Force between 2 parallel magnetic dipole moments

  • #1

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?
 

Answers and Replies

  • #2
Charles Link
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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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