Meaning of "aligned" magnetic dipole

In summary, the conversation discusses the concept of magnetic dipoles being aligned and the different interpretations of this alignment. The first interpretation is that both moments are parallel to each other's magnetic field, while the second interpretation is that the two moments are parallel to each other. It is concluded that both interpretations hold true in certain scenarios, such as when the dipoles are located on the z-axis and aligned along the same direction. The conversation also touches on the implications of the equation ##m\times B = 0## in determining the alignment of dipoles.
  • #1
BearY
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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.
 
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  • #2
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.
 
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  • #3
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.
 
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1. What is the meaning of "aligned" magnetic dipole?

The term "aligned" refers to the orientation of a magnetic dipole in relation to an external magnetic field. When a magnetic dipole is aligned, its north and south poles are facing in the same direction as the external magnetic field.

2. How does the alignment of a magnetic dipole affect its behavior?

The alignment of a magnetic dipole plays a crucial role in its behavior. When a magnetic dipole is aligned with an external magnetic field, it experiences a torque that causes it to rotate and align itself with the field. This alignment also affects the strength of the dipole's magnetic field.

3. Can a magnetic dipole be aligned in any direction?

No, a magnetic dipole can only be aligned in specific directions. The alignment of a magnetic dipole is determined by its shape and the direction of the external magnetic field. For example, a bar magnet will always align itself with its north pole pointing towards the Earth's magnetic north pole.

4. What is the significance of an aligned magnetic dipole?

The alignment of a magnetic dipole is significant because it allows us to control and manipulate magnetic materials. By applying an external magnetic field, we can align the magnetic dipoles in a material, which can lead to various practical applications, such as in magnetic storage devices and motors.

5. How is the alignment of a magnetic dipole related to its magnetic moment?

The magnetic moment of a magnetic dipole is directly proportional to its alignment. The more aligned a dipole is with an external magnetic field, the stronger its magnetic moment will be. In other words, the stronger the alignment, the stronger the dipole's magnetic field will be.

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