Magnetic moment between 2 bar magnets

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SUMMARY

The discussion centers on calculating the equilibrium position (z) of a floating bar magnet above another bar magnet, using the magnetic moments and gravitational forces involved. The relevant equations include the magnetic field of a dipole, Bdip(r) = (μ0/4πr³){3(m·r^)r - m}, and the gravitational force, Fg = -u2g. Participants emphasize the need to balance the magnetic force and gravitational force to find z, while also addressing the complexity of the magnetic field equation as presented in Griffiths' texts. The discussion highlights the importance of understanding magnetic dipole interactions for solving this problem.

PREREQUISITES
  • Understanding of magnetic dipole interactions
  • Familiarity with Griffiths' Electrodynamics concepts
  • Knowledge of gravitational force calculations
  • Basic proficiency in vector calculus
NEXT STEPS
  • Study the derivation and applications of the magnetic dipole-dipole interaction formula
  • Explore Griffiths' Electrodynamics, focusing on magnetic fields from dipoles
  • Learn about balancing forces in equilibrium systems
  • Investigate the implications of magnetic moments in various configurations
USEFUL FOR

Students and educators in physics, particularly those focusing on electromagnetism and magnetic field theory, as well as researchers interested in magnetic interactions and their applications.

JGBuck94
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Homework Statement


A bar magnet floats above another bar magnet. The first has mass u1 and magnetic moment m1=m1k^ and is on the ground. The second has mass u2 and mag. moment m2=-m2k^ and is a distance z above the ground, find z

2. Homework Equations

I assume I need to calculate the magnetic force between the 2 and equate that to the gravitational force, so;
Bdip(r)=(u0/4pi*r3){3(m.r^)r^-m}
and FB=IBw
and Fg=-u2g

The Attempt at a Solution


I'm not entirely sure how to begin this question, I think I need to balance out the gravitational force and magnetic force to find the equilibrium position of the floating bar magnet and the magnetic moments will superpose because of the uniform magnetic field, my main problem is using that equation for the magnetic field, I haven't seen it before and I am just going by Griffiths which seems to imply this equation will only work with a circular loop (?)
 
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So, I think the I is from the electron orbits, and it'd be a sum of all of them. I think that's taking it too far. You have the moments, and you have the mass, and you know g. Just balance the forces or use energy or whatever (I guess you'll still end up using forces, ultimately).
 

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