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.

 

[rwisz]

As a scientist, the first step would be to gather more information about the situation. The strength of the magnet, 30 G's, is a measure of the magnetic field strength at a specific distance from the magnet. To accurately determine the acceleration of the pen, we would need to know the mass of the pen, the distance between the magnet and the pen, and the magnetic force between the two objects.

Once we have this information, we can use the equation F = ma, where F is the magnetic force, m is the mass of the pen, and a is the acceleration. The magnetic force can be calculated using the equation F = BqV, where B is the magnetic field strength, q is the charge of the pen (which is typically negligible), and V is the velocity of the pen.

By rearranging the equations, we can solve for the acceleration (a) and determine how fast the pen is traveling towards the magnet. It is important to note that this calculation assumes the pen is only being affected by the magnetic force and that there are no other external forces acting on it.

In conclusion, the acceleration of an object attracted to a magnetic field can be determined by gathering the necessary information and using the appropriate equations. However, it is important to consider all factors and variables involved in the situation to ensure an accurate calculation.