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Circular symmetry

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Title: Circular symmetry  
Author: World Heritage Encyclopedia
Language: English
Subject: Rotation, Disk (mathematics), Gaussian beam, Point groups in two dimensions, Rotation (mathematics)
Collection: Rotation, Symmetry
Publisher: World Heritage Encyclopedia

Circular symmetry

Circular symmetry in mathematical physics applies to a 2-dimensional field which can be expressed as a function of distance from a central point only. This means that all points on each circle take the same value.

An example would be magnetic field intensity in a plane perpendicular to a current-carrying wire. A pattern with circular symmetry would consist of concentric circles.

The 3-dimensional equivalent term is spherical symmetry. A scalar field has spherical symmetry if it depends on the distance to the origin only, such as the potential of a central force. A vector field has spherical symmetry if it is in radially inward or outward direction with a magnitude and orientation (inward/outward) depending on the distance to the origin only, such as a central force.

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