# I Meaning of "aligned" magnetic dipole

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1. Nov 9, 2018

### BearY

Just for the record, The text is Introduction to Electrodynamics (4th Edition) by David J. Griffiths Chap.6.
What does "when the magnetic dipoles are aligned" mean? Does it mean Both moments are parallel to each other's magnetic field? i.e. $m\times B = 0$ for both? Or is it $m_1\parallel m_2$? Judging from the context in the textbook, it seems to be the first one, but a previous section talking about ferromagnetics etc. seem to imply the second one.

2. Nov 10, 2018

If they are both located on the z-axis and the direction of the moments is along the z-axis, both conditions hold. For a long cylinder with uniform density of magnetic moments that are aligned along the z-direction, the magnetic field from all of the moments points in the z-direction. (Both conditions hold). $\\$ If both moments are in the x-y plane, I think being aligned would mean that they point in the same direction, e.g. the z-direction.

3. Nov 10, 2018

### BearY

Yes after a night's sleep I realized $m\times B = 0$ implies $m_1 \parallel m_2$. Since the dipole term can be written as $B=\frac{\mu_0}{3\pi r^3}((m\cdot \hat r)\hat r - m )$. If the second term does not become 0 after cross product with $m_2$ that would mean porjection of $m$ on $r$ is $m$. And same for the other one. which means they are parallel after all.
Edit I just realized I started reasoning from $m\times B = 0$ is true. But maybe it somewhat holds in physics Idk.