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The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The magnetic field of a small [note 6] straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m). The equations are non-trivial and depend on the distance from the magnet and the orientation of the magnet.
A magnetic field is a vector field, but if it is expressed in Cartesian components X, Y, Z, each component is the derivative of the same scalar function called the magnetic potential. Analyses of the Earth's magnetic field use a modified version of the usual spherical harmonics that differ by a multiplicative factor.
More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment, which produces the first term in the multipole expansion [note 1] of a general magnetic field. Both the torque and force exerted on a magnet by an external magnetic field are proportional to that magnet's magnetic moment.
The Villari reversal is the change in sign of the magnetostriction of iron from positive to negative when exposed to magnetic fields of approximately 40 kA/m. On magnetization, a magnetic material undergoes changes in volume which are small: of the order 10 −6.
The magnetic field is only varied along a single axis; its scalar value h is positive in one direction and negative in the opposite direction. The ferromagnet is assumed to have a uniaxial magnetic anisotropy with anisotropy parameter K u. As the magnetic field varies, the magnetization is restricted to the plane containing the magnetic field ...
[1] [2] A diagram showing a representative set of neighboring field lines is a common way of depicting a vector field in scientific and mathematical literature; this is called a field line diagram. They are used to show electric fields , magnetic fields , and gravitational fields among many other types.
By convention, declination is positive when magnetic north is east of true north, and negative when it is to the west. Isogonic lines are lines on the Earth's surface along which the declination has the same constant value, and lines along which the declination is zero are called agonic lines. The lowercase Greek letter δ (delta) is frequently ...
Magnetic scalar potential of flat cylinder magnets encoded as color from positive (magenta) through zero (yellow) to negative (cyan). The scalar potential is a useful quantity in describing the magnetic field, especially for permanent magnets.