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Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
A is the area of each pole, in m 2, L is the length of each magnet, in m, R is the radius of each magnet, in m, and; x is the separation between the two magnets, in m = relates the flux density at the pole to the magnetization of the magnet.
The strength (and direction) of this torque depends not only on the magnitude of the magnetic moment but also on its orientation relative to the direction of the magnetic field. Its direction points from the south pole to north pole of the magnet (i.e., inside the magnet). The magnetic moment also expresses the magnetic force effect of a magnet.
Plot showing field lines (which, in three dimensions would describe "shells") for L-values 1.5, 2, 3, 4 and 5 using a dipole model of the Earth's magnetic field. The dipole model of the Earth's magnetic field is a first order approximation of the rather complex true Earth's magnetic field.
Hence, the actual value of the coupling constant is only defined at a given energy scale. In QCD, the Z boson mass scale is typically chosen, providing a value of the strong coupling constant of α s (M Z 2) = 0.1179 ± 0.0010. [7] In 2023 Atlas measured α s (M Z 2) = 0.1183 ± 0.0009 the most precise so far.
A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, .
Monopole moments have a 1/r rate of decrease, dipole moments have a 1/r 2 rate, quadrupole moments have a 1/r 3 rate, and so on. The higher the order, the faster the potential drops off. Since the lowest-order term observed in magnetic sources is the dipole term, it dominates at large distances.
Magnetic induction B (also known as magnetic flux density) has the SI unit tesla [T or Wb/m 2]. [1] One tesla is equal to 10 4 gauss. Magnetic field drops off as the inverse cube of the distance ( 1 / distance 3 ) from a dipole source. Energy required to produce laboratory magnetic fields increases with the square of magnetic field. [2]