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Related Concept Videos

Magnetic Fields01:27

Magnetic Fields

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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...
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Magnetic Field due to Moving Charges01:23

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A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
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Magnetostatic Boundary Conditions01:28

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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...
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Magnetic Vector Potential01:15

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In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
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Maxwell's Equation Of Electromagnetism01:29

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James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is...
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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...
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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Chaotic magnetic fields in Vlasov-Maxwell equilibria.

Abhijit Ghosh1, M S Janaki1, Brahmananda Dasgupta1

  • 1Saha Institute of Nuclear Physics, I/AF Bidhannagar, Calcutta 700 064, India.

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Researchers found stationary solutions for Vlasov-Maxwell equations by analyzing particle motion invariants. These equilibria can exhibit chaotic behavior, linked to a specific Hamiltonian structure.

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Area of Science:

  • Plasma physics
  • Computational physics

Background:

  • The Vlasov-Maxwell equations describe the behavior of plasmas.
  • Understanding stationary solutions is crucial for plasma confinement and stability.

Purpose of the Study:

  • To derive stationary solutions of the Vlasov-Maxwell equations.
  • To investigate the relationship between particle motion invariants and plasma equilibria.
  • To explore the potential for chaotic dynamics in these equilibria.

Main Methods:

  • Exploiting single particle motion invariants.
  • Establishing functional relations between current and vector potential.
  • Analyzing the associated Hamiltonian for specific invariant combinations.

Main Results:

  • Derived stationary solutions for Vlasov-Maxwell equations.
  • Demonstrated linear or nonlinear functional relationships between current and vector potential.
  • Showed that specific Vlasov-Maxwell equilibria possess a Hamiltonian exhibiting chaos.

Conclusions:

  • Stationary plasma equilibria can be characterized by particle motion invariants.
  • The derived equilibria are not always stable and can exhibit complex chaotic dynamics.