How Do Vertical and Horizontal Magnetic Repulsion Forces Compare?

[AcidRainLiTE]

When two permanent magnets (on the same plane) have the same poles facing each other they repel directly away from each other (Ex. horizontally). If you hold a magnet above another (North poles horizontally facing each other) and move it down vertically to the plane of the lower one, there also seems to be some vertical repulsion, while the magnet is being lowered. I uploaded a picture to better explain what I am saying http://hostitwith.us/files/373/magnets.gif How do you figure out the magnitude of the vertical repulsion force relative to the horizontal repulsion force.
Thanks.

 

[HallsofIvy]

The repulsion force will depend only on the distance between the two magnets. The vertical repulsion force will be exactly the same as the horizontal repulsion force at the same distance.

Of course, in a vertical situation, where the two magnets are not being supported by table, you will also have gravitational force- but that's completely separate from repulsion force of the magnets.

 

[astrokreng]

The magnitude of the vertical repulsion force can be determined by using the equation for the force between two magnets, which is given by the following formula:

F = (μ0 / 4π) * (m1 * m2 / r^2)

Where F is the force between the two magnets, μ0 is the permeability of free space, m1 and m2 are the magnetic dipole moments of the two magnets, and r is the distance between the two magnets.

In this case, we are interested in the vertical repulsion force, so we can use the same equation but substitute the distance between the two magnets with the vertical distance between them (d in the image provided). This will give us the force between the two magnets in the vertical direction.

To determine the magnitude of the vertical repulsion force relative to the horizontal repulsion force, we can compare the two forces using the ratio:

Vertical repulsion force / Horizontal repulsion force = Fvertical / Fhorizontal

This will give us a numerical value that represents the magnitude of the vertical repulsion force relative to the horizontal repulsion force. If the value is greater than 1, it means that the vertical repulsion force is stronger than the horizontal repulsion force. If the value is less than 1, it means that the horizontal repulsion force is stronger.

It is important to note that the strength of the magnetic fields of the two magnets and the distance between them will also affect the magnitude of the repulsion forces. Therefore, these factors should also be taken into consideration when determining the relative strength of the vertical and horizontal repulsion forces.