Formation of rupture in a conducting fluid layer under the action of an oscillating tangential magnetic field

Possible equilibrium shapes of the free surface of a conducting fluid layer subjected to oscillating tangential magnetic field are studied. Exact solution corresponding to the formation of rupture in a fluid layer is derived using the conformal mapping method. The width of the rupture has been defined; it depends on the problem parameters, viz. the value of the external magnetic field and the surface tension coefficient.