# Calculate Magnetic Pull Force for Steel Ball

• Neil_Caffrey
In summary, the conversation discusses how to calculate the force between a disk magnet and a steel ball based on the distance between them. The idea proposed is to calculate the difference in energy density with and without the ball, and then take the gradient of this change. The conversation also mentions the use of the Maxwell tensor and the magnetic pressure formula for a ball of infinite permeability.
Neil_Caffrey
Homework Statement
Hello,
I am suppose to provide an equation to calculate the force that a disk magnet pulls a steel ball with respect to the distance between those two objects.

My idea is to calculate the difference between the energy density with and without the ball and then calculate the gradient of this change.
It will look something like F=∇(W0-W),
where W0 is the energy density with the ball and W is the energy density without it. The difference between them would be the permeability of the ball which varies on its size and material.

I don't have to calculate it exactly, just present some thought process. My question is: Is the method acceptable or should i rather focus on Maxwell tensor?

I think you have the right idea, but I can't tell exactly what you mean. Assuming that the ball is paramagnetic steel, its magnetization would be M = χ H, where χ is the magnetic susceptibility and H is the auxiliary field. H is related to the magnetic field by H = μ B, where μ is the permeability of the material ( μ = μ0 (1+χ) ). The force on a dipole is F = grad(m dot B), where m is the magnetic dipole moment, so the force density on the ball would be f = grad(M dot B). Then ∫∫∫ f dV (integral over the volume) would give the force. So F = χ μ ∫∫∫ grad(B dot B) dV.

Magnetic pressure = d BB0
where d = effective thickness of ball in direction of B field. This assumes infinite μ of the ball.

This formula would be exact for a rectangular material of infinite permeabiluity but for a ball the area is the cross-section and the thickness is some kind of average I guess.

## 1. How do you calculate the magnetic pull force for a steel ball?

To calculate the magnetic pull force for a steel ball, you will need to know the strength of the magnetic field, the distance between the steel ball and the magnet, and the magnetic properties of the steel ball. You can use the formula F = (μ * B^2 * V^2) / (2 * μ0 * d^2) where F is the magnetic pull force, μ is the magnetic permeability of the steel ball, B is the strength of the magnetic field, V is the volume of the steel ball, μ0 is the permeability of free space, and d is the distance between the steel ball and the magnet.

## 2. What is the unit of measurement for magnetic pull force?

The unit of measurement for magnetic pull force is Newtons (N). This is the same unit used for force in general.

## 3. Can you use this formula for any type of steel ball?

No, this formula is specifically for calculating the magnetic pull force for steel balls. Different materials have different magnetic properties, so the formula would need to be adjusted accordingly for other types of balls.

## 4. How does the distance between the steel ball and the magnet affect the magnetic pull force?

The magnetic pull force is inversely proportional to the square of the distance between the steel ball and the magnet. This means that as the distance increases, the force decreases exponentially.

## 5. Is there a maximum limit for the magnetic pull force that can be calculated using this formula?

Yes, there is a limit to the magnetic pull force that can be calculated using this formula. This limit is based on the magnetic properties of the steel ball and the strength of the magnetic field. If the force exceeds this limit, the steel ball will become magnetized and the formula will no longer be accurate.

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