physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

and in particular in the theory of

magnetism Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...

, an antidynamo theorem is one of several results that restrict the type of

magnetic fields A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...

that may be produced by

dynamo file:DynamoElectricMachinesEndViewPartlySection USP284110.png, "Dynamo Electric Machine" (end view, partly section, ) A dynamo is an electrical generator that creates direct current using a commutator (electric), commutator. Dynamos were the f ...

action. One notable example is

Thomas Cowling Thomas George Cowling Fellow of the Royal Society, FRS (17 June 1906 – 16 June 1990) was an England, English astronomer. Early life and education Cowling was born in Hackney, London, the second of four sons of George Cowling and Edith El ...

's antidynamo theorem which states that no

axisymmetric Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which i ...

magnetic field can be maintained through a self-sustaining dynamo action by an axially symmetric current. Similarly, the

Zeldovich Yakov Borisovich Zeldovich ( be, Я́каў Бары́савіч Зяльдо́віч, russian: Я́ков Бори́сович Зельдо́вич; 8 March 1914 – 2 December 1987), also known as YaB, was a leading Soviet physicist of Bel ...

's antidynamo theorem states that a two-dimensional, planar flow cannot maintain the dynamo action.Zeldovich, Y. B. (1957). The magnetic field in the two-dimensional motion of a conducting turbulent fluid. Sov. Phys. JETP, 4, 460-462.

Consequences

Apart from the

Earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...

, some other bodies such as

Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...

and

Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...

, and the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

have significant magnetic fields whose major component is a

dipole In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: *An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system i ...

, an axisymmetric magnetic field. These magnetic fields are self-sustained through fluid motion in the Sun or planets, with the necessary non-symmetry for the planets deriving from the

Coriolis force In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...

caused by their rapid rotation, and one cause of non-symmetry for the Sun being its

differential rotation Differential rotation is seen when different parts of a rotating object move with different angular velocities (rates of rotation) at different latitudes and/or depths of the body and/or in time. This indicates that the object is not solid. In flu ...

. The magnetic fields of planets with slow rotation periods and/or solid cores, such as

Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...

Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never fa ...

, and

Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury (planet), Mercury. In the English language, Mars is named for the Mars (mythology), Roman god of war. Mars is a terr ...

, have dissipated to almost nothing by comparison. The impact of the known anti-dynamo theorems is that successful dynamos do not possess a high degree of symmetry.

References

Geomagnetism Magnetohydrodynamics Physics theorems No-go theorems {{geophysics-stub

Consequences

See also

References