  We investigate analytically the magnetic instability in a rotating and
electrically conducting fluid induced by an imposed magnetic field with its
associated electric current. The short-wavelength approximation is used in the
linear stability analysis, i.e. the length scale of the imposed field is much
larger than the wavelength of perturbations. The dispersion relationship is
derived and then simplified to give the criteria for the onset of the magnetic
instability in three cases of imposed field, namely the axial dependence, the
radial dependence and the mixed case. The orientation of rotation, imposed
field and imposed current is important for this instability.
