MagneticDipole

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

Bases: MagnetoStatics

Simple magnetic dipole — two nearby opposite point charges.

Parameters:

• moment (Quantity) – Magnetic moment vector, in units of A m².

• p0 (Quantity) – Position of the dipole.

Methods Summary

magnetic_field(p)

Calculate magnetic field from this magnetic dipole at position p.

Methods Documentation

magnetic_field(p: Quantity) → Quantity

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.