论文标题
Helmholtz的两个智障场的定理及其在Maxwell方程式的应用
Helmholtz's theorem for two retarded fields and its application to Maxwell's equations
论文作者
论文摘要
证明了Helmholtz定理的扩展，该扩展指出，两个智障的向量字段$ {\ bf f} _1 $和$ {\ bf f} _2 $唯一确定了满足适当的初始条件和边界条件的唯一确定。 $ \ nabla \ cdot {\ bf f} _ {2} $及其耦合卷发$ - \ nabla \ nabla \ times {\ bf f} _ {1} - \ partial {\ partial {\ bf f} _ {2} _ {2}/\ poartial t $ and t $ and nabla nabla nabla \ \ \ \ \ \ \ \ \ \时代f} _ {2} - （1/c^2）\ partial {\ bf f} _ {1}/\ partial t $，其中$ c $是字段的传播速度。当将该定理的推论应用于麦克斯韦的方程式时，直接获得了延迟的电场和磁场。定理的证明依赖于矢量波方程溶液独特性的新颖证明。
An extension of the Helmholtz theorem is proved, which states that two retarded vector fields ${\bf F}_1$ and ${\bf F}_2$ satisfying appropriate initial and boundary conditions are uniquely determined by specifying their divergences $\nabla\cdot{\bf F}_{1}$ and $\nabla\cdot{\bf F}_{2}$ and their coupled curls $-\nabla\times{\bf F}_{1}-\partial {\bf F}_{2}/\partial t$ and $\nabla\times{\bf F}_{2}-(1/c^2)\partial {\bf F}_{1}/\partial t$, where $c$ is the propagation speed of the fields. When a corollary of this theorem is applied to Maxwell's equations, the retarded electric and magnetic fields are directly obtained. The proof of the theorem relies on a novel demonstration of the uniqueness of the solutions of the vector wave equation.
