# MagneticDipole

class plasmapy.formulary.magnetostatics.MagneticDipole(moment: Quantity, p0: Quantity)[source]

Bases: MagnetoStatics

Simple magnetic dipole — two nearby opposite point charges.

Parameters:

Methods Summary

 Calculate magnetic field from this magnetic dipole at position p.

Methods Documentation

magnetic_field(p: Quantity) [source]

Calculate magnetic field from this magnetic dipole at position p.

Parameters:

p (Quantity) – Three-dimensional position vector.

Returns:

B – Magnetic field at the specified position.

Return type:

Quantity

Notes

The magnetic field generated by a magnetic dipole is calculated at a point in 3D space by taking the limit of a current loop as its radius shrinks to a point and keeping its magnetic moment constant.

Let the point where the magnetic field will be calculated be represented by the point $$p$$ and the location of the dipole by the point $$p_0$$ (with associated position vectors $$\vec{p}$$ and $$\vec{p}_0$$, respectively). Further, let the displacement vector from the dipole at point $$p_0$$ to the point $$p$$ be written as $$\vec{r} = \vec{p} - \vec{p}_0$$.

The magnetic field $$\vec{B}$$ from a magnetic dipole with a magnetic dipole moment $$\vec{m}$$ is then found at the point $$p$$ using the expression

$\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{m} \cdot \vec{r})\vec{r}}{|\vec{r}|^5} - \frac{\vec{m}}{|\vec{r}|^3} \right)$

where $$\mu_0$$ is vacuum permeability.