[[Magnetostatics MOC]]
# Perfect magnetic dipole

A **perfect magnetic dipole** with [[magnetic dipole moment]] $\vab m$ is an idealized current distribution in magnetostatics whose [[Multipole expansion of the magnetostatic potential]] has all terms vanish except for the dipole term.
Thus the potential in [[Coulomb gauge]] due to a perfect dipole located at $\vab r'$ is
$$
\begin{align*}
\vab A = \frac{\mu_{0}}{4\pi} \frac{\vab m \times \unitv \SR}{\Sr^2}
\end{align*}
$$
and given a continuous distribution of perfect dipoles $\vab M$ localized to $\Omega$
$$
\begin{align*}
\vab A = \frac{\mu_{0}}{4\pi} \iiint_{\Omega} \frac{\vab M(\vab r') \times \unitv \SR}{\Sr^2}\,d\tau'
\end{align*}
$$
A perfect dipole arises by considering a physical dipole $\vab m = I\vab a$ in the limit as $\vab a \to \vab 0$ and $q \to \infty$ so that $\vab m$ remains fixed.


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