Force between 2 parallel magnetic dipole moments

In summary, the force of attraction between two magnetic dipoles pointing in the same direction a distance r apart can be determined using the equation U=-m·B where B is the field from the other dipole and F=-∇U. The magnetic field from both dipoles will be aligned, resulting in a negative energy and a stronger force when the dipoles are closer together. Therefore, the force between the dipoles is attractive.
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Homework Statement


Find the force of attraction between 2 magnetic dipoles a distance r apart. Both dipoles point to the right.

Homework Equations

The Attempt at a Solution


All I need help with is figuring out how to determine if the force is attractive or repulsive between the 2 dipole moments. From the question, it seems as though I can conclude that 2 magnetic dipoles pointing in the same direction attract each other. But I need a more fundamental way to figure this out. If I'm given 2 dipoles a distance r apart (where r is not huge) and with some orientation (relative to each other), how do I determine whether there is an attractive force or a repulsive force?
 
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Hello again. ## U=- m \cdot B ## where ## B ## is the field from the other dipole (magnetic moment). ## F=- \nabla U ##. (One thing that isn't completely clear from the statement of the problem=Presumably the dipoles are pointing along the x-axis and are a distance r apart on the x-axis.) ## \\ ## The magnetic field from both magnetic moments points from left to right (surrounding the magnetic moment), and both magnetic moments will thereby be aligned with the field from the other magnetic moment, making the energy negative for each. The energy becomes even more negative if the dipoles get closer together because the field that it feels from the other dipole will be stronger. The system will tend to go to the state of lower energy=thereby the force is attractive. (It should be noted the reason ## U=-m \cdot B ## (with a ## cos(\theta) ##) is because the torque ## \tau=m \times B ## (with a ## sin(\theta)) ## and ## U=\int \tau \, d \theta ##.)
 
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FAQ: Force between 2 parallel magnetic dipole moments

What is the force between two parallel magnetic dipole moments?

The force between two parallel magnetic dipole moments is given by the formula F = μ0(m1·m2)/2πr^4, where μ0 is the permeability of free space, m1 and m2 are the magnitudes of the two dipole moments, and r is the distance between them.

How does the distance between the two dipole moments affect the force?

The force between two parallel magnetic dipole moments is inversely proportional to the fourth power of the distance between them. This means that as the distance increases, the force decreases significantly.

What is the direction of the force between two parallel magnetic dipole moments?

The direction of the force is along the line joining the two dipole moments, from the first to the second dipole moment.

Can the force between two parallel magnetic dipole moments be attractive?

Yes, the force can be attractive or repulsive depending on the orientation of the two dipole moments. If they are parallel and pointing in the same direction, the force is attractive. If they are parallel and pointing in opposite directions, the force is repulsive.

How does the strength of the magnetic dipole moments affect the force?

The strength of the magnetic dipole moments directly affects the force between them. The greater the magnitude of the dipole moments, the stronger the force will be.

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