1、 1 矢量场的旋度矢量场的旋度 斯托克斯定理斯托克斯定理Rotation of Vector Field,Stokes Theorem)(xALl dAcAnSLl dAsl dALs0limnnsl dAAALslimrot0)(xA0AsLsdAsdA)(2323222221212222dxhdxhdxhdzdydxdl)3,2,1()()()(222ixzxyxxhiiii2)()()(1111111312321321321321333222111333222111AhhxAhhxAhhxhhhAxhexhexhexhexhexhe1211323322212112131331121221
2、3133212211qHHeqHHeqeqHHeqeqHHeqeqHHeqeqHHeqHHeqe2322131133323223313113232332qHHeqHHeqeqHHeqeqHHeqeqHHeqe)()()()()()(1112221213331113312223332321332211221332211321AhxAhxhheAhxAhxhheAhxAhxhheAhAhAhxxxehehehhhhA)()()(13321322132113213212xhhhxxhhhxxhhhxhhh321,eee),(321xxx332211321),(eAeAeAxxxAA1122)(eAA
3、iiAA22)(332222)()(eAeAxyzZ为常数平面y为常数平面x为常数平面(x,y,z)pyezexezeyexezyxzzyyxxzyxzyxzyxzyxeAeAeAAzyxAAAzyxeeeAzAyAxAAzeyexe)()()(22222222222zxyz为常数平面r为常数平面为常数平面ezererzererezrerAzAezAArArAAzrereerAzAArrArrAzueurerueuzrrzzrzrzrzr)()1(111)(11zzrrzreAeAeAAzuurrurrrueArrArr)()()(1)(11)(12222222222)()(2AAArrrrA
4、rrAAAArrAAA222222222)(2)(zzAA22)(zry(r,)ereex为常数r为常数为常数321 ,xxrxcos ,sinsin ,cossinrzryrxsin ,1321rhrhhArArArrrAureurerueurerererrrsin1)(sinsin1)(1sin11sin1122eArArrerArAreAArArrAArrerereArrrrr)(1)(sin11)(sinsin1sin1sin1sin12eAeAeAAururrurrrurr)()()(sin1)(sinsin1)(1222222222222AAArAArrrsin1)(sinsin12)(222)sin2ctg(sin2)()sincossin2(2)(22222222AAArAAAAArAArr
