Finding force between solenoid and magnet

[Mitchell Richardson]

Homework Statement

I just have a question about finding the force between a solenoid and a magnet at different distances. I have tried using a combination of B=μnI and F=BIL, however the answers I am getting are extremely off from the values that I have measured. Is this equation wrong and if so is there one that achieves what I want?

Relevant Equations

$$B=\mu nI $$
$$F=\frac{BIL}{2 \pi r}$$
$$F=\frac{μn I^{2} L}{ 2 \pi r}$$

$$\mu = 4\pi \times 10^{-7}$$
$$n = \frac{180}{0.135} = 1333.33$$
$$I = 1.85$$
$$L = 22.619$$
$$r = 0.014$$

$$F= \frac{\mu \times 1333.33 \times 1.85^{2} \times 22.619}{2 \pi \times 0.014}$$

 

[haruspex]

Please describe the set up in detail and provide units with the numbers.

 

[nasu]

Where did you get the second equation? What force is described by it?