Magnetic field distribution in a magnetic liquid spike

The Rosensweig, or normal field instability, is a well known phenomenon where formation of a spike like shape appears on a magnetic liquid surface when it is exposed to a sufficiently large external magnetic field. While the surface shape of magnetic liquid has an impact on the magnetic field distribution and vice versa, it is somehow essential to know the magnetic field distribution within the magnetic liquid. The aim of the magnetic field calculation is to show that the magnetic field density is distributed similarly as the shape of the free surface. The calculation is placed in the 3D space and performed at the equilibrium state of magnetic liquid using the Finite Element Method based software Opera Field. Only a single spike of the magnetic liquid is included in the computational model, while the pattern of the surface deformation is assumed to be hexagonal and distributed periodically over the surface.