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AxiomOfChoice

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Suppose you have an axially symmetric magnetic field for which the azimuthal component [tex]B_\phi = 0[/tex]. This is all you know. What are some possible vector potentials [tex]\vec A[/tex] (such that [tex]\vec B = \nabla \times \vec A[/tex]) that would produce this field? (So we're working in cylindrical coordinates.)

The obvious one I've thought of is just [tex]\vec A = A \hat \phi[/tex]. But I'm not sure what form [tex]A[/tex] should take in terms of [tex]B_r[/tex] and [tex]B_z[/tex], where [tex]\vec B = B_r \hat r + B_z \hat z[/tex].

The obvious one I've thought of is just [tex]\vec A = A \hat \phi[/tex]. But I'm not sure what form [tex]A[/tex] should take in terms of [tex]B_r[/tex] and [tex]B_z[/tex], where [tex]\vec B = B_r \hat r + B_z \hat z[/tex].

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