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Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Magnetic Fields01:27

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
A magnetic field is defined by the force that a charged particle experiences...
Magnetic Field Lines01:19

Magnetic Field Lines

The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the magnetic field lines forms a closed loop. The field lines emerge from the north pole (N), loop around to the south pole (S), and continue through the bar magnet back to the north pole.
Magnetic field lines follow several hard-and-fast rules:
Magnetic Susceptibility and Permeability01:31

Magnetic Susceptibility and Permeability

In linear magnetic materials, like paramagnets and diamagnets, magnetization is proportional to the magnetic field intensity. The constant of proportionality, a dimensionless number, is called magnetic susceptibility. The value of the susceptibility depends on the type of material.
When diamagnetic materials are placed under an external magnetic field, the moments opposite to the field are induced. Hence, the susceptibility for diamagnets has a minimal negative value of 10-5–10-6. Since...

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Related Experiment Video

Updated: May 14, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Long-range correlations and coherent structures in magnetohydrodynamic equilibria.

Peter B Weichman1

  • 1BAE Systems, Advanced Information Technologies, 6 New England Executive Park, Burlington, Massachusetts 01803, USA.

Physical Review Letters
|February 2, 2013
PubMed
Summary
This summary is machine-generated.

This study derives the 2D magnetohydrodynamic equations, revealing long-ranged correlations between magnetic and velocity fields. These findings describe coherent structures like eddies and jets, impacting solar tachocline simulations.

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Last Updated: May 14, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Area of Science:

  • Plasma Physics
  • Fluid Dynamics
  • Astrophysics

Background:

  • The 2D magnetohydrodynamic (MHD) equations govern plasma behavior.
  • Previous variational treatments used simplified assumptions for thermodynamic distributions.
  • Understanding coherent structures in MHD is crucial for astrophysical phenomena.

Purpose of the Study:

  • To derive the equilibrium theory of 2D MHD equations.
  • To investigate the nature of conserved integrals and field correlations.
  • To compare new findings with previous variational approaches and pure fluid equilibria.

Main Methods:

  • Derivation of the full infinite hierarchies of conserved integrals for 2D MHD.
  • Development of an exact description using coupled elastic membranes.
  • Analysis of long-ranged correlations between magnetic and velocity fields.

Main Results:

  • An exact description emerges in terms of two coupled elastic membranes.
  • Long-ranged correlations between magnetic and velocity fields are identified.
  • Coherent structures, including compact eddies and zonal jets, are observed, similar to pure fluid equilibria.

Conclusions:

  • The derived theory offers a novel perspective on 2D MHD equilibria.
  • Findings differ significantly from previous variational treatments.
  • The results have implications for understanding phenomena like the solar tachocline.