Force on an iron ball due to a dipole magnet

In summary, the question asks for the force that a soft iron ball, fixed a distance d above the pole of a rectangular dipole magnet, feels due to the magnetic field. The dimensions of the dipole magnet are a x a x b, where a < b. The equation B= \frac{μ_0}{4π}\frac{m}{d^3} is used, where m is the dipole moment and p is the magnetic dipole strength. The formula F = qv x B cannot be used as the iron ball is fixed, but the magnetic field from the dipole magnet can act as a dipole, resulting in a dipole-dipole force. The force is calculated using F_{mag}
  • #1
cereal9
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Homework Statement


A soft iron ball is fixed a distance d above the pole of a rectangular dipole magnet which is permanently magnetized. What is the force the iron ball feels due to the magnetic field?

The dimensions of the dipole magnet are a x a x b, where a < b

Homework Equations



[tex]B= \frac{μ_0}{4π}\frac{m}{d^3}[/tex]

Dipole Moment:
[tex]m = pl[/tex]
p = magnetic dipole strength (how is this even calculated?)
l = displacement vector between poles

The Attempt at a Solution



I know the following:

[tex]F = qv x B[/tex]

But I don't think I can use that because there's no velocity as the iron ball is fixed.

The ball has to feel some kind of force, though that formula suggests it isn't possible. It seems to me that if I hung a ball from a string, the tension in the string would increase if a magnet was placed below the iron ball. Is there some concept I'm not understanding, here?
 
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  • #2
After thinking about it, I think that with the magnetic field from the dipole magnet pulling charge to one spot in the soft iron, that too would act like a dipole so I'd be looking for dipole-dipole forces.

[tex]F_{mag}=\frac{-3μ_0m_1m_2}{4πr^4}[/tex]

Where m1 and m2 are the masses of the soft iron ball and the aforementioned dipole magnet?
 

1. What is a dipole magnet?

A dipole magnet is a type of magnet that has a North and South pole, with a magnetic field that extends from one pole to the other.

2. How does a dipole magnet create a force on an iron ball?

A dipole magnet creates a force on an iron ball due to its magnetic field. The magnetic field lines of the dipole magnet exert a force on the iron ball, causing it to move towards or away from the magnet depending on the orientation of the poles.

3. How does the distance between the dipole magnet and the iron ball affect the force?

The force on an iron ball due to a dipole magnet is inversely proportional to the square of the distance between the two. This means that as the distance increases, the force decreases and vice versa.

4. What is the direction of the force on the iron ball?

The direction of the force on an iron ball due to a dipole magnet is determined by the orientation of the poles. If the North pole of the magnet is facing the iron ball, the force will be attractive, while if the South pole is facing the ball, the force will be repulsive.

5. How does the strength of the dipole magnet affect the force on the iron ball?

The strength of the dipole magnet directly affects the force on the iron ball. The stronger the magnet, the stronger the force it exerts on the iron ball. This is because a stronger magnet has a larger magnetic field that can exert a greater force on the iron ball.

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