Hydrostatics of a magnetic fluid in the vicinity of a magnetized plate

Abstract

The theory allowing to describe possible free surface shapes of the magnetic fluid surrounding the thin flat magnetizable plate with infinite magnetic susceptibility is presented. In order to solve the Maxwell's equations and hydrostatics equation for magnetic fluid together with appropriate boundary conditions at the magnetic luid free surface the methods of the theory of complex variable are used. Distribution of the magnetic field and pressure in the magnetic fluid surrounding the plate are found. The equation describing the free surface shapes of the magnetic fluid is derived. The graphs of the free surface shapes of the magnetic fluid near the plate are given for various values of the volume of the fluid surrounding the plate. The angle between the plate and the applied external magnetic field vector in infinity is supposed to be equal to zero, 90°, 45° and 135°. The free surface shapes are shown to be dependent on the plate size, its orientation relative to the applied magnetic field vector, magnitude of the magnetic field and the magnetic fluid volume surrounding the plate. It is shown that the small volumes of the magnetic fluid is concentrated near the edges of the plate in the form of drops. As the fluid volume increases the size of the drops increases too. At the certain critical magnetic fluid volume the drops are linked at the certain distance from the plate. Near I he central part of plate the vapor cavities are being formed. The size of the cavities is decreasing when the luid volume is increasing.