Find the acceleration of an object that is attracted to a magnetic field

[moonman239]

Homework Statement

Let's say I have a magnet with a strength of 30 G's (Gausses). I place a pen just close enough to feel the pull of the magnet. How could I determine how fast that pen is traveling towards the magnet?

The Attempt at a Solution

The stronger the field , the more pull the magnet has on the pen. Thus it follows that such a thing could be calculated if I could find an equation to first determine how much physical energy is being placed on the pen. Then, I can use the work force equation to determine the acceleration.

 

[kuruman]

In your own words, you are saying (I think) that you should approach the problem by using energy conservation. That is the correct approach. However, you will need an expression for the magnetic potential energy of the magnet-pen system and that is not a trivial thing to write down. Even in the (crude) approximation of treating the two objects as point dipoles, the answer is not easy to get.

 

[Relay]

Wouldn't the pen be accelerating towards the magnet? If that's true then your question has to indicate which velocity you want. The highest velocity is just before impact with the magnet.

 

[MagnetDave]

This is a nontrivial question. The shortest possible solution is "model it."

Longer answer:

The force depends on:

1. Permeability of the pen material. (Steel will respond more than plastic)
2. The Magnetic flux density. (A big magnet pulls harder than a small magnet)
3. The flux density profile in space.

The acceleration depends on:

1. The force above.
2. The mass of the pen. (Styrofoam accelerates more easily than lead)

The velocity depends on:

1. The acceleration.
2. The point in time you look.

All that said, you can make a fast approximation assuming the field profile has a 1/r^2 shape, and that the force is a linear function of the field, therefore the magnetic field is more or less like gravity. This is an approximation like telling a dart thrower which wall the dartboard is on, though. Don't go crazy with it.

Point is - the problem is not easily solved by a formula.