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AxiomOfChoice

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**What does "axially symmetric" mean mathematically?**

If we, for example, say that a magnetic field [tex]\vec B[/tex] is axially symmetric, does that mean that (in cylindrical coordinates) we have [tex]\frac{\partial \vec B}{\partial \phi} = 0[/tex], where [tex]\phi[/tex] is the azimuthal angle?