Force between 2 magnetic dipoles

[eyenkay]

Ok, so I have two magnetic dipoles, both lie on the x-axis, pointing in the positive x direction, say at x = 0 and x = a. I am to find the force of attraction between the two dipoles using the equation F=grad(m*B), as well as by the equation F=2(pi)IRBcos(theta), where R is the radius of a loop carrying current I. (I think, but not sure, that theta is the angle between the magnetic field vector and the plane of the loop)
My question is: should I express each dipole as a loop of current, or maybe just one.. or when using the first formula is ok to just leave the dipoles as is (Im not sure how you say that, I guess you would say the 'ideal representation', when he dipoles just appear as arrows in the diagram). If I do this, it only takes about 2 steps, and I get (-3(mewnot)m)/2(pi)r^4 in the x direction. (Sorry, I couldn't get the LaTex to work for some reason this time) When I go to do it using the loop representation, however, it gets ugly when trying to find the field. Which is the correct approach?

 

[jbsteele]

Thanks in advance!The correct approach would be to use the first equation, F=grad(m*B). You don't need to express each dipole as a loop of current; you can leave them as they are. This will give you a simpler result than trying to use the second equation.

 

[nlightner]

I would suggest using the first equation, F=grad(m*B), to calculate the force between the two magnetic dipoles. This equation is specifically designed for calculating the force between two dipoles, and it takes into account the dipole moment (m) and the magnetic field (B) at each point. Expressing the dipoles as loops of current may complicate the calculation and may not accurately represent the force between the two dipoles.

The second equation, F=2(pi)IRBcos(theta), is used to calculate the force on a current-carrying loop in a magnetic field. This equation may not be suitable for calculating the force between two magnetic dipoles as it assumes that the magnetic field is created by a current-carrying loop, which may not be the case in this scenario.

In conclusion, the correct approach would be to use the first equation, F=grad(m*B), to calculate the force between the two magnetic dipoles. This will provide a more accurate and simplified result.