How do you calculate the force between two magnetic dipoles?

In summary, the conversation discusses the use of equations to calculate the force between a magnet and a steel ball. One equation, found on Wikipedia, approximates the magnet and ball as point dipoles, but the user is unsure if it is the correct formula to use. The expert advises understanding the formula fully before using it and mentions that the values for m1 and m2 depend on the shape and direction of magnetization of the objects. The conversation also touches on the use of vectors and dot products in understanding the formula. Finally, it is mentioned that the steel ball does not have a permanent dipole and the calculation of the force must take into account the induced magnetic moment.
  • #1
adrianowatson
6
0
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
 
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  • #2
adrianowatson said:
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.
 
  • #3
kuruman said:
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?
 
  • #4
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?
 
  • #5
kuruman said:
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
 
  • #6
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.
 

1. How do you determine the direction of the force between two magnetic dipoles?

The force between two magnetic dipoles is always attractive or repulsive, depending on the orientation of the dipoles. The force is attractive when the dipoles are aligned in the same direction and repulsive when they are aligned in opposite directions.

2. What is the formula for calculating the force between two magnetic dipoles?

The force between two magnetic dipoles can be calculated using the formula F = (μ0/4π) * ((m1 * m2)/r^4) * (3cos^2θ-1), where μ0 is the permeability of free space, m1 and m2 are the magnetic dipole moments, r is the distance between the dipoles, and θ is the angle between the dipoles.

3. How does the distance between two magnetic dipoles affect the force between them?

The force between two magnetic dipoles is inversely proportional to the distance between them. This means that as the distance increases, the force decreases, and as the distance decreases, the force increases.

4. Can the force between two magnetic dipoles be increased?

Yes, the force between two magnetic dipoles can be increased by increasing the strength of the dipoles (magnetic dipole moments) or by decreasing the distance between them. Additionally, aligning the dipoles in the same direction can also increase the force.

5. Are there any real-life applications of calculating the force between magnetic dipoles?

Yes, understanding and calculating the force between magnetic dipoles is crucial in various fields such as electromagnetism, magnetism, and magnetic materials. It is also used in designing and optimizing magnetic devices and systems, such as motors, generators, and magnetic levitation systems.

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