  A milestone of dynamo theory is Cowling's theorem, known in its modern form
as the impossibility for an axisymmetric velocity field to generate an
axisymmetric magnetic field by dynamo action. Using an anisotropic electrical
conductivity we show that an axisymmetric dynamo is in fact possible with a
motion as simple as solid body rotation. On top of that the instability
analysis can be conducted entirely analytically, leading to an explicit
expression of the dynamo threshold which is the only example in dynamo theory.
