Magnetic fields in media with differential rotation. 1

Equations are derived, which describe the behaviour of arbitrary off-axis symmetrical magnetic fields in differentially rotating medium with the magnetic diffusion coefficient depending only on radius. Using the equations, the results are obtained, which can explain the absence of magnetic fields for certain fast-rotating stars. At a very fast rate of the star rotation a large differential rotation can occur, which does not permit to generate magnetic field even in the presence of additional rates, sufficient for the generation at a lower value of differential rotation