用毕奥萨伐尔计算磁偶极子的磁场分布

-李建青(武汉理工大学物理系,武汉430070)(:2004-03-01)本文提供了一种用毕奥-萨伐尔定律求解磁偶极子的磁场分布公式的方法.此方法简单明了,求解过程严谨,为针对低年级大学生开设的/大学物理0课程中导出磁偶极子磁场的公式提供了一个很好的途径.磁偶极子;小环流;磁场;毕奥-萨伐尔定律CALCULATINGTHEMAGNETICFIELDOFAMAGNETICDIPOLEBYBIOT-SAVART.SLAWLiJianqing(PhysicsDepartment,WuhanUniversityofScience&Technology,Wuhan430070)AbstractThispaperoffersaconciseandrigorousmethodtocalculatethemagneticfieldbyamagneticdipoleusingBio-tSavart.slaw.Itisgivenagoodwaytodemonstratemagneticfieldformulaforamagneticdipoletojuniorstudentsinstudyingphysics.KeyWordsmagneticdipole;coincarryingcurrent;magneticfield;Bio-tSavart.slaw1,./0,,.,5656[1],A,B=$@A[2];[3~6],.56[7~9],/0.-.2-1,I,ROxyz,,z.Pxz,P114Vol.14No.42004r,Idl,R,r=xi+zkR=RcosUi+RsinUj(1)rc=r-R=(x-RcosU)i-RsinUj+zkIdl=IRdUSU=IRdU(-sinUi+cosUj)-,IdlPdBdB=L04PIdl@rrc3=L04PIRdUSU@(r-R)|r-R|3(2)^SU@(r-R)=(-sinUi+cosUj)@[(x-RcosU)i-RsinUj+zk]=zcosUi+zsinUj+(R-xcosU)k|r-R|3=(x2+z2+R2-2xRcosU)3/2(3)(3)(2),dB=L0IR4PzcosUi+zsinUj+(R-xcosU)k(x2+z2+R2-2xRcosU)3/2dU,PBB=RLdB=L0IR4P#Q2P0zcosUi+zsinUj+(R-xcosU)k(x2+z2+R2-2xRcosU)3/2dU^By=L0IR4P#Q2P0zsinU(x2+z2+R2-2xRcosU)3/2dU=0_B=L0IR4P#Q2P0zcosUi+(R-xcosU)k(x2+z2+R2-2xRcosU)3/2dU(4)(4),,.[3]~[6],.,.3rmR,r=x2+z2,(),(4)Rr2:(x2+z2+R2-2xRcosU)-3/2=r-31+R2r2-2xRcosUr2-3/2Ur-31-2xRcosUr2-3/2Ur-31+3xRcosUr2(5)(5)(4),B=L0IR4P#Q2P0zcosUi+(R-xcosU)kr31+3xRcosUr2dU=L0IR2P3zxRr5P2i+PRr3-3x2Rr5P2k=L0IPR24P3zxr5i+2r2-3x2r5k(6)x2=r2-z2,r=xi+zk(6)B=L0IPR24P3z(xi+zk)r5-1r3k=L0IPR24P3zrr5-1r3k(7)2pm=IPR2kpmz=pmrcosH=pm#r(8)(8)(7),B=L04P3(pm#r)rr5-pmr3(9),,.,(9).2,2,(47)15Vol.14No.42004.,,,.,,,.2(HIPS),.2:1946;1950;1952(Rumford);1955;19551963.1966310,78.,,.[1]11:,1988.272~232[2],..:,1996.78~81[3],,..287~290[4],..:,1984.211~224[5],..:.:.1999.227~240(15):k=cosH^r-sinH^SH(9),B=L04P3(pmrcosH)rr5-pm(cosH^r-sinH^SHr3=L04P2pmcosH)r3^r+pmsinHr3^SH(10)[1],.[M].:,1978.95~97[2].[M].:,1982.73~75[3]...,1983,2(11):12~17[4].[J].,1999,18:(1):14~17[5].[J].,1999,18(6):20~22[6].[J].,2001,20(2):19~20[7].[M].:,1999[8],.[M]..:,1998[9]Halliday,Resnick,Walker,etc.FundamentalsofPhysics,6thed.JohnWiley&Sons,Inc.2002(23),,.,.[1],.GaN).,1999,20(2):89[2],..:,1993.295~296[3]..:,1987.753[4]KubotaK,etal.J.Appl.Phys.1989,66(7):2984;84(11):6312[5]DemiryontH.etal.AppliedOptics,1985,24(4):490[6]StriteS,MorkocH.J.Vac.Sci,Technol.1992,B(4):123747Vol.14No.42004