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法拉第定律: 时变磁通量穿过闭合的电路会在电路中感应出电动势.
Lenz's Law:the emf is an equal and opposite reaction to the flux change.
楞次法则: 电动势相等且相反于通量的变化.
Ampere's Law:the line integral of the magnetic field around a closed path equals the net current enclosed (the current direction is implied by the direction of the path according to the right hand rule)
安培定律: 闭合回路四周磁场的线积分等于被包围住的电流.
Lorentz force equation:Give a charge moving in an electric field and a magnetic field, the total force on the charge is the superposition of electric and magnetic forces.
洛仑兹力等式: 电荷在电场和磁场移动,电荷受力为电场力和磁场力之和.
Coulomb's Law:a distribution of stationary charge produces a static electric field (electrostatic field).
库仑法则: 静态分布的电荷产生静态电场.
Biot-Savart Law:the magnetostatic field produced by a steady current.
毕奥.萨伐尔定律: 匀速移动的电荷产生静态磁场.
Gauess's Law:the total outward electric flux through an closed surface is equal to the total charge enclosed by the surface.
高斯定律: 通过任意闭合表面的总电通量等于该表面包含的电荷.
Divergence Theorem:is a vector theorem that allows a surface integral of the normal component of the vector to be transfomed into a volume integral of the divergence of a vector, or vice versa.
散度定理: 将矢量表面积分转换为体积积分的散度形式.
Stoke's theorem:defines the transformation of a line integral of a vector around a closed path into a surface integral over the surface bounded by the path.
斯托克斯定理: 闭合回路的线积分等于以回路为边界的曲面的旋度积分.
在静电场中,对于闭合路径而言,电场线积分为零,即电场旋度为零.显然法拉第定律将受到限制.完整的法拉第定律对静态场和动态场均有效.利用楞次定律对其进行变换可得出上述的完整法拉第定律等式. 从变化的法拉第等式中可以看出线积分与表面积分暗含了两种电动势贡献:变压器电动势(transformer emf)和运动电动势(motional emf).
这两种电动势的产生顾名思义,前者是变化的磁场引起,后者是在磁场中运行产生的.
参考[1]中有两个很好的例子:螺旋电导管(solenoid), 环形变压器(toroidal core transfomer).
由于发现位移电流(Displacement Current)的存在,完善了动态场安培定律.
完整的电流密度公式如下所示:
位移电流不是电荷定向移动的电流,而是变化的电场.参考[1]中的传导电流与位移电流的例子可以帮助理解这个公式.公式里可以看到三种形式电流:传导电流(conduction current), 运流电流(convection current), 位移电流(displacement current).
[结尾]
麦克韦斯方程虽然不是整个过程中的重点,但它却是这一过程的基础 |
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