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1 2. 1/122 x,y,z 11 (Moon & Spencer, Field Theory Handbook ) 11 (Orthogonal coordinate system) 2-1 (Rectangular coordinate system, Cartesian coordinate system )xyzAzAyAxAxyzaxayazxyzA A=A (a) (b) (c) A x,y,z (b) ax,ay,az 2.

2 2/12 ax ay=azay az=axaz ax=ay( ) (c) A x,y,z , , A A=Axax+Ayay+AxazA=Acos ax+Acos ay+Acos az cos cos cos (directional cosine) cos =AxA,cos =AyA,cos =AzA2-2 ( , ,z)(Circular Cylindrical Coordinate System) x,y (0 ) r r r x y 0 2 ( , ,z) z P( , ,z)xya a azz P(a) (b) 2. 3/12 a ,a ,az (b) a a =az ,a az=a ,az a =a ( ) x= cos =x2+y2y= sin = tan 1yxz=zz=z( )2-3 (r, , )(Spherical Coordinate System) r 0 x 0 2 (r, , ) rxyzrsin rcos P(r, , ) ar a a rxyz (a) (b) ar,a ,a (b) ar a =a a a =ara ar=a ( ) x=rsin cos r=x2+y2+z22.

3 4/12y=rsin sin = tan 1x2+y2zz=rcos = tan 1yx( )2-4 2-4-1 u1,u2,u3 A=A u1u1+A u2u2+A u3u3( ) u1,u2,u3 A=A axax+A ayay+A azaz=Axax+Ayay+Azaz A=A a a +A a a +A azaz=A a +A a +Azaz ( a ,a ,az A =Axax a +Ayay a +Azaz a A =Axax a +Ayay a +Azaz a ( Az=Axax az+Ayay az+Azaz az 2. 5/12a ayaxa ax a =cos ay a =sin az a =0ax a = sin ay a =cos az a =0( ax az=0 ay az=0az az=1 A =Axcos +Aysin +Az0A = Axsin +Aycos +Az0Az=Ax0+Ay0+Az1 A A Az=cos sin 0 sin cos 0001 AxAyAz AxAyAz=cos sin 0sin cos 0001A A Az ( )( ) 2-4-2 A=Axax+Ayay+Azaz( ) A=Arar+A a +A a ( )2.)))

4 6/12 ar,a ,a Ar=Axax ar+Ayay ar+Azaz arA =Axax a +Ayay a +Azaz a ( )A =Axax a +Ayay a +Azaz a ax ar=sin cos ay ar=sin sin az ar=cos ax a =cos cos ay a =cos sin az a = sin ( )ax a = sin ay a =cos az a =0 ArA A =sin cos sin sin cos cos cos cos sin sin sin cos 0 AxAyAz( ) AxAyAz=sin cos cos cos sin sin sin cos sin cos cos sin 0 ArA A ( )2-4-3 ArA A =sin cos sin sin cos cos cos cos sin sin sin cos 0cos sin 0sin cos 0001A A Az2. 7/12 ArA A =sin 0cos cos 0 sin 010A A Az( ) A A Az=sin cos 0001cos sin 0 ArA A ( ) 2-1 A=1rsin a 2-2 R=xax+yay+zaz 2-3 A= a + a 2-4 2-5 2-6 2.

5 8/122-5 dl dl=axdx+aydy+azdz( )dl2=dx2+dy2+dz2 dl=a d +a d +azdz( )dl2=d 2+ d 2+dz2 dl=ardr+a rd +a rsin d ( )dl2=dr2+rd 2+rsin d 2 P Q dl=axdx+aydy+azdz dldzdydxxyzPQdl=axdx+aydy+azdzPx,y,zQx+d x,y+dy,z+dz z d dz d d 2 dl=a d +a d +azdz 2. 9/12 zPdl Q +d , +d ,z+dz dl=a d +a d +azdz P( , ,z) d +d d rd rsin rsin d dl=ardr+a rd +a rsin d rsin d rd drrsin dl rsin d rsin rsin d dl=ardr+a rd +a rsin d ( )-( ) ( ) dlx=axdx A dl=A axdx=Axdxetc.

6 NdS=ndSdS2. 10/12ndS=ndSdS2-6 dlx=axdx dly=aydy .dlx dly=ax aydxdy=azdxdy=azdSz( )dlx=dxaxdly=dyaydxdydSz=azdSz=azdxdydSz dSydSx ( dSz ) ( az ) - dSx=dly dlz=axdydz=axdSxdSy=dlz dlx=aydxdz=aydSy( )dSz=dlx dly=azdxdy=azdSz dS n dS=ndS( ) n dS =a d azdz=a d dz=a dS dS =azdz a d =a d dz=a dS ( )z dSz=a d a d =az d d =azdSz2. 11/12dzPd d dzdS =a dS =a d dzdS =a dS =a d dzdSz=azdSz=az d d r dSr=ardSr=a rd a rsin d =arr2sin d d dS =a dS =a rsin d ardr=a rsin drd ( ) dS =a dS =ardr a rd =a rdrd dSr dS dS Flux = A dSS2.

7 12/122-7 A B C A B C 3 A B dV=dlx dly dlz=dxdydz( ) dV=dl dl dlz= d d dz( ) dV=dlr dl dl =r2drsin d d ( ) 2-7 r 2-8 r 2-9 r l 2-10