Axially symmetric B field vector potential?

1. Dec 6, 2009

AxiomOfChoice

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

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

Last edited: Dec 6, 2009
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