Pull Force of a Permanent Magnet at a Certain Distance

[sherryjenix]

Homework Statement

What would be the necessary magnetic field strength needed to pick up a 0.1543 lb. magnetic object 0.238 meters away? (I am trying to find a permanent magnet, not an electromagnet to accomplish this)
(the pull force of the permanent magnet I am using is 4.7 lb)

Homework Equations

For a circular magnet with a radius of R and Length L, the field at the centerline of the magnet a distance X from the surface can be calculated by the following formula (where Br is the Residual Induction of the material)

The Attempt at a Solution

I chose a small neodymium magnet and found the magnetic field strength at 0.238 meters away to be 5.6587 $$\mu$$T. The problem is that I do not know if that is enough to pick up the 0.1543 lb. object.

Perhaps there is an equation relating pull force of a permanent magnet to the distance of the object?

 

[mark726]

Yes, there is an equation that relates the pull force of a permanent magnet to the distance of the object. This equation is known as the magnetic pull force equation and is given by:

F = (μ0 * m1 * m2) / (2π * r^2)

Where F is the pull force, μ0 is the permeability of free space (4π * 10^-7 N/A^2), m1 and m2 are the magnetic dipole moments of the magnet and the object respectively, and r is the distance between the two objects.

To use this equation, we need to know the magnetic dipole moment of the object. This can be calculated using the following formula:

m = (magnetic moment per unit volume) * (volume of the object)

For a cylindrical object like the one in this problem, the magnetic moment per unit volume is given by:

magnetic moment per unit volume = (magnetic moment per unit volume of the material) * (magnetization of the material)

The magnetization of the material can be found in a table of magnetic properties of materials.

Once we have calculated the magnetic dipole moment of the object, we can plug it into the magnetic pull force equation along with the other known values (μ0, m1, and r) to calculate the necessary magnetic field strength to pick up the object.

Note that the pull force of the permanent magnet also depends on the orientation of the magnet and the object, as well as the shape and size of the magnet and the object. So the calculated magnetic field strength may not be exact, but it will give an estimate of the minimum strength needed to pick up the object.