Mathematical modeling of the free surface of a magnetic fluid surrounding a magnetized plate

We propose a mathematical model that allows one to describe the shape of the free surface of a magnetic fluid surrounding a thin flat magnetized plate with infinite magnetic susceptibility. The Maxwell equations and the hydrostatics equations for magnetic fluid with the corresponding boundary conditions on the free surface of the magnetic fluid are solved. By methods of complex analysis, we find the distribution of the magnetic field and the pressure in the magnetic fluid surrounding the plate. An equation for the shape of the free surface of a magnetic fluid near the plate is written, and graphs of equilibrium shapes of the free surface of the magnetic fluid in a neighborhood of the plate are given for various volumes of the fluid and the angle between the plate and the vector of the external magnetic field.