Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

The Divergence

散度

The divergence of a vector field


in rectangular coordinates is defined as the scalar product of the del operator and the function

The divergence is a scalar function of a vector field. The divergence theorem is an important mathematical tool in electricity and magnetism.

Applications of divergence

散度的应用

Divergence in other coordinate systems

其他坐标系中的散度
在直角坐标系中，矢量场的散度定义为del算符与该函数的标量积。散度是矢量场的一个标量函数。散度定理是电磁学中一个重要数学工具。
 Index

Vector calculus
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Applications of Divergence

散度的应用

The divergence of a vector field is proportional to the density of point sources of the field. In Gauss' law for the electric field


the divergence gives the density of point charges. In Gauss' law for the magnetic field

the zero value for the divergence implies that there are no point sources of magnetic field.
矢量场的散度与该场的点源密度成正比。在电场的高斯定律中，散度给出了点电荷的密度。在磁场的高斯定律中，散度的零值表明不存在磁场的点源。
 Index

Vector calculus
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Divergence, Various Coordinates

发散，各种坐标

Compared to the divergence in rectangular coordinates:

In cylindrical polar coordinates:
and in spherical polar coordinates:
与直角坐标系中的散度相比：在柱坐标系中：以及在球坐标系中：
 Index

Vector calculus
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