The magnetodynamics stability of the bounded annular cylinder (tar) penetrated by unsteady magnetic field has been treated. Eigenvalue relationships are established and discussed. The influence of the magnetic force and self-gravitating force of the instability of the model has been investigated. Axisymmetric disturbance makes the self-gravitating force destabilized only for long wavelengths. The non-axisymmetric disturbances destabilize long and short wavelengths.  The MHD studies the stability problems material applications in several fields of science. For example, the water proceeding from a circular cylinder nozzle. The stability of short wavelengths and instability of long wavelengths affected the magnetic region. The effect on the magnetic region has an influence stabilizing in all modes. Surface tension is stable in all modes for short wavelengths, but unstable for long wavelengths. Special cases of stability for several models have been considered.

axisymmetric, magnetodynamic instability, capillary magnetic field.