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We present a study of boundary conditions for solutions of dynamo generated magnetic fields under cylindrical geometry. These solutions are applicable both to galaxies, and to the accretion disks which are thought to be present in objects like AGN, compact binaries, and YSOs. It is important to consider the form of external fields, as the solution of the problem depends critically on the boundary conditions and consequently on the eigenfunctions of the solutions present outside. In previous work the match has been approximated by either setting $B_r$ to zero, as is done in the galactic context in the case of curl-free fields, or by using an asymptotic form of the disk solutions. We obtain solutions to the external fields which are parameterized to range from vacuum to force-free configurations. We find that the solution with a vacuum boundary conditions has a maximum at the disk surface which is contrary to the assumption usually made. The conducting boundary conditions appropriate to situations when outflows are present, will also be discussed.
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