The instability which leads to the splitting of a conducting liquid cylinder by the current flowing through

Magnetocapillary and electrocapillary instabilities of a conducting liquid cylinder are considered, which cause the splitting of the cylinder throughout its length. Linearized magnetohydrodynamic equations describing such instabilities are considered, and their increments are found in the limit of low viscosity and high conductivity. It is demonstrated that splitting instabilities may arise only when the current reaches some critical value dependent only on the surface tension coefficient, electric potential, and conductor diameter.