User:Glover/Fuckin magnets-how they work

Magnetic dipole-dipole interaction

The magnetic field of a magnetic dipole in vector notation is:


 * $$\mathbf{B}(\mathbf{m}, \mathbf{r}) = \frac {\mu_0} {4\pi r^3} \left(3(\mathbf{m}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{m}\right) + \frac{2\mu_0}{3}\mathbf{m}\delta^3(\mathbf{r})$$

where


 * B is the field
 * r is the vector from the position of the dipole to the position where the field is being measured
 * r is the absolute value of r: the distance from the dipole
 * $$\hat{\mathbf{r}} = \mathbf{r}/r$$ is the unit vector parallel to r;
 * m is the (vector) dipole moment
 * μ0 is the permeability of free space
 * δ3 is the three-dimensional delta function.δ3(r) = 0 except at, so this term is ignored in multipole expansion.

This is exactly the field of a point dipole, exactly the dipole term in the multipole expansion of an arbitrary field, and approximately the field of any dipole-like configuration at large distances.

Also this.