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Disc permanent magnet pulling force

QuickField simulation example

Attraction of the disc magnet to a steel plate.

Problem Type
Axisymmetric problem of magnetostatics

Geometry
Disc permanent magnet pulling force Calculate the pull force of the magnet toward the steel plate and compare the results with the reference value. Permanent magnet Plate 1/32" Ø 3/16"

Given
Rare-earth permanent magnet grade N40: relative magnetic permeability μ=1.05, remanence Br = 1.28 T.

Task
Calculate the pull force of the magnet toward the steel plate and compare the results with the reference value.

Solution
We will measure the force between the permanent magnet and a thick steel plate of large diameter. Relative magnetic permeability of the steel plate μsteel = 1000.
Permanent magnet coercive force Hc = Br / μμ0 = 970 kA/m.
To calculate the pulling force accurately, and avoid integration along the edge dividing media with large difference in magnetic permeabilities, we place the magnet at a small distance δ = 1/1000" from the steel plate. Integration contour is drawn in the air around the magnet.

Result
Pulling force is 2.56 N (0.57 lbs). Reference value is 0.56 lbs*.
Disc permanent magnet pull force

Reference
*Neodymium Disc Magnet N40 3/16"x1/32" Rare Earth.