Gauss law.ppt

1 Chapter23 Gauss Law 2 1 Electricfieldline ElectricfieldlineandFlux 电场线和电通量 Magnitude thenumberoflinesperunitareaisproportionaltothemagnitudeof Direction thedirectionofthetangenttoafieldlineatapointgivesthedirectionof Faraday forceline 3 4 电偶极子 5 一对等量正点电荷 6 一对异号不等量点电荷 7 平板电容器 8 Charactersofelectricfieldlines Electricfieldlinesoriginatefrompositivechargeandterminateatnegativecharge 电场线从正电荷发出到负电荷终止 中间不会间断 不会闭合 不会交叉 ThesecharacterscanbedescribedbyGauss sLaw 9 ElectricFlux 电通量 Surfacevector 面矢量 1 ElectricFluxforthesurface Sand S Then 通过某曲面电场线的条数 Thenumberofelectricfieldlinescrossacertainsurface 10 2 theelectricfluxforanarbitraryGaussiansurface 3 theelectricfluxforaclosedGaussiansurface Thedirectionofsurfacevectorextendsfrominwardtooutward 11 1 thefluxofelectricfiledduetoapointchargethroughasphericalsurface Gauss Law Gauss lawrelatesthenetfluxofanelectricfieldtothenetchargethatisenclosedbythesurface 12 设外有一封闭曲面 两曲面之间没有电荷 由电场线的连续性可知 即同一点电荷激发的场强的电通量与封闭曲面的形状无关 只与点电荷电量有关 2 thefluxofelectricfiledduetoapointchargethroughanarbitraryclosedsurface 13 3 thefluxofelectricfiledduetoanychargedsystemthroughanarbitraryclosedsurface 14 AchargedisolatedConductor Electrostaticequilibrium 静电平衡 Conductorhasmanyfreeelectrons Whenaconductorischargedorplacedinaelectricfieldtheconductionelectronswillquicklydistributethemselvesinsuchawaythatthenetinternalelectricfieldiszero andthereisnomovementofcharge 当导体带电或至于外静电场中 导体内电荷很快移动使导体内部电场为零 且导体上无电荷移动 15 1 Aconductorisplacedinanexternalstaticelectricfield 内部电场为零表面电场垂直于表面 16 2 achargedisolatedconductor 17 Aconductorwithacavity 中空的导体 Thereisnonetchargeonthecavitywalls allthechargeremainsontheoutersurfaceofconductor 18 ApplyingGauss Lawtoobtaintheelectricfieldduetochargedsystem 适用范围 高斯定理适用于求解具有空间对称性的电荷体系的电场 关键 分析对称性选取合适的高斯面 把积分化成乘积 对称性原理 皮埃尔 居里1894 对称的原因 对称的结果 19 ApplyingGauss sLaw1 CylindricalSymmetry 轴对称或旋转对称 Findtheelectricfielddistributionduetoauniformlychargedlongcylindricalrod 均匀带电长杆 20 ApplyingGauss sLaw2 PlanarSymmetry 平移对称 Findtheelectricfielddistributionduetoauniformlychargednonconductingsheet 均匀带电板 21 Exercise Findtheelectricfieldduetotheequalsurfacedensitybutoppositesignchargedlargeplates 22 ApplyingGauss sLaw3 SphericalSymmetry 球对称 FindtheelectricfielddistributionduetoauniformlychargedsphereshelloftotalchargeQandradiusR 均匀带电球壳 Solution SelecttheGaussiansurfaceS1andS2 23 Findtheelectricfieldd