16 Sept10 Maxwell Eqns

5-o

F z 7 t 'VUB = fLoJ + l-ue"ir

\/

/

,t'',-

wx

vxL/'^

D . t -

Hb

7- .)v / . t - L -

T : fvx(E

\Fo

, , lb+

,/.

Jl,n'-4A":tra*l-

hvvxM.

w14 '-

J E

;7

a ^ hf co "'f.

el-

,l-

Pdte,,^J4G,^-" ̂-i*q J* =r

L.n^4 xt ;.r ^ ;r.o**trT il-./.ztr@.

t41-*lt j"-l^a- Ve 4<t = r"w-*'hz-

* F./u ,r,-a.^i* 7^

uJ- uf.

*) +e'eL

- t'I | - 6r- t +F1

W" "t'--,- "7f*t-"* u-.u 2un'lT*^ ; 1.,t-- f tt 1D,

L"-.-o^.,,o- ff*j o1L4 a''r'z',t n 48;4 ,'^'tF /*-

a*A /--

4 ^^2- M; r), &tuNL .a-.-r^ r.>^-,ea,.t u-n-2. o->-

G*h4, Jt b "* /h ^"t/- /-, ,r,''.,^,-rr".a, b,-.'---d ch^5i ",

Ln^A 94 n- 7^"-t; "u;.4 trta.bot- .1;42<_E &B rn/n D& H 6^ o ff'" +,.'- pT"^n"",- .Sl- r- .>"at- v

b""-fr-f^tt- A t 2-...tt c<- ol}^ V zclwc' "l; /,L i4 I p aril 1--u-" ' "1" p; el."',n '

Page 6: Lec16 Sept10 Maxwell Eqns

(,) t"-l^"t.,

(") l"r|-^t L

e/; lLl "^,^c-

'u\ f f .'L,4't ''

l l } \ , - -oe-L.atae4 L) a-,d E /

, I I . . . /A.r'rt) I "'tt>t.t vr.e-d t^I Lr'\-? a''.

UL L r'7r'Laa.aataLd

be*,u*^ 4 cz,-4 H V"nJrY,)

4o ,'.*,

h; o;, "".4 ,*-to t 7 D ov 11 vo c'l-t't 2

-fL,4^ a,+ all 2

Lrf-.i '

f ,# .,+ a,.il b ^'lk D ,4.-d H GL.nDl- b4 "/az4"2La.'L'1

I l , d l , / I d \ . t 1t - @ L t - ' /,1

C----

, -A /,-'Ef z if1^

,Yc--|-^a<^

Yknl. n^"t.*- rl o+.""-L f-Lr' UL-nz,+ k f *^*

tr.t-"Zrt^ ^- a*^-V'r'*-k'u '''''''oloZ ̂l ! c"^ ^/"'r +

ca,lu;, Y il c f'n ahut n7--*. tfua

b.^r 3 tq-nr'ol- C^1r^^-/.^t l't^V*L {t'"La n

LL,'lon^ 9 ls, -e,,--t ff,' L".'.,d 'a"'"t'-t*' 9L '

va.,4 .e-,^,-)--t -l- c^L"^.-!'l; h 'k''-'t- '/.''-"- tL 'za'-'"

"- ' o- rrl^ r^.r\a cz,-' Glc^'r^l; fl A ';n /''*'- x-' a

aL. .F .- ,l-,- tt* og*- gTLti ^rL'-L /-L L Ir'

fF^ Q^*.. L^A f,- A - =S D.Jrz, ' QrTdzt '

, i tt V'e)"- ryXt:!

0J^'fnru*