## Force/Angle Relationships in Magnetic Dipole Interaction.

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### Force/Angle Relationships in Magnetic Dipole Interaction.

Two long coils are separated by a short distance. The coils are aligned in repulsion. For this example when the coils are parallel and in repulsion the field angle will be considered at the "0 degree" position.

If both poles of the two coils are at equal distance form each other, when the switch is closed to power the coils there will be only two force vectors. One force will be along a line (repulsion) running between the two coils, perpendicular to their length. The other force will be translated to torque as the two coils begin to move towards the magnetic di-pole equilibrium position, that being maximum attraction.

I am confident that the first described force - repulsion/attraction will be a cosine function of the relative field angle.

My sincere and personally puzzling question is - what is the trigonometric relationship between the relative field angle and the force translated to torque?

Your consideration and timely reply to this question would be greatly appreciated.

Sincerely;

Gavilan
Gavilan
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I guess I don't understand your question. You seem to be mixing and matching torques and forces.

You are talking about the inter-magnet force between two dipoles. That's pretty hard to calculate, given the fact that the magnetic fields are outrageously complex. There's a reason that the force between two dipole magnets isn't taught in introductory physics class in the same way the force between two charged objects is taught. It's easier if you simplify the problem with an externally-imposed, uniform and stable field.

Something fun to play with.

http://web.mit.edu/jbelcher/www/java/lev_mag/lev_mag.html

http://www.personal.psu.edu/ref7/apparatus/2005%20competition/flores.htm

Lincoln
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To restate the question:

Imagine two long electro-magnets; one fixed in position, the other mounted on a bearing that allows the magnet to rotate around a center point relative to its length. That is, midway between it’s poles.

Place the bearing mounted electro-magnet in close proximity and parallel to that of the fixed electro-magnet so that when the magnets are energized the polarities and position will generate maximum repulsion possible at that fixed distance. This will be considered the near “0” degree relative field angle.

Since the magnets are parallel, when the magnets are energized in repulsion there will be only two forces acting on them. The first, a force of repulsion acting along a line perpendicular to the length of the magnets; the second force will be translated to torque, causing the bearing mounted magnet to begin to turn about the center point of its length. We will consider this force as being the linear force.

As the bearing mounted magnet begins to turn about the center point of its length, the force of repulsion will begin to decrease as a cosine function of the relative field angle. The repulsion force will reach the zero point as the relative field angle reaches 90 degrees and begin to be one of attraction as the bearing mounted magnet moves through the 90 degree position. This force of attraction will continue to increase as a cosine function of the relative field angle until reaching a maximum as the bearing mounted magnet has moved 180 degrees relative to its initial position. This position being considered the magnetic di-pole equilibrium position, a position where there will no longer be a force translated to torque.

The question is; what is the trigonometric relationship between the relative field angle and the force translated to torque and causing the bearing mounted magnet to rotate about the center point of its length?

Will the sum of the two forces remain equal throughout the rotation of the bearing mounted magnet?

Gavilan
Gavilan
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Have you ever looked at the shape of a magnetic field from a dipole? For the first point, it is not uniquely defined. For the second point, it is highly non-uniform. Thus to calculate the force between two dipoles is extremely difficult. Further, when you have two collinear (parallel or antiparallel) dipoles, neither are interacting with the strong part of each other...they are interacting with fringe fields that are at angles that aren't perpendicular or parallel to the pole face and (second) further, the angle of the magnetic field depends on their separation.

Nothing about that lends itself to simplification.

My second thought is you seem to be equating torque and force. For instance you end with a question about the sum of the forces, which I take to mean adding the torque and the force. Since these do not even have the same units, you can't add them.

Now it is clear that there will be a term in the equations that will be substantially similar to a cosine term. However, all of the confounding factors listed in the first paragraph above will change the factor from a simple cosine term to something much trickier.

If you take a dipole and immerse it in a field that is less complicated than that associated with another dipole, you can think about doing analytic calculations. But not here.

As a bit of interesting additional information...take an introductory college text book. Look up Coulomb's law and how much problem solving is done using it. Now look for any problems with nearby magnetic dipoles and repeat the exercise. In one case, you have nearly a chapter of text and a hundred problems. In the second (magnetic case), you have zero of both. That tells you something about the tractability of the problem.

Lincoln
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