第12章電磁気学とローレンツ変換 - sp.u-tokai ...

1 1/17 29 3 24 1 40 I. ( )xE ( )xB ( ) ( )x E B 1 , , , 0ttr = + = - = = DBH jEDB( ) ::r j( ) : , ,xyzxyz = + + ij k( ) (): , ,xyzH H H H ( ) H (), ,xyzH H H q u E q=F E B q= F u B u B 2 ()q=+ F E u B( ) B H H B M Magnetization magnetizationM = MjM( ) Mj B M ()0m+B =H M( ) Buzyx uBBuzyx Bu 2 12/17 29 3 24 1 40 ()

2 0 Mttm = + =+ +DjjjDBH D E E D P Polarization porlarizationP = PjP( ) Pj D P ()0e=+DEP( ) 0 Ptte = - = - D jBBE( ) 0 01ce m=( ) E B (): , ,xyzu u u u ()0 1 2 322222222: , , ,,,,1111yxzcccccm = ---- v v v v vuuuuuuu( ) mv E B II.

3 II. ( ) F fm 3/17 29 3 24 1 40 () ()0220 1 2 30222211: , , ,, , ,, , ,11xyzxyzfccfff fffcccm = - == =- - u Fuu Ff f fF F FFufu( ) ( ) ( ) 0221fcc =-u Fu( ) ()( )()xxyyzzqqq = = = =+++ 0u u BFE u BEuuuu E u E u E( ) ()()0,0,0 = =0u u B ()0222222111xxyyzzxxyyzzqfqcccccc++++ ===---u E u E u Eu E u E u Eu Fuuu( ) ()222222111qqccc+ ===-- -+E u BuuBfuEuF( ) ()()()zzyyzyyxxxzyxzx =- =- =- u B u B u Bu B u B u Bu B u B u B( ) ()()()

4 222222222222222222111111111xzyzzyxxyzxxz xxyyxzyxxxyxzyyyzyxzzyyzzzccqqqcccccqqqc ccccqqqccc+-++===-- --+-++===---+-++===--- - -u Bu B u Bu Bu B u BEu B u BEEfuuuEu B u BEEfuuuEu B u BEEfu Bu B uuuBu( )4/17 29 3 24 1 40 0222222221, , 111xxyyzzxzyyxzzyxxyyzzxzxyfqccqqqccc++= -+-+-+-===---u E u E u EuE u B u BE u B u BE u B u Bfffuuu( ) ( ) u II. ( ) mv ()1 2 3222220222: ,,,,111,,1yxzcccccm = ------ - vv v vvuuuuuuu( ) ( ) mv 1232222220221111xxyyzzyyxxzzxzyfqqqccccc cccccc ++ ==++------= - uuuu E u E u EEEEEEuEuuuv vv0232222312222202222222111111111xzyxxxy yyxzyyyzzzyzxxxxxyyzzxzzyzzccccqqqcccqcc ccqqcccq +- ==+-=-+ - +- ==+-=-+ - +-------=-E u B u BEEfBBB BuE u B u BEEfBBBuBuEuuuuuuuuufuB Buv vvvv v12222022222111zzxxyxyycccccqqcc =+-=-+ - --EEBBB Buuuuuuvvv( ) ( ) ()()

5 0 1 2 30, , ,, , ,xyzfffff=f f f 0,1,2,3f 0001231232331102, , yxzyxzzyxyzxfqcccfqfqfqccc = =-+=-+=-+ ---v vvv vv vv vvvvEEEEEEB BB BB B( )5/17 29 3 24 1 40 ( ) 4 4 F 00312312, =fffqFfff = = vvvvvv( ) 0000yxzxyyzyxzxzccccFcc --- - = - - EEEEB BEBBEB B( ) ( ) ( ) ( ) ( ) ( ) ( ) {}0210213233011121310310222322030.

6 , 0,1,2,3 FFFFFFFFFFFFFFFFFFFmnm n0 = == ( ) ( ) 0111111213000010203021222021323322201333 3320300031 FFqKqFfFFfFFfFFFFfFFFFF0 == 13230201 2 vvvvvvvv( ) ()()()()03301111332000102212222211333133 2113100200300322123 FFfqFqFqFfqfFFFFFFFFFfFF0=+++=+++=+++=++ +vvvvvvvvvvvvvvvv( ) ( ) 6/17 29 3 24 1 40 0,1,2,3 0f ()0 33 0 1 2 3000 100212fFFFFq 0=+++vvvv( ) 0,1,2,3n= ()0 1100 00303220 FfqFFFnnnnnnnn=========+++vvvv( ) n 3000fqFnnn== v( ) ()()()()30 33031 33033 3300 1110 221 222211112 100001 002 00333 33 002223 232131130 FFfFfFFFqfFFFFFqFqFqFqFqFfqFqFFFnnnnnnnn nnnn====0=+++==+++==+++==+++= vvvvvvvvvvvvvvvvvvvv( ) ( ) 1 ()

7 41 0,1,2,3fqFnnnmmm=== v 0142130123fffqFffmnmnnmmmm= = = = = = v( ) F ( ) F Fmn , , , FFFF mnmnnmmn( ) 4 Fmn 30303030fqFffqFfqFffqFfmmmmmmmmnnnnnnnnn nnnmmmnmnnmm==== = = = = vvvv( ) Fmn 7/17 29 3 24 1 40 ( ) fqF=v( ) fm nv fm nv II.

8 ( ) ( ) U ( ) ( ) ( )( ) ( )( ) ( )( ) ( ) 11111 TfUUTTTTfUfUUUUUUmm =----- = = = == = = vvv( ) x v ,f v 2200112222332200111122223310 01110 011001 0000 110 01110 011001 0000 1ffffffUUffffUUbbbbbbbbbbbb -- - -- - = = -- -- = = -- vvvvvvvvvv cb = v( ) 1U UI-= Fmn ?

9 ??F =( ) fqF =v fqF=v fqFfqF = =vv ( ) 1fUqFqFUf- = = vv( ) 1U- 111111UU IUUUUfqF UfqF U-=----- = =vv( )( ) ???F = 11fU F UFqq--== vv( ) 11U F UF-- =( )8/17 29 3 24 1 40 U 1111 UIUIUUU F UFFUU U UU UF--==-- = = ( ) FUFU =( ) F (), 0,1,2,3 Fmnm n= II. U 1U- ( ) UFU F ( ) 333330000, 0 TUUUUFUFUFFFFUUUUUUn nssmmrmrmrrrnsns nnsssssrrrssr ======= = === ( ) 3, 0FU U Fmnm nrsr sr s= = ( ) , , FFFmnnmmn 1111.

10 FFUFUFFU FUFFU FUmnnmmn---- = = =( ) ( ) Fmn ( ) ( ) 0000yxzzxyyzzxyxccccFcc --- - = - - EEEEB BEBBEB B( ) 9/17 29 3 24 1 40 22222222110 00 01111110 00 01111001 0001 0000 1000 1 FUFUF cbbbbbbbbbbbbb -- ---- -- === ---- v( ) F ( ) 222222220110 00 011110110 00 011110001 0001 0000 1000 10xyxzxzyyyzzxccccFccbbbbbbbbbbbb --- -- ---- - -- = ---- - - EEEEB BEBBEB B( ) 2222222211011110111101111011yxzyyxzyyzxx yzzyzzyzccccccFccccbbbbbbbbbbbbbbbb ----+ -- --+ -- = --- -- +-+ -- EEEBBEEEBBEEBBBEEBBB( ) x v E B ( )