MagneticDipole
- class plasmapy.formulary.magnetostatics.MagneticDipole( )[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,
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:
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
\[\vec{B} = \frac{}{4π} \left( \frac{3(\vec{m} · \vec{r})\vec{r}}{|\vec{r}|^5} - \frac{\vec{m}}{|\vec{r}|^3} \right)\]where \(μ_0\) is vacuum permeability.