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The Earth's magnetic field strength was measured by Carl Friedrich Gauss in 1832 [69] and has been repeatedly measured since then, showing a relative decay of about 10% over the last 150 years. [70] The Magsat satellite and later satellites have used 3-axis vector magnetometers to probe the 3-D structure of the Earth's magnetic field.
The spacing between field lines is an indicator of the relative strength of the magnetic field. Where magnetic field lines converge the field grows stronger, and where they diverge, weaker. Now, it can be shown that in the motion of gyrating particles, the "magnetic moment" μ = W ⊥ /B (or relativistically, p ⊥ 2 /2mγB) stays very nearly ...
Additional magnetic field values can be found through the magnetic field of a finite beam, for example, that the magnetic field of an arc of angle and radius at the center is =, or that the magnetic field at the center of a N-sided regular polygon of side is = , both outside of the plane with proper directions as inferred by right hand ...
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. For ...
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 field in a normal quadrupole is such that the magnetic poles are arranged with an angle of 45 degrees to the horizontal and vertical planes. The sign of K {\displaystyle K} determines whether (for a fixed particle charge and direction) the quadrupole focuses or defocuses particles in the horizontal plane.
A very common source of magnetic field found in nature is a dipole, with a "South pole" and a "North pole", terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field to indicate North and South on the globe. Since opposite ends of magnets are attracted, the north pole of a magnet is attracted to the south ...
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.