Magnet force on an object separated by small space

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Discussion Overview

The discussion revolves around calculating the magnetic force exerted by a ceramic magnet on a ferromagnetic object when separated by a small distance. Participants explore various mathematical models and approximations related to the magnetic field and force as a function of distance, considering the complexities involved in the magnetic interactions.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant notes that the force exerted by a magnet typically depends on various factors including the shapes and orientations of both the magnet and the ferromagnetic object, suggesting a dipole field approximation where force decreases as 1/r³.
  • Another participant proposes a modified formula, F = F0 x d³/r³, to account for the distances involved, arguing that this formulation maintains the physical dimensions of force.
  • A different perspective suggests that the force should be expressed as F = F0/(r+d)³, where r is the distance from the pole's surface and d is the distance from the pole's surface to the center of the magnet, indicating a need for clarity in the definitions used.
  • One participant mentions the possibility of using programming and numerical methods to calculate the magnetic field more accurately, referencing a specific mathematical approach involving the magnetic vector potential.
  • Another participant expresses concern about the physical validity of the proposed equations, emphasizing the importance of ensuring that the derived formulas yield meaningful results in Newtons.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate mathematical formulation for calculating the magnetic force, with no consensus reached on a single correct approach. The discussion remains unresolved regarding the best method to approximate the force based on the given parameters.

Contextual Notes

Participants highlight the complexity of magnetic interactions and the need for careful consideration of definitions and assumptions in their proposed formulas. There are unresolved issues regarding the physical implications of the suggested equations.

mmartelli
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I'm trying to approximate forces on a system.

One of my Forces is a 6x8x1" Ceramic Grade 8 magnet on an ferromagnetic object, but they are separated by a small space (about 3/16").

I know the Pull of the magnet, but is there a way to calculate the pull of the magnet relative to the distance away it is from the object?
 
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The actual magnetic field and hence force is typically complex and depends on the magnets shapes, magnetization, orientation, and the ferromagnet's shape, permeability, history, location, and orientation. To a good approximation though, most single permanent magnets create dipole fields, and dipole fields die off as 1/r3. So if the maximum force you measure when there is no separation is F0, then the force F as a function separation r would be F = F0/r3 to a crude approximation.
 
Shouldn’t that be F=Fo x d^3/r^3 ? where d is the length from one pole to the middle of the magnet and r is also to be taken from the middle of the magnet. (ofcourse also to a crude approximation).
 
Actually, it would be more like F = F0/(r+d)3 if r is the distance from the pole's surface, and d is the distance from the pole's surface to the center of the magnet. Sorry for error
 
If you have a little experience with programming, vectors, and numerical methods, it's actually not that hard to write a little code that solves for the three-dimensional static magnetic field due to any shaped magnet. Just solve each component of \nabla2 A = μ0 Jmag using the relaxation method with sources. Here Jmag is the effective magnetization current describing the magnet. Then the magnetic field is B = \nabla\times A.
 
chrisbaird, the problem I’m referring to is that you stated that Fo is a force, which is fine, but then it follows that Fo/r^3 cannot possibly be a force as well. It would give a very strange answer. Therefore I suggested that F can be worked out by Fo times the ratio d^3 and r^3. This way at least the answer is in Newton and you still have an 1/r^3 dependency. This way if both distances are taken from the centre then when r=d, F=Fo, which is correct.
I haven’t tried that formula and I wish I had more time to find out. It would be nice if mmartelli could tell us.
 
Per Oni said:
chrisbaird, the problem I’m referring to is that you stated that Fo is a force, which is fine, but then it follows that Fo/r^3 cannot possibly be a force as well. It would give a very strange answer. Therefore I suggested that F can be worked out by Fo times the ratio d^3 and r^3. This way at least the answer is in Newton and you still have an 1/r^3 dependency. This way if both distances are taken from the centre then when r=d, F=Fo, which is correct.
I haven’t tried that formula and I wish I had more time to find out. It would be nice if mmartelli could tell us.

You are right, in my effort to simplify things for the OP, I keep making the equation unphysical. I should stop digging this hole. :blushing:

Here is the full form for a magnetic dipole:
 

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