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Laminar electrically conducting Couette flows with the hydrodynamically stable quasi‐Keplerian rotation profile and nonuniform conductivity are probed for dynamo instability. In spherical geometry, the equations for the poloidal and the toroidal field components completely decouple, resulting in free decay, regardless of the spatial distribution of the electric conductivity. In cylindrical geometry the poloidal and toroidal components do not decouple, but here also we do not find dynamo excitations for the cases that the electric conductivity only depends on the radius or – much more complex– that it only depends on the azimuthal or the axial coordinate. The transformation of the plane‐flow dynamo model of Busse and Wicht (1992) to cylindrical or spherical geometry therefore fails. It is also shown that even the inclusion of axial flows of both directions does  not  support the dynamo mechanism. The Elsasser toroidal‐velocity antidynamo theorem, according to which dynamos without any radial velocity component cannot work, is thus not softened by nonuniform conductivity distributions.

On the toroidal‐velocity antidynamo theorem under the presence of nonuniform electric conductivity