Y 4 I 11 n u 1 r I t u n IIU 1 taaawqlhnut iunr ~ ~ ~ ~ n 8 t Y n hnrhum z k l r t r n:ihtmlnbu~udodra:

U ~ Y ~ M ~nuahluntu tn&di;?ur t u " ~ s n ~ t u ~ o a ~ u n u r i (coordinate h;~u n l r a ~ ~ ~ ~ n d U , : u w t ~ d m d ~ d ~ i ~ f i ~ ~ ~ ~ ~

IIYU~I;~ I t d d ~ , : ~ , ~ d M I t i t R ~ U U ~ I J ~ T , * ~ I W asperaive nin I C - +

~ ~ u ? m i l u n ' r ( n l ~ r n ~ n u ~ u ~ ~ ~ ~ l m t ~~i;:p.hta:) nluunu+zt - ur:auuil;q J nt:uw - o r l j r ; f inQ~~tr tkr&: ,

t = A cooat (de-1

4 v I

fqu~u uut :u l lmn~unnwnm z 2v.q im;~ndu&

.A Llk~ ki' 1fun;q propalation vector k :

a k E kz'

I ' I

kx br?u?u i t iLum, id anonu?unqr rfnniuunu h u h n w ; uar ky ua: I I I r

rz h~ i~nu iu ' lun?u~r i Bu7Ku f iauw i au duuiil? x n?yu e L L?iuuq? u v 4 4 J I 4 * ndu A iiiuunmclu tlsounlflvqrm'~ i 5ut :u:nip A tdaflnq inuaun,u tr

1 4 4 ' 4 a u ~ r ; i b i naoud~llni~ ; rXlr:nn~ i naaunld i%r;u:nid & / C Q B ~ noun dni 8 4 4 ' 4 4 * \funun7ur:u:n7iuui?nau k& idauniinuaun~u tr 'lur:u:nisnqu ; uqn

I I I v I unr-Ju~o~n'lajao~ao~a,vuou inifin?fido~aapruin k f u i r ir : i$uln?q kx 8

0

n?w<u<uqfi r iflud?dr:nnu nap i ?n i no; ; dri~nuinii~u r

I 4 1 4 nau i nnounn?udunv (deb) diu?t n 1 IUU i ~ ~ U U U

~ ~ ( x s y s z p t ) - A COB(US * k~')

d0 - udt - kder - 0

dz' u V - - 4 dt Ti ( d o d l

0 ' 4 n~~uiukurn~rnr:~~ulurufian~~:raurnnrduo rat ?:;?dn?q:rfiurnnlarna 4 J J 4wrolnb;~r fludud4 *?fin& i nosun tifa 1 junnuuu2urnu

4 4 * # 4 4 r u a ~ Y ~ r l u u n a u a ~ ~ l u u " n 1 u n ~ u a a ~ n o u u ~ n ~ ~ ~ u n t . r ~?uw~rnn?uun 4 4 4 ' " 4 J

kx, ky ua: kgihitumuqn rmnua8la lunauu~ n n u l u l m n n a u n l ~ l u $ ~ n ~ ~ ~ f f u ~ J 4 4 J 4 J v '

naen wmnaunik tnacunfia???: r nsaun\dn~ua~$rm?~~~~auf'ru I nun~t~;f iw& V # ' v

t t d u l n q l a? kx lutun?t p. .g) tiluau rt~tmuqInunu kx nqu -kx urt: v I

unu a1 nqu -=, inu\ur~uu& y(x.y.z,t ) KPUT~ It?d'ID?tn.[;i?#q ' J 8

kx. L Y ua: tz r3u~qnun:rd;juUn~n~n1i~ al, e2 u*: = j GtnwVu 4 r r r r d nauuau~:u~?~nou~~aau~uil:nnu 2

4 4 ' l u u d r a 1 t iaw~ro%tu,ntrmneu~~,~u~ d4ulv?tnr+uuI~un?ttqu

I I 4 4 ~nul;fiunlr ( r l ..b) un: (*. .a) I I I N ~ ; ~ ~ M ~ U ~ ~ U U ~ U I ~ S I ~ ~ I ~ U ~

4 4 d

wi~muB o UP:+IU~U~IIU k Ifj;~unLvsdann;oqfufiupqro~+ua

v n w ~ ~ ~ h ~ ~ ~ u u n ~ t ( L . .L) h c2 pad'!! divergonco g r r d i m t q~ +

a a 2 I f u u l h div ird * I?II V.V* u ~ J ~ ~ J L fun v $ ~ h l 8 1 d ~ i - . p ~ r = d p'iN

nni : niuuA*in~~iq;iilufinaw d l a p e r a i n ~ m ~ u ~ ~ u

I J ( Y ~ ~ , ~ ) * A sink Y y cos(k,t - w t ) ( t i .bn)

v v 4 nqt [ilonr;? sinkYy L Y ~ r n 4 i 4 ~ n l ; f i ~ n ~ a . o ~ 1 ~ u f l n ~ 3 : ex = o n y - o ua:

v ilnuquuqull;rnindq~H~no*nnr~mdq t r r ,:;IL r 13mr o l ~ ~ u l n ~ m a u ~ u I r ~ ~ i 1 u ~ n ~ ~ :

r tu7fu 4 ' 4

n?qamhqnu!~n??un cutoff - .r 4 b t r q i k l t o ? mde ii(niia~m m - 1 Zulrnv (* .w) tau mode

4 4 4 &andu&d 4.. d ~ ~ l a n ~ ~ i t u ~ n r ~ H U ~ B O J ~ ~ ~ U U ~ ~ ~ ~ U ' P ~ ~ r - o 8 4 b unu

4 4 f i t n ? l u ~ f i r n q t n r : ~ ~ u t : w ; q ~ ~ w [La: kz ( I T ~ U ~ U mode nil lryb - n

' - 4 ' drmpth t m r n u ~ ~ ~ n ~ ~ u d l n l u n n ~ r n r : ~ ~ u ~ u ~ u n d u r : u ~ u i n h a u n * l u ~ r lu

~ r ~ u n m u b < W C / ~ tunvdfu(nh;) iirmrunqrdu

-K Z z $~(y , z , t ) - A rink y corwt a ( .#*me) Y

J J j v AilUInilBU 1 UU9774 ( crirwrorr trawling wavam )

- 4 d A - %A rin(kl-r - ut) - %A mLD(k2-r - ut) (H*UW)

f i rad

nmutfndr nmuiim/u, un: e

C I -

cose

J v ' 4 " n~dn?un?w i 19ndu n + ~ t i ~ tl ~ : ~ ~ M n d u l n d o & 9 w i ~ ~ ~ ~ ~ u n a u ~ n n u n ~ u n ~ ~ u 4 A v ' 4 w w 4~ V ' 4 4

i ;? nnu r, .c:~wwnaunnnud-n y ropnau r1 nr tl ua: k, wnau i nnou

v = c cose (d .ne) g -

I I v v i r ?cl~u~ton'~quu?~ v4 un: v huunlr ( d . a ) UU: ( r l ..*I Q n y y 'I~ulrwwbu-

I 8

4 ~u3n7tnt:'07u F4u I

0 C = - I -

kZ cose

+ * c 2 d (kg)

d(r2) - c2d (kf )

3uiltndncll'tr:l; 2

r . c2r: + k ~ d (~.nb)

v I ; ? R J ~ # \ Y ? ( ~ ~ U ? Y O ~ ~ ~ ~ ( I I ~ I ~ ' I M ~ I ~ r, - 0 ~iiii w - wc.o.ua:m~n~tnwi7aq

v I

r tau $ #'UI r . n r l n n ~ w l u i t ~ n ~ t n ~ : ~ ~ u f t ~ u ~ u n ~ ~ ( r l .bb mode C.O.

I . m t n ~ ~ i ~ n l ; n m u d cvtott ds~;~ui)nrarn,qudk~~fidLf iul~l~ finrunt;

2 2 2 2 2 - U- - % s i n 0 + k2=

C 2

C

2 2 2

IC:= = - n s i n e l ) C -

v

?pJqnd?Vf!tl?? a:noun7~1un"~nun ( cr i t i ca1 angle for rota1 internal 2

ref l e f t ion)

n~llUJdUU11 (Snell ' s law)

011: 2 2 n rin e l > 1

4 * .c n wuu L ~ l n I x ; i l

I I 4 k~uuna:aauJr :nau ex, py ua: rz L ~u~~n~uaun1rnauuum11'ud~uTunau

4 D

nondispersiveUn: 1 i l d l u l r nulaunlr nnuUUun~ua+~rua?ui?uJt :nouuOuvw ii

4 ' r LJX nnuuu ~ u ~ n \ i l ~ u ~ ~ ~ m l m l r :nau~aucu~ul&ua:au~uuu~~an~'~ufu

1 I D a 4 a f . 'lu&autlr:nauuaunod E MY^ B w n t f ~ u n u S f i n l u v ~ ~ ~ ~ a . ~ ur: K-&

I I 4 " 4 8

L t ~ ~ u t u ~ ~ a ~ f i d u u ~ r ~ n h n u i ~ n a ~ ~ ~ n u u ~ u ~ o ' a r l ~ ; a u ' ~ ~ u u s d n ~ ~ n n b u ~n'udui . 4 ~ u l m a ~ n a u u ~ ~ ' ~ n n * I n ~ u d ~ L ~ ~ : i l t ~ ~ ~ ~ ~ ~ u ' l ~ n ~ u ~ u n ~ ~ (d ttas (de#m) v ' v"

n a ~ l h Y ?9:?rnm?tra~ %mil JY :~nnbnudunl? ( r l .ad uas ( r l .cn)

P ( 2 . t ) , 0 V-E - p

a i i a A - - -cV r E a t

ku'u a u ~ d l ( ~ ? u a : r u w u ~ ~ ~ ~ n ~ ? ~ ~ a ? n # u 3 f l m ? 4 ~ a L ii&d i @

n~rn9ugaoq E ua: B Y

@

a??t~?r?dt:nau x ua: n m pX, E ,I uaz B h a m ? f ( d . ~ ~ ) 4 ' Y n

Y

Pa: (d,Cb) l l ~ d ' l ~ d f s n 8 ~ x 9B4dUn?Y (d .CC) ~tl=d?Udl :ntlIJ y 9flJUlm7Y (d.(lb)

a E , -- cat' ar (d .&d)

1 aE aB 1 aB cat' 3' -- c a t - 3

mndunqt (d .&dl E~ uas i & t ; D ~ U ~ U i J U I J U ~ ~ U ~ Inu&daqarrnqrayfiG~u

i l .n~ubu~nd.r &MI ax urn: 5 U W ~ ? ~ ~ ~ U ~ ? U M ~ J ~ " U I ~ k&0*7 E~ i3uAwB

I : U : L n B~ i kAn.1In*9u i ;u(rUu v f a 8 n f ~ d d ~ b i rqnr711;q E~ i jll I

f j n ~ r a ~ k 2 un: t trqnr~ui;fu#;q B V i~ t ;u t i iu?f i n?ua~iilu?fi,m

v

I i n d t l d h 1 k I d~tta: 1 ~ J ~ J I ~ ( Linear and e l l ip t i ca l polarization)

I I v I 14 I ruqrr p uar 9, ~~ihw~~(rUun~~lh?uurrnltm~ k m a l l unf luI~nurnI

I I

t luqun?q~qh kh~d~n'$d;q~ndur:u~~u; I M / ~ I & ~ U P il;d;i SU#UU un 4 u 1

I dAitA6uqu;&nru r ua: r ln& 'Lunrwunnu i fun i & ~ h d r ; t 3.n iumu x 8 I I 4

k18uduqulrhi? P ua:tiu~rrunn?tn B~ i r r i hquu n?uad i lluvfht r q~quqrnilnau I

u ~ ~ r i n ~ G d t ~ d a q ~ r ; i a 4 i iunqu Y u": 5 ua: B~ \ i t hquu ua: i t lk

a~nroatlar ,dnqm ex uar a, dd~d~&drlu k& t r ~ ~ ; ; d n ~ . r n i ? ~ d r o t ~ d a ~ ~ r -

tabu i f u n i h ldnq1r tdht3~~f i ; ~ r ~ r i ~ n u ~ r ~ u a : i d u n n o ~ ~ d a ~ ~ t t ~ ~ u u n d 4

.. I v I - I 5 dlmbfu B~ t n # ~ ~ n u q u a ~ ? l ~ i r qdr:namn.\~urnurn a ~ ~ 4 l t h q r r i rqaqrrqrn

I v t;qI~in'+hulnu&,q o q h f l i l ~ @ q i ~ t f i i 3 4 I Z U ~ ~ U U U ~ U 4 ua: B~ (;w t h u m

8

ua;h I r m y u u n re @Y (11 ~+.\;unu x k r ~ b ~ ~ a ~ u u q u ~ ~ ? k e u n u y brr v I I

r:m4aynquuu,~msr*l~uu~ttrih ~duaunqr ( r l . r d ) ruynoLaunqr (d .~d)

a 11 1 as as - A - k ) = ii;r t 3 t C (d .be )

aE * - - = -cu~io(rt-t~) a~ a t 3% * at" (#.be)

vn4ulG1~rn7r (d.bo, 1as(d.b.)8n7rdrkm a d~ituwVu = us: t r h u f

ffim 8, ~ ~ G i u ~ u c l A r w ~ w ~ A u ~ a t t Inimihuh e 8 u*: n Y s

h m n l t w n ~ ~ n c d d o , ~ l n ' ~ $ q ~ &

l a z # t ) I = IS(z*t) I -

n L I cliaud 2-3 = o (d .bb)

h r t - G

nduiI~s &In w

tuu& nhunk a n w X

Es(&, t) .- A cowt coekr (d .bm )

8

unt r ~ d t n k ~ i d i 8 f i m n n q s t w f i ~ n u n t J w~ndutn~oudt ~u~uon::niui l :uu . &6h t rm~u'l?nit1rsra~nb~4~u~ulo~ &1rhr?;kdn?t~lrun3td7nrrn7t1~nntlJ

ndj, ~ u ~ w ~ ~ ~ a ~ n r t inlCf$uPn,n% n njolnfiunu z ucl:ila.rlmul I&J I iin:ou 4 I b Y

AZ n ~ ~ u n u z ( ~ u l n ~ d f m t ~ a a ~ n ~ r t d a u u u r l a ~ n f ~ ~ ~ u ~ y ~ n t a n.?uunlu I V # b

W ~ Z . t) I h ~ ? u m ~ ~ ~ l u d l q ~ t l ~ u ~1171d1udt"u~nt i lnq! !lnnnl~clmmuw;u v

nf+i~~ug~m~urlfrc~nt MZ

(Id .bd)

- sz(i&i - sI(.+~.t) (d M I

4 ,( i3- \ ,.*

LIlO sZ(zB t) - pcs'k' >n;(z,t) i

= 3 r * * 3 e 6 s . \ x (Id .do )

kul?iCnrmotn~t ~ ~ # ~ ~ d ~ ~ ~ s d i d ~ & i i i 1 1 ? ~ ? n t i in, U z ao;?rodfrrpl ~ s ~ ( z ~ t) 4 J v v v I J

I ran+u~om z at t w u r ~ t a ~ u r a ~ ~ ~ s n u ~ ~ u n ~ u ~ ~ r ~ ~ ~ ~ i u w 1 iiuNun?u?un CMZ nt t v I Y I nsun?tn?&rotnqtnu~ kuudrur, sg;g,c) ;k~i~udht?ratn~t~saaatnbtt lu ' w 4 J A ' 8 m~u~uwunau:lnqlu% +Z nlcl nlr isrrnstnk t ~ u l u t l h ~ n r L fin7 i n'nqmuan~ t

v v 1

retdhdnata1aum11rl?u7(u~~aoan il?udt:nou z s Z t mt f lux vector s ' N J I

ntl~un i hbnt qae tn qtlafin~d t ~UIU~~I +Z m*Iu?unun ( ~ V U ~ U erg/cn2. eec

t I

nouuii.ji?niflor ( Poynting vector )

dun~rk?~Jrotddh; b

r((r+rddm I

= C E B 2 2 = cor (at - ka) - sz 4s y 4f 0 (d .d4)

u w ~ n ~ i m q u ~ a ; i d n t 8 u ~ d i h r ~ ~ m u & ~ ~ ~ 7 u u ~ n I t 0 d n ~ u ~ ~ ~ i f t b t h Aauw 8 4 . A a 4 444 ' 4 '

uutadnnfhtnu?niln?7wuluuunf4~11~mn~finan1\ '7~~~~~~~011~~1n~~ kA fm: 0 I I

B~~ufmqkttma~s~;ldnaa~~atrtmt n a v h nk~lu#qnunrstaad%iatcn, ' I '

tiuAncduha~4n t annguldnbluqrzm;w t 8~tf lunbjtwf iuauq~ L 8uq;;~uum$ ' 4 # 0 v #

~?UWUJ~UP Bn: ~ ~ I ~ I J U ~ ~ ~ J ~ U I ~ I U ~ V ~ P ~ # u ~ n ~ u u ~ w $ n ~ u ~ ; t ~ d q &nkjlu*au 0 I 1 11 0

ur:nfi~wfiunq~eaa~nb andrzu J r n d u m f i h u n ? q u ~ z w t m~rlntrmt 2 L , . 4' 0 I

tqnn-nmr +n?q nb~~quvnudn?rr?m ~ M I P L & un: t 5 ~ ~ m k m q ~ ma+n t amtusiu t 4 ~IU~IJIJ~ e x lun$ud lu i tP~~~un;~u fun~t t l . ~nq~nn?u~~~~u~a t l ra~u~nn~e~a"~ tan m:

J I I

ntiuquu;twin ey f l a ~ u n n w L ~ ~ ~ u 1 iqrcl+r?a

270

uuu~nl~nud

7.1 Shw t b t i{wt - (klx + kg) 1

z - A t

2 where k - u2/c2 = k: + k: i a r ~ o l u t i o n of the two-dimanional wave

equation

A A 7.2 An electromagnetic wave (E,B) Propagatsle i n the x--direction down 8

perfect ly conducting h a l l a r tube of a r b i t r a r y cross rectdon. The t angen t ia l 4

component of E a t the conducting wallr must be zerc a t a l l time, a

Show t h a t the rolut ion E - E(y,z) cos(wt - kxx) rubeticutad i n the

wave equation yie ld8

2 where k2 - uZ/c2 - k m d k 18 the wave number appropriate t o the x-direction. X X

7.3 If the waveguide of problem 7.2 i s of rectangular crosr- rsc t ion of

width 8 i n the y-birectiou a d height b i n the z-direction, show t h a t the

boundary conditionr Ex - 0 at y = 0 and 8 and at z = 0 and b i n the wave

equatioa of problem 7 .2 giver

7.4 Slaw, from problem 7.2 8bd 7.3, that the l m a t por r ib lo v i l w of o

(tho cutoff froqrydcy) f o r kx t o be r u l im &von by m = a - 1.

W b u i . of the "cr i sscrou tradkrg d1 d.rctiptioo of wavmr i n 8

mveguido. It k 8a i l u r t r a t ioa of the face th r t b r e e d ~ i o n , t r a v e l i n g

hrroaic wan8 form a " c q l e t e set" of fwucglonm fo r describing three-

d i v l u i o r u l wavers. Of course t h r e d i m a a s i a a d rtur$ing 88~88 a l so foma

a complete se t .

7.6 (a) $how tha t for gLur, of m x 1.52 tt# critical m g l e f o r internal

ref lect ioo ir about 41.2 deg. . .

(b) Whrt k the ct i t ica l &la for water of iadu 1,337 W i l l r water

p r i m in the shape of ,.a Imorcefrr r i gh t t r iurg le &m ntrodir.ction of

l i @ t without my 1088 (by r a i r ~ c c ~ i n t o air). Hrrt msrta~. tha t the

water extrado riJIt up to tho .it.. Thm worry about the g l u s mictoscopr

slide8 that t o w the sidea of your wrtjrt prism.

7.7 Show tha t the retrodirective 81Us gbw prism w o r h a t ather angles of

incidence than the o o m l r b , ' i n the r eme that it d i rec ts

the light back in t b opposite direction from th. in t idaut direction.

7.8 Calculate the arm peuotratfoo distance (tb. muu ampkitud. attanrution

d i s u n u r-' - 6) fo r vis ible l i @ t of wanlength 5500 ratrodirected by

tha g l u s prism.(We meaa th. dlsWlccr n o w t o the rur glass-t-ir surface.)

&smo the iacident light bum is at wrm8l iocidenca. Take the index of

refractlon to be 1.52. h a 6 - 2.2 lom5

7.9 For l i gh t (or microv@ms) in a waveguide we found that , i f the f r e q w c y

i a below cutoff, the r direct ian (along tha guide) is "reactive." Th.

other two directions wore wt zuc t ivo , fr it possible b p r b c i p l e by

some ingenious method t o construct a "generalized waveguide" i n which the

waves w i l l be reactive %n aa l three direstions x, y, and z?

7.10 Cri t ica l aagle for reflection from the ionosphere. Replace the

glass to the l e f t of z - 0 i n Fig.7.3 by vacuum, Replace the a i r t o the

r ight of z = 0 by a plasma-the ion0 alized so as to have a sharp -

bouadary (and a uniform composition). Show tha t Eor every angle of incidence

0 there i e a cutoff frequency w which depends on and that a t normal 1 C.O.

incidence t h i s cutoff frequency is the plasma o s c i l l a t i o r ~ freqwacy w . P

Show that for every frequency o above the plasma oercillatt.igsr f req~eacy w

there 'is a c r i t i c a l angle fo r t o t a l reflection such %hat for angles of

incidauce greater than the c r i t i c a l the wave &a exponendal i n the ionosphere.

a s an example, take the plasma osci l la t ion Erequency,to be v - 25 HEz P

(megahertz) and find the c r i t i c a l angle for microwaves of frequency

v = 100 M H z . ADS. For fixed el, w = w /cosO1. For fixed frequency w C.O. p *

above w cos6 P p e r i t * ~p'"

-5

7.11 Obtain the claoeical wave equation for 8, a s tluggested follow&ng

7.12 3Radiatim pressure of the sm. Given tha t the solar constant (outoide 1

I

the earth's atmoephere) is 1.94 small calories per square centimeter per t

6 2 minute (whieb is 1.35 x 10 ecg/cm sec), calculate t. dWelcm2 the radiation

pressure on the earth (at normal incidence) under the two a~lsumptione (a)

and (b) . Than compare the resui t to atorospherfc pressure of sir at see level.

(a) The earth is black and absorbs r i l l the l ight .

(b) The earth i c r a perfect mkror e&l re laec ts e l l the l ight . / * *

!

7.13 P l m s elactromglutic v+-+ $&jr that, fo r . l . t t t ~ ~ ~ o o . t i c p h

wawm in vacuum, thore Muxife4'8 q u a t i o w that give tha rolatiorr between

H .ad Bx are "quIva'.ent" to.* Mmxwell quatiom relatlq Ex and 0 Y 7'

in the euue tha t OM met of tqwtionr can be ob tabed from the other m m l y

by rotat ing the coordiaate rp.trrr by 90 deg about tha r axla (vh%ch $8

a 4 the propagation u im) . Wko 8 -LCB mhoVfPg the o r i a r t a t i o w of B, B,

a n d t h e x a n d y a x e 8 ,

7.14 Stanaing electroolt#netic wavea in vacuum. Shar t h a t i f Ex(r, t ) I #

the atanding wave Ex - A c o w t e, then B (2.t) 10 the mtOndh8 WU- B

7.15 Energy relatiow icr electromagnetic mtanding vavem. A s m u r , 8 mtsadlng

Qave of the form given ia prab .7.14, ?Snd the electric and magnetic

enargy densitiem a d the Popnting vector mi fuactioa of apace aud time.

Cons>der a region of length )Cli extending from a node i n Ex t o an antiaode

i n Ex. Sketch a p lo t of Ex rad B m u a 2 over thrt re& at the ti... Y

t - 0, ~ / 8 , and ~ / 4 , Sketch p10E of the electric w r g y demity, the x-f m'

magnetic energy density, orrd the total W i t y over that region fo r the rl

lrame timea. Give the direct ion and magnitude of the Poylrting vector St

fo r those same times.

7.16 First-order coupled linear diffeltcatial equrtiona f o r v a w op a

s t r ing . Consider a continuow hombgeneow mtriog of liueat r u m denmity

Po a d eqilibrium t.nslon To. As you knu, 8uch a 8CM8 u u r r y &n-

dispersive raves d t h velocity v = a. Deflne the rave quanticiem

F (z,t) and ~ ~ ( z , t ) a s follows: 1

Thur F i r l / v tiour the t r . a rwrre raturn force exerted an the portion of 1

tha r t r i ng t o the r i gh t of z by tha t t o the l e f t of r , md P ir the traw 2

averse pomentum per unit length. Shar tha t P1 and P2 r a t i r f y the f i r r t -

order coupled equcrtionr

Show t ha t one of there equations i r "trivial", 1.8.. is arraati . l ly m

ident i ty . Show tha t the othet is equivalent to Newton'r secoaa low. Notice

tha t there equations a r e s imilar i n form to Maxwell's two 8quationr re la t ing

Ex and B with EX aaalo$ow t o F1 and B t o P2, SiaJlar ly , o m of the Y' Y

two Mawell equations can be regarded a s a " t r i a l ideat i ty ," i f o m lrrrow

the special theory of re la t iv i ty .