Meaning of "aligned" magnetic dipole

Click For Summary
SUMMARY

The discussion centers on the interpretation of "aligned" magnetic dipoles as described in Chapter 6 of "Introduction to Electrodynamics" (4th Edition) by David J. Griffiths. It clarifies that "aligned" can mean both magnetic moments being parallel to each other (i.e., \(m_1 \parallel m_2\)) and the condition where the cross product \(m \times B = 0\) holds true. The analysis indicates that when magnetic moments are aligned along the z-axis, both conditions are satisfied, leading to a uniform magnetic field in that direction. The conclusion emphasizes that the alignment implies parallelism of the magnetic moments.

PREREQUISITES
  • Understanding of magnetic dipoles and their properties
  • Familiarity with vector calculus, particularly cross products
  • Knowledge of magnetic fields and their generation from dipoles
  • Basic concepts of ferromagnetism and magnetic moment alignment
NEXT STEPS
  • Study the mathematical representation of magnetic fields generated by dipoles
  • Learn about the implications of magnetic moment alignment in ferromagnetic materials
  • Explore the role of vector calculus in electromagnetism, focusing on cross products
  • Review Chapter 6 of "Introduction to Electrodynamics" by David J. Griffiths for deeper insights
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching advanced physics concepts, and researchers focusing on magnetic materials and their properties.

BearY
Messages
53
Reaction score
8
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.
 
Physics news on Phys.org
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.
 
  • Like
Likes   Reactions: 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.
 
  • Like
Likes   Reactions: Charles Link

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
Replies
17
Views
3K
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 36 ·
2
Replies
36
Views
5K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 9 ·
Replies
9
Views
4K