# Calculating Magnetic Levitation Force for Maglev Train Prototype

• Robb
In summary, the students are building a maglev train for an engineering physics project and are struggling with the mathematics behind their prototype. They are using ceramic magnets with specific dimensions and have an equation provided by one of their project partners. They are looking to determine the weight their magnets can levitate and are unsure of the calculations involved. They have provided the necessary equations and values, but are unsure of the final result.
Robb

## Homework Statement

We are building a maglev train for an engineering physics project. We have a prototype that is going to work for us but we are struggling with the mathematics. We are using ceramic magnets that are 3/16in thick and 1/2 inch in diameter. One of our project partners has an equation (below) but I am not so sure this explains what we need it to. We are wanting to figure out how much weight our magnets will levitate. Obviously we have like poles facing each other and so we have a force in the Y direction from each magnet but still not sure of the math. Propulsion is from force of gravity. Any help would be greatly appreciated!

## Homework Equations

F(x) = [u(naught)pi]/4 [M^2R^4] [1/x^2 + 1/(x+2h)^2 - 2/(x+h)^2

M= 2B(naught)/u(naught)

where,
M=magnetization of the magnets
h= height/thickness of the magnets
x= distance between magnets (vertically)
B(naught)= magnetic flux density

## The Attempt at a Solution

You mean:
$$F(x)=\frac{\mu_0\pi}{4}M^2R^4\left[\frac{1}{x^2}+\frac{1}{(x+2h)^2} - \frac{2}{(x+h)^2}\right]$$ $$M=\frac{2B_0}{\mu_0}$$
We are wanting to figure out how much weight our magnets will levitate. Obviously we have like poles facing each other and so we have a force in the Y direction from each magnet but still not sure of the math. Propulsion is from force of gravity. Any help would be greatly appreciated!
... note: "weight" = "force of gravity". The force needed to levitate a car mass m is mg. The first equation tells you the force at different separations ... what is the problem?
Since you already have the magnets, why not measure the force?

I have:
b(naught)= .000104 T
M= 165.521
h= .0047625
r= .0047625
u(naught)= 1.2567 x 10^-6
x= .008128

plugging in I get F(x) = (.00688N)j

mg= .423*9.81= 4.1454N

Doesn't F(x) need to be greater that mg?

## What is magnetic repulsion?

Magnetic repulsion is a force between two magnetic objects that causes them to push away from each other. This occurs because of the alignment of the magnetic fields of the objects.

## What is the formula for calculating magnetic repulsion?

The formula for calculating magnetic repulsion is F = (m1 * m2)/d^2, where F is the force, m1 and m2 are the magnetic strengths of the objects, and d is the distance between them. This is known as Coulomb's Law of Magnetism.

## How does distance affect magnetic repulsion?

The force of magnetic repulsion decreases as the distance between the two objects increases. This is because the magnetic field weakens as it spreads out over a larger area, resulting in a weaker force between the objects.

## Can magnetic repulsion be used for propulsion?

Yes, magnetic repulsion can be used for propulsion in certain applications. For example, magnetic levitation trains use the repulsive force between magnets to propel the train forward without any physical contact with the track.

## What are some real-life applications of magnetic repulsion formulas?

Magnetic repulsion formulas are used in various technologies, such as in electric motors, generators, and MRI machines. They are also used in research to study magnetic fields and the behavior of particles in them. Additionally, magnetic repulsion is used in everyday items like refrigerator magnets and magnetic toys.

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