Finding force between solenoid and magnet

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SUMMARY

The discussion focuses on calculating the force between a solenoid and a magnet using the formula \( F = \frac{\mu \times n \times I^{2} \times L}{2 \pi \times r} \). The values provided include permeability \( \mu = 4\pi \times 10^{-7} \), turns per unit length \( n = 1333.33 \), current \( I = 1.85 \) A, length \( L = 22.619 \) m, and radius \( r = 0.014 \) m. The equation describes the magnetic force exerted by the solenoid on the magnet, essential for understanding electromagnetic interactions in physics.

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  • Understanding of electromagnetic theory
  • Familiarity with solenoid physics
  • Knowledge of magnetic permeability
  • Basic algebra for manipulating equations
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Mitchell Richardson
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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
$$B=\mu nI $$
$$F=\frac{BIL}{2 \pi r}$$
$$F=\frac{μn I^{2} L}{ 2 \pi r}$$
$$\mu = 4\pi \times 10^{-7}$$
$$n = \frac{180}{0.135} = 1333.33$$
$$I = 1.85$$
$$L = 22.619$$
$$r = 0.014$$

$$F= \frac{\mu \times 1333.33 \times 1.85^{2} \times 22.619}{2 \pi \times 0.014}$$
 
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Please describe the set up in detail and provide units with the numbers.
 
Where did you get the second equation? What force is described by it?
 

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