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圆对称

数学物理领域,一个定义域为二维空间的函数,假若只与离某参考点的距离有关,则此函数具有圆对称性(circular symmetry)。对于一组以此参考点为圆心的同心圆,在同一个同心圆的每一个位置,函数值都相同。

在一个与带电流电线垂直的平面,磁场具有圆对称性。一个具有圆对称性的图案是由同心圆构成的。

球对称性

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延伸至三维空间,对应的术语是球对称性(spherical symmetry)。假若,一个标量场只与离某参考点的距离有关,则此标量场具有球对称性。例如,连心势重力势电势都具有球对称性。

假若,一个矢量场,方向都是朝内的径向方向或都是朝外的径向方向。大小仅与离参考点的距离有关,则此矢量场具有球对称性。例如,有心力重力静电力都具有球对称性。

圆柱对称性

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在三维空间里,设定一条直轴。在三维空间的每一个位置,假若一个函数只与这位置离一条直轴的距离有关,则称此函数具有圆柱对称性(cylindrical symmetry)。以设定的直轴为圆柱轴心,位于同一个圆柱面的点都具有同样的函数值。

例如,一条笔直的无限长电线,其电流所造成的磁场,具有圆柱对称性。离此无限长电线同距离位置的磁场,大小都相同。

参阅

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圆对称
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