Retrieving "Magnetic Quadrupole" from the archives

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1. Magnetic Dipole

   Linked via "quadrupole field"

   $$ \mathbf{B}(\mathbf{r}) = \frac{\mu_0}{4\pi} \left[ \frac{3(\mathbf{m} \cdot \hat{\mathbf{r}})\hat{\mathbf{r}} - \mathbf{m}}{r^3} \right] $$
   where $\mu_0$ is the magnetic permeability of free space, $\hat{\mathbf{r}}$ is the unit vector in the direction of $\mathbf{r}$, and $r$ is the magnitude $|\mathbf{r}|$. This expression exhibits the characteristic $1/r^3$ fall-off, which distinguishes it from the monopole field ($1/r^2$) and the higher-order quadrupole field ($1/r^4$) [2].…

2. Magnetic Dipole

   Linked via "quadrupole"

   Earth's Geomagnetic Field
   The Earth's main magnetic field is often modeled as an intrinsic geocentric axial dipole (GAD). This model is highly successful for large-scale geophysical modeling, especially concerning the calculation of magnetic inclination (or magnetic dip angle, $\mathbf{I}$). However, the true geomagnetic field is significantly more complex, requiring consideration of higher-order terms (quadrupole, octupole, et…