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Because magnetic monopoles do not exist, the magnetic field at a large distance from any static magnetic source looks like the field of a dipole with the same dipole moment. For higher-order sources (e.g. quadrupoles) with no dipole moment, their field decays towards zero with distance faster than a dipole field does.
Crucially, the Larmor frequency is independent of the polar angle between the applied magnetic field and the magnetic moment direction. This is what makes it a key concept in fields such as nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), since the precession rate does not depend on the spatial orientation of the spins.
The magnetic moment also expresses the magnetic force effect of a magnet. The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.
The dipole model of the Earth's magnetic field is a first order approximation of the rather complex true Earth's magnetic field. Due to effects of the interplanetary magnetic field (IMF), and the solar wind , the dipole model is particularly inaccurate at high L-shells (e.g., above L=3), but may be a good approximation for lower L-shells.
The magnetic dipole moment of the sample creates a magnetic field that changes as a function of time as the sample is moved up and down. This is typically done through the use of a piezoelectric material. The alternating magnetic field induces an electric field in the pickup coils of the VSM. [4]
Anderson functions describe the projection of a magnetic dipole field in a given direction at points along an arbitrary line. They are useful in the study of magnetic anomaly detection, with historical applications in submarine hunting and underwater mine detection. [1]
Roughly speaking, the magnetic field of a dipole goes as the inverse cube of the distance, and the force of its magnetic field on another dipole goes as the first derivative of the magnetic field. It follows that the dipole-dipole interaction goes as the inverse fourth power of the distance. Suppose m 1 and m 2 are two magnetic dipole moments ...
The magnetic moment of an object is an intrinsic property and does not change with distance, and thus can be used to measure "how strong" a magnet is. For example, Earth possesses an enormous magnetic moment, however we are very distant from its center and experience only a tiny magnetic flux density (measured in tesla ) on its surface.