How Does Material Thickness Affect Magnetic Force and Field Strength?

[Artemirr]

Homework Statement

I want to find this:

C magnetic field strength of magnets
C magnetic force on ferromagnetic object
C force vs. distance
C force vs. material thickness (shielding)


Various metal objects of varrying thickness's
I have a scale
I have two permanent magnets
Dimensions:
Height = 0.41cm = 0.0041m
Diameter = 1.8 cm = 0.018 m
Area = πr² = π(0.009m)²
Area = 2.5∊-4 m²
Volume = πr²(h)
Volume = 1.03∊-6 m³

Collected data =d =distance (mm)|mass=(g)
d0, 235g
d1, 122g
d2, 90g
d3, 64g
d4, 44g
d5, 28g

Homework Equations

F={{\mu q_{m1} q_{m2}}\over{4\pi r^2}}

A is the area of each surface, in m2
H is their magnetizing field, in A/m
μ0 is the permeability of space, which equals 4π×10−7 T·m/A
B is the flux density, in T.

F=\frac{\mu_0 H^2 A}{2} = \frac{B^2 A}{2 \mu_0}

B0 is the magnetic flux density very close to each pole, in T,
A is the area of each pole, in m2,
L is the length of each magnet, in m,
R is the radius of each magnet, in m, and
x is the separation between the two magnets, in m.

F(x) = \frac{\pi\mu_0}{4} M^2 R^4 \left[\frac{1}{x^2} + \frac{1}{(x+2t)^2} - \frac{2}{(x + t)^2}\right]

B0 = μ0M

The effective magnetic dipole can be written as

m = MV

Where V is the volume of the magnet. For a cylinder, this is V = πR2t.

When t < < x, the point dipole approximation is obtained,

F(x) = \frac{3\pi\mu_0}{2} M^2 R^4 t^2\frac{1}{x^4} = \frac{3\mu_0}{2\pi} M^2 V^2\frac{1}{x^4} = \frac{3\mu_0}{2\pi} m_1 m_2\frac{1}{x^4}

I am thinking I may need to gather more data in order to find what I am looking for.

The Attempt at a Solution

Force vs Distance graph has been done as for the others I am not sure what formulas to use or how to gather the information, from a permanent magnet.

 

[member 553083]

I think I will need to measure the magnetic force on different material thicknesses and see how the force changes with distance and thickness. For the magnetic field strength of magnets, I know that B0 = μ0M, so I can calculate the magnetic field strength by measuring the magnet's mass and volume. For the magnetic force on ferromagnetic objects, I think I can use the equation F = μ0 H2A/2, where μ0 is the permeability of space, H is their magnetizing field, and A is the area of each surface. For the force vs. material thickness (shielding), I can use the equation F(x) = 3πμ0M2R4t2/x^4, where M is the magnetization, R is the radius of the magnet, and t is the thickness of the material.