Charge Conservation

电荷守恒

The fundamental idea of charge conservation is contained in Maxwell's Equations. If we take the divergence of the differential form of Ampere's law:

电荷守恒的基本思想包含在麦克斯韦方程组中。如果我们对安培定律的微分形式取散度：

The first term above is zero by identity, and using Gauss' law:

上式中的第一项由恒等式得零，利用高斯定律：

the result is:

结果是:

The implication here is that the current through any enclosed surface is equal to the time rate of charge within the surface. This is an important test of Maxwell's equations since all experimental evidence points to charge conservation.

这里的意思是，通过任何闭合曲面的电流等于该曲面内电荷的变化率。这是检验麦克斯韦方程组的重要测试，因为所有实验证据都指向电荷守恒。

Maxwell's Equations

麦克斯韦方程

Index

Maxwell's equations concepts

麦克斯韦方程组的概念

HyperPhysics***** Electricity and Magnetism

HyperPhysics ***** 电学和磁学

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The Wave Equation

波动方程

Maxwell's Equations contain the wave equation for electromagnetic waves. One approach to obtaining the wave equation:

麦克斯韦方程组包含了电磁波的波动方程。获得波动方程的一种方法是：

1. Take the curl of Faraday's law:

对法拉第定律取旋度：

2. Substitute Ampere's law for a charge and current-free region:

2. 代入安培定律（在无电荷和电流的区域中）：

This is the three-dimensional wave equation in vector form. It is hard to visualize in this form. It looks more familiar when reduced a plane wave with field in the x-direction only:

这是矢量形式的三维波动方程。以这种形式来看很难想象。当将其简化为仅在x方向传播的平面波时，看起来更熟悉：

Since the electric field is in the x-direction only, the propagation is perpendicular to the x-axis and can be in any direction in the yz plane, depending upon the values of the derivatives. This equation is in the general form of the two-dimensional wave equation.

由于电场仅在x方向存在，传播方向垂直于x轴，在yz平面内可以是任何方向，具体取决于导数的值。该方程具有二维波动方程的一般形式。

Discussion of wave equation

波动方程讨论