Magnetohydrostatics

Magnetohydrostatics is a branch of theoretical physics that studies the equilibrium states of electrically conducting fluids in the presence of magnetic fields. It combines the principles of magnetohydrodynamics, which deals with the dynamics of conducting fluids, and electrostatics, which deals with static electric charges. In magnetohydrostatics, the fluid is assumed to be at rest, and the magnetic field is also assumed to be unchanging in time.

The core concept is the balance between the magnetic forces acting on the fluid and the pressure gradients within the fluid. When a conducting fluid is present in a magnetic field, electric currents can be induced within the fluid due to its motion or external electric fields. These currents, in turn, generate their own magnetic fields, which interact with the original field. This interaction leads to magnetic forces, often referred to as the Lorentz force, which can compress or confine the fluid.

A key equation in magnetohydrostatics is the condition for equilibrium, which typically involves the pressure gradient being balanced by the magnetic forces. For a perfectly conducting fluid, this means that magnetic field lines are "frozen" into the fluid, and the fluid pressure must be sufficient to counteract the magnetic pressure. Applications of magnetohydrostatics include the study of stellar interiors, such as the Sun's core, where plasma is confined by magnetic fields, and the design of fusion reactors, where strong magnetic fields are used to contain superheated plasma. It also finds relevance in geophysics for understanding the Earth's magnetic field and its interaction with the planet's conductive interior.