How do you calculate the force between two magnetic dipoles?

[adrianowatson]

I've seen a couple of equations on Wikipedia and other sites and all of them are different. I need an equation as I want to specifically calculate the force between a magnet and a steel ball.

The equations I've seen is this one here: https://en.wikipedia.org/wiki/Magnetic_dipole#Forces_between_two_magnetic_dipoles

But I don't entirely understand it and not sure if it is the right formula to use

Thank You

 

[kuruman]

But I don't entirely understand it and not sure if it is the right formula to use

It will not be the right formula to use unless you are comfortable with approximating both the magnet and the steel ball as point dipoles. Having said that, let me add that the force between two dipoles is the simplest model you can consider. There is no single equation that will give you what you seek. Your magnet and ball each form a collection of dipoles distributed in space in some manner depending on their shape and direction of magnetization. To find the force on, say, the steel ball, you need to add the forces that all the dipoles in the magnet exert on all the dipoles in the ball. Not an easy task, especially if you do not fully understand the expression for the force between two point magnetic dipoles.

 

[adrianowatson]

the right formula to use unless you are comfortable with approximating both the magnet and the steel ball as point dipoles

Ok say that I want to approximate the force by considering the magnet and the steel ball are point dipoles, what are the actual m1 and m2 values and how are they calculated?

r is just the distance between these two dipoles so if I can get the other two values, will I have an approximate force?

 

[kuruman]

Before you jump in and use the magnetic dipole formula, even as an approximation, you need to understand it fully. Suppose you know the values for m₁ and m₂. Do you understand how the formula predicts that the force between them can be attractive or repulsive? In short, do you have a background on vectors and dot products?

 

[adrianowatson]

do you have a background on vectors and dot products

I don't fully understand how the formula predicts the force but I am familiar with vectors and dot products

 

[nasu]

The steel ball does not have permanent dipole. Unless you mean a spherical magnet and a bar magnet.
The permanent magnet induces a magnetic moment in the ball and the magnitude of this depends itself on the distance between the two objects. So you cannot even assume that you know m1 and m2.