Formulae: Field of a magnetic moments (dipoles)
Overview Digital Fluxgate Magnetometer Ringcores Formulae    Magnetic field inside    simple coils    Voltage induced    in coils    Field of a magnetic    moments (dipoles)   Additional Information:		Definition and unit of the magnetic dipole moment depends from the unit system. In the CGS (Gauss) unit system the dipole is defined by the following equation: with magnetisation and volume V In the SI system two types of magnetic dipoles are defined. The magnetic dipole moment MCoulomb is defined as the product of polarisation and volume. It can be described by the torque of a magnet in a homogeneous field of 1A/m. The magnetic Moment MAmpere is defined as the product of magnetisation and volume. It can be described by the integrated magnetisation of a magnet or the moment generated by a current in a loop with a defined area.   with magnetisation   and volume V with polarisation   and volume V   The conversation factor between MGauss and MAmpere is 10³:   The conversation factor between MCoulomb and MAmpere is µ0: Although MGauss and MCoulomb have the same dimensions it is not possible to convert the moments directly. The conversation factors has to be used. In the following chapters for all three types of dipole moments M the induction B on the position P will be calculated.     1. Field of the magnetic dipole moment MGauss The following units have to be used in all equations: Position of calculated field (x, y, z, r): Magnetic moments (mx, my, mz) The generated magnetic induction (Bx, By, Bz) will be calculated in   [cm] [G cm³] [nT]     2. Field of the magnetic dipole moment MAmpere The following units have to be used in all equations: Position of calculated field (x, y, z, r): Magnetic moments (mx, my, mz) The generated magnetic induction (Bx, By, Bz) will be calculated in   [m] [Am²] [nT]     3. Field of the magnetic dipole moment MCoulomb The following units have to be used in all equations: Position of calculated field (x, y, z, r): Magnetic moments (mx, my, mz) The generated magnetic induction (Bx, By, Bz) will be calculated in   [m] [V s m] [nT]     4. Examples   Example Magnetic Moment Remarks Planets    Earth MGauss = 8.0 1022 G cm³ MAmpere = 8.0 1022 A m² MCoulomb = 1.0 1019 V s cm equatorial surface field: 30,500 nT    Mercury 3.2 1019 A m² 340 nT    Jupiter 1.4 1027 A m² 428,000 nT    Saturn 4.6 1025 A m² 21,500 nT    Uranus 4.0 1024 A m² 22,800 nT    Neptune 1.9 1024 A m² 13,000 nT   Tools    Screw driver 1.0 10-1 A m²      NiCd Battery 3.0 10-1 A m²     Spacecrafts    Phobos < 5.0 103 A m²      Equator-S        Cluster        Bird 2.0 A m²