1204.0275v1. Earth's magnetic field. Computer simulation of the Earth's field in a period of normal polarity between reversals.[1] The lines represent magnetic field lines, blue when the field points towards the center and yellow when away. The rotation axis of the Earth is centered and vertical. The dense clusters of lines are within the Earth's core.[2] The North Magnetic Pole wanders sufficiently slowly to keep ordinary compasses useful for navigation.
At random intervals, however, averaging around several hundred thousand years, the Earth's field reverses and the North and South Magnetic Poles switch places. The magnetosphere is the region above the ionosphere and extends several tens of thousands of kilometers into space, protecting the Earth from cosmic rays that would otherwise strip away the upper atmosphere, including the ozone layer that protects the Earth from harmful ultraviolet radiation. Importance[edit] Variations in the magnetic field strength have been correlated to rainfall variation within the tropics.[11] Magnetic dipole. Dipole moment m. The magnetic field around any magnetic source looks increasingly like the field of a magnetic dipole as the distance from the source increases. External magnetic field produced by a magnetic dipole moment[edit] An electrostatic analogue for a magnetic moment: two opposing charges separated by a finite distance. Each arrow represents the direction of the field vector at that point.
The magnetic field of a current loop. The ring represents the current loop, which goes into the page at the x and comes out at the dot. In classical physics, the magnetic field of a dipole is calculated as the limit of either a current loop or a pair of charges as the source shrinks to a point while keeping the magnetic moment m constant.
With 4π r2 being the surface of a sphere of radius r; Alternatively one can obtain the scalar potential first from the magnetic pole limit, and hence the magnetic field strength (or strength of the H-field) in ampere-turns per meter is is the magnetization. or [4][5] Magnetic moment. The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. A loop of electric current, a bar magnet, an electron, a molecule, and a planet all have magnetic moments. Definition[edit] The magnetic moment is defined as a vector relating the aligning torque on the object from an externally applied magnetic field to the field vector itself.
The relationship is given by [1] where is the torque acting on the dipole and is the external magnetic field, and m is the magnetic moment. This definition is based on how one would measure the magnetic moment, in principle, of an unknown sample. Units[edit] Where A = Ampere m = meter J = Joule In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU, Gaussian, and EMU. And EMU CGS or Gaussian-CGS Where statA = statAmpere cm = centimeter erg = erg abA = Abampere Two representations of the cause of the magnetic moment[edit] Current loop representation[edit] Multipole expansion. Expansion in spherical harmonics[edit] Most commonly, the series is written as a sum of spherical harmonics.
Thus, we might write a function as the sum Here, are the standard spherical harmonics, and are constant coefficients which depend on the function. The term represents the monopole; represent the dipole; and so on. Here, the represent the components of a unit vector in the direction given by the angles and , and indices are implicitly summed.
Is the monopole; is a set of three numbers representing the dipole; and so on. In the above expansions, the coefficients may be real or complex. In the multi-vector expansion, each coefficient must be real: For describing functions of three dimensions, away from the coordinate origin, the coefficients of the multipole expansion can be written as functions of the distance to the origin, —most frequently, as a Laurent series in powers of. . , from a source in a small region near the origin, the coefficients may be written as: with Example Spherical form[edit] .