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Induction Equation
In magnetohydrodynamics, the induction equation is a partial differential equation that relates the magnetic field and velocity of an electrically conductive fluid such as a plasma. It can be derived from Maxwell's equations and Ohm's law, and plays a major role in plasma physics and astrophysics, especially in dynamo theory. Mathematical statement Maxwell's equations describing the Faraday's and Ampere's laws read: \nabla \times \mathbf= -, and \nabla \times \mathbf = \mu_0\mathbf, where: *\mathbf is the electric field. *\mathbf is the magnetic field. *\mu_0 is the vacuum permeability. *\mathbf is the electric current density. The displacement current can be neglected in a plasma as it is negligible compared to the current carried by the free charges. The only exception to this is for exceptionally high frequency phenomena: for example, for a plasma with a typical electrical conductivity of 107 mho/m, the displacement current is smaller than the free current by a factor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetohydrodynamics
In physics and engineering, magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single Continuum mechanics, continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in Plasma (physics), plasmas and liquid metals and has applications in multiple fields including space physics, geophysics, astrophysics, and engineering. The word ''magnetohydrodynamics'' is derived from ' meaning magnetic field, ' meaning water, and ' meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970. History The MHD description of electrically conducting fluids was first developed by Hannes Alfvén in a 1942 paper published in Nature (journal), ''Nature'' titled "Existence of Electromagnetic–Hydrodynamic Waves" which outlined his discovery ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Current Density
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In SI base units, the electric current density is measured in amperes per square metre. Definition Assume that (SI unit: m2) is a small surface centered at a given point and orthogonal to the motion of the charges at . If (SI unit: A) is the electric current flowing through , then electric current density at is given by the limit: j = \lim_ \frac = \left.\frac \_, with surface remaining centered at and orthogonal to the motion of the charges during the limit process. The current density vector is the vector whose magnitude is the electric current density, and whose direction is the same as the motion of the positiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfvén's Theorem
In ideal magnetohydrodynamics, Alfvén's theorem, or the frozen-in flux theorem, states that electrically conducting fluids and embedded magnetic fields are constrained to move together in the limit of large magnetic Reynolds numbers. It is named after Hannes Alfvén, who put the idea forward in 1943. Alfvén's theorem implies that the magnetic topology of a fluid in the limit of a large magnetic Reynolds number cannot change. This approximation breaks down in current sheets, where magnetic reconnection can occur. History The concept of magnetic fields being frozen into fluids with infinite electrical conductivity was first proposed by Hannes Alfvén in a 1943 paper titled "On the Existence of Electromagnetic-Hydrodynamic Waves", published in the journal '' Arkiv för matematik, astronomi och fysik''. He wrote: "On the Existence of Electromagnetic-Hydrodynamic Waves" interpreted the results of Alfvén's earlier paper "Existence of Electromagnetic-Hydrodynamic Waves", publishe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accretion Disc
An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is most frequently a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other forces induce instabilities causing orbiting material in the disk to spiral inward toward the central body. Gravitational and frictional forces compress and raise the temperature of the material, causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of oscillation modes in accretion disks is referred to as diskoseismology. Manifestations Accretion disks are a ubiquitous phenomenon in astrophysics; active galactic nuclei, protoplanetary disks, and gamma ray bursts all involve accretion disks. These disks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galaxies
A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. Galaxies, averaging an estimated 100 million stars, range in size from dwarfs with less than a thousand stars, to the largest galaxies known – supergiants with one hundred trillion stars, each orbiting its galaxy's centre of mass. Most of the mass in a typical galaxy is in the form of dark matter, with only a few per cent of that mass visible in the form of stars and nebulae. Supermassive black holes are a common feature at the centres of galaxies. Galaxies are categorised according to their visual morphology as elliptical, spiral, or irregular. The Milky Way is an example of a spiral galaxy. It is estimated that there are between 200 billion () to 2 trillion galaxies in the observable universe. Most galaxies are 1,000 to 10 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star
A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sky, night; their immense distances from Earth make them appear as fixed stars, fixed points of light. The most prominent stars have been categorised into constellations and asterism (astronomy), asterisms, and many of the brightest stars have proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. The observable universe contains an estimated to stars. Only about 4,000 of these stars are visible to the naked eye—all within the Milky Way galaxy. A star's life star formation, begins with the gravitational collapse of a gaseous nebula of material largely comprising hydrogen, helium, and traces of heavier elements. Its stellar mass, total mass mainly determines it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Resistivity
Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwell's equations. Common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others. The presence of either a positive or negative electric charge produces an electric field. The motion of electric charges is an electric current and produces a magnetic field. In most applications, Coulomb's law determines the force acting on an electric charge. Electric potential is the work done to move an electric charge from one point to another within an electric field, typically measured in volts. Electricity plays a central role in many modern technologies, serving in electric power where electric current is used to energise equipment, and in electronics dealing wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid
In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are Matter, substances which cannot resist any shear force applied to them. Although the term ''fluid'' generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of ''solid'' vary as well, and depending on field, some substances can have both fluid and solid properties. Non-Newtonian fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Substances with a very high viscosity such as Pitch (resin), pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases. A fluid in medicine or biology refers to any liquid constituent of the body (body fluid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Conductivity
Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is , then the resistivity of the material is . Electrical conductivity (or specific conductance) is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter (sigma), but (kappa) (especially in electrical engineering) and (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Velocity Field
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is scalar, the ''flow speed''. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall). Definition The flow velocity ''u'' of a fluid is a vector field : \mathbf=\mathbf(\mathbf,t), which gives the velocity of an '' element of fluid'' at a position \mathbf\, and time t.\, The flow speed ''q'' is the length of the flow velocity vector :q = \, \mathbf \, and is a scalar field. Uses The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow: Steady flow The flow of a fluid is sai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
