A Problem with Cowling's Theorem

Abstract

 Cowling's theorem is indispensable for the study of the magnetic fields of celestial bodies and conductive fluids. Cowling's paper argues that it is impossible that an axially symmetric field shall be self-maintained. However, the discussion of this paper uses Ohm's law equation, which does not include the electromotive force due to vector potential. It is unnatural to prove with a formula that does not include this physically existing electromotive force. Furthermore, since the fluctuation (growth) of the magnetic field is derived from a natural formula that includes the electromotive force, it is natural to think that such a phenomenon exists. Furthermore, the energetic considerations of the induction term of the equation allow the possibility of fluctuation (growth) of the magnetic field to be described in detail. Then, it can be found that the conversion of convective energy to electrical energy and from electrical energy to convective energy occurs simultaneously. Since the absolute value of these energies is the same, they cancel out and become zero, so at first glance nothing seems to happen. However, individual energies exist, and fluctuations (growth) are possible while the absolute value remains the same. Therefore, an increase in the axisymmetric magnetic field due to axisymmetric convection is possible.