The Dynamo theory proposes a mechanism by which a celestial body such as the Earth generates a magnetic field. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges

## History of theory

In 1905, shortly after composing his Special relativity paper, Albert Einstein described the origin of the Earth's magnetic field as being one of the great unsolved problems facing modern physicists. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Earth 's magnetic field (and the surface magnetic field) is approximately a Magnetic dipole, with one pole near the North pole (see Since then, there have been many studies of the geodynamo problem based on historical measurements of the earth’s field and these works often descend into the domain of the theoretical mathematician.

## Formal definition

Dynamo theory describes the process through which motion of a conductive body in the presence of a magnetic field acts to regenerate that magnetic field. This theory is used to explain the presence of anomalously long-lived magnetic fields in astrophysical bodies. In such bodies, dynamo action depends on the presence of highly conducting fluids such as the liquid iron of the Earth's outer core or the ionized gas of the sun. Dynamo theory of astrophysical bodies uses magnetohydrodynamic equations to investigate how the flow of the conducting materials in the interior of an object can continuously regenerate the magnetic fields of planetary and stellar bodies. Magnetohydrodynamics (MHD ( magnetofluiddynamics or hydromagnetics) is the Academic discipline which studies the dynamics of electrically It was actually once believed that the dipole, which comprises much of the Earth's magnetic field and is misaligned along the rotation axis by 11. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a 3 degrees, was caused by permanent magnetization of the materials in the earth. This means that dynamo theory was originally used to explain the sun's magnetic field in its relationship with that of the Earth. However, this theory, which was initially proposed by Joseph Larmor in 1919, has been modified due to extensive studies of magnetic secular variation, paleomagnetism (including polarity reversals), seismology, and the solar system's abundance of elements. Sir Joseph Larmor ( 11 July 1857 Magheragall, County Antrim, Northern Ireland – 19 May 1942 Holywood Paleomagnetism is the study of the record of the Earth's magnetic field preserved in various Magnetic Minerals through time A geomagnetic reversal is a change in the orientation of Earth's magnetic field such that the positions of magnetic north and magnetic south become interchanged Also, the application of the theories of Carl Friedrich Gauss to magnetic observations proved that Earth's magnetic field had an internal, rather than external, origin. Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German

In the case of the Earth, the magnetic field is believed to be caused by the convection of molten iron, within the outer liquid core, along with a Coriolis effect caused by the overall planetary rotation that tends to organize currents in rolls aligned along the north-south polar axis. In physics the Coriolis effect is an apparent deflection of moving objects when they are viewed from a Rotating frame of reference. When conducting fluid flows across an existing magnetic field, electric currents are induced, which in turn creates another magnetic field. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of When this magnetic field reinforces the original magnetic field, a dynamo is created which sustains itself. Similar magnetic fields are present in many celestial bodies including most stars such as the Sun (which contains conducting plasma) and active galactic nuclei.

## Kinematic dynamo theory

Dynamo theory is a very complex concept to study. Often, college courses and research focuses mainly on kinematic dynamo theory, which is a more simplistic version of the former. It involves the vector velocity field, V, which is prescribed, instead of also varying according to the forces exerted upon the fluid. In Mathematics a vector field is a construction in Vector calculus which associates a vector to every point in a (locally Euclidean space. In Physics, velocity is defined as the rate of change of Position. To examine this sector of the theory, an assumption that must be made is that the magnetic field has to be sufficiently small so that it cannot affect the velocity field. Because of this, the approach cannot divulge anything about the long-term behavior of a dynamo system. This analysis begins with the magnetohydrodynamic theory version of Ohm's law once it has been modified to include resistivity (resistivity is the reciprocal of conductivity σ, J is the current density), which is often assumed to be a constant in order to further simplify the investigation. Ohm's law applies to Electrical circuits it states that the current through a conductor between two points is directly proportional to the Electrical resistivity (also known as specific electrical resistance) is a measure of how strongly a material opposes the flow of Electric current.

Using Maxwell's equations simultaneously with the curl of the aforementioned equation, one can derive what is basically the linear eigenvalue equation for magnetic fields (B) which can be done when assuming that the magnetic field is independent from the velocity field. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric One arrives at a critical magnetic Reynolds number above which the flow strength is sufficient to amplify the imposed magnetic field, and below which it decays. In Fluid mechanics and Heat transfer, the Reynolds number \mathrm{Re} is a Dimensionless number that gives a measure of the Ratio

The most functional feature of kinematic dynamo theory is that it can be used to determine what fields or systems are or are not dynamos. By applying a certain velocity field to a small magnetic field, it can be determined through observation whether the magnetic field tends to grow or not in reaction to the applied flow. If the magnetic field does grow, then the system is either capable of dynamo action or is a dynamo, but if the magnetic field does not grow, then it is simply referred to as non-dynamo.

The membrane paradigm is a way of looking at black holes that allows for the material near their surfaces to be expressed in the language of dynamo theory. In Black hole theory the black hole membrane paradigm is a useful " Toy model " method or "engineering approach" for visualising and calculating A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e

## Nonlinear dynamo theory

The kinematic approximation becomes invalid when the magnetic field becomes strong enough to affect the fluid motions. In that case the velocity field becomes affected by the Lorentz force, and so the induction equation is no longer linear in the magnetic field. In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation In most cases this leads to a quenching of the amplitude of the dynamo. Such dynamos are sometimes also referred to as hydromagnetic dynamos. Virtually all dynamos in astrophysics and geophysics are hydromagnetic dynamos.

## References

• Demorest, Paul. "Dynamo Theory and Earth's magnetic Field. " 21 May 2001. [1]
• Fitzpatrick, Richard. "MHD Dynamo Theory. " 18 May 2002. [2]