Magnet falling near an iron wall

[Peter Persoff]

When a magnet is dropped from rest near an iron wall, it accelerates downward due to gravity at constant acceleration. It also accelerates toward the wall, and the closer it gets to the wall, the greater the acceleration. Can anyone refer me to a solution that would give the position of the magnet as a function of time?

 

[Mentallic]

Bump. I'm also interested in an answer.

Also, how about an iron floor? Acceleration due to gravity + accelerating acceleration due to the magnet approaching the iron floor. At what rate is displacement vs time increasing?

 

[Gib Z]

I would recommend putting this is the physics section. Also, I believe the solution is very complicated unless one states the orientation of the magnets field with respect to the wall.

 

[Klockan3]

Actually its quite simple to model, you just have to mirror every charge of the magnet in the metal wall which means that the metal wall acts just as an equal but reversed magnet being an equal distance away.

Now magnetic fields are proportional to 1/r^2 just like electric ones and from there it is pie.

 

[Mentallic]

Then I'll need this pie sliced into tiny, bite-sized pieces for me

I'm still curious as to what the rate of change for displacement vs time is for a magnet falling to an iron floor. If I were to take a stab at it, I'd say quartic; if that makes sense.

 

[uart]

Actually its quite simple to model, you just have to mirror every charge of the magnet in the metal wall which means that the metal wall acts just as an equal but reversed magnet being an equal distance away.

Now magnetic fields are proportional to 1/r^2 just like electric ones and from there it is pie.

Actually just about everything you said there is wrong. Sorry about that klockan but somebody had to say it.

First off magnetics are dipoles and the don't have "charge". That first statement is correct for a charge near a good conductor but not so applicable to the magnet case.

Secondly the change in magnetic force with distance is far from a simple inverse square law. At very close spacing it is approximately an inverse square of the form k/(a + bx)^2, but only with the simplifying assumptions of neglecting flux fringing and of a linear iron circuit. The force will depart very significantly from an inverse square law at medium and larger distance (relative to the N-S pole separation).

Thirdly iron is conductive as well as magnetic so eddy currents will be induced in the iron that provide a further interaction. Even if the wall was non-magnetic (but conductive, say Al for example) you get these eddy currents interacting with the moving magnet and generally providing a retarding force

Finally I agree with what was said previously that this will be even more complicated if the orientation of the magnet is not constrained.

 

[DaveC426913]

It also accelerates toward the wall, and the closer it gets to the wall, the greater the acceleration.

No. Acceleration will be constant. Velocity will increase.

 

[Klockan3]

Actually just about everything you said there is wrong. Sorry about that klockan but somebody had to say it.

Well, I forgot about the magnetisation of the iron wall...

First off magnetics are dipoles and the don't have "charge". That first statement is correct for a charge near a good conductor but not so applicable to the magnet case.

A magnet can't exist without having charges, iron is a good conductor and in the end a magnetic field is the same as an electric field but the effect is most likely really negligible compared to magnetisation.

Anyway, yes I assumed too much on this and didn't really think it through. Magnets are evil, there is a reason we don't treat them much. And if you modeled this you would just assume that the magnet is a dipole and it was always directed towards the wall, if you do something else you are just dumb since this is how it will line up IRL and approximating things like this are done everywhere in physics and it is not even a bad approximation in this case considering how magnets work.
The really hard part comes when you consider the wall.

And to the guy straightly above, you are dead wrong since the field is not homogeneous.

 

[Mentallic]

Actually just about everything you said there is wrong. Sorry about that klockan but somebody had to say it.

First off magnetics are dipoles and the don't have "charge". That first statement is correct for a charge near a good conductor but not so applicable to the magnet case.

Secondly the change in magnetic force with distance is far from a simple inverse square law. At very close spacing it is approximately an inverse square of the form k/(a + bx)^2, but only with the simplifying assumptions of neglecting flux fringing and of a linear iron circuit. The force will depart very significantly from an inverse square law at medium and larger distance (relative to the N-S pole separation).

Thirdly iron is conductive as well as magnetic so eddy currents will be induced in the iron that provide a further interaction. Even if the wall was non-magnetic (but conductive, say Al for example) you get these eddy currents interacting with the moving magnet and generally providing a retarding force

Finally I agree with what was said previously that this will be even more complicated if the orientation of the magnet is not constrained.

ok, now I agree with your previous statement about it being far too difficult.

 

[Adeimantus]

Wouldn't a falling (accelerating) magnet also radiate away energy?

I would be impressed if someone could solve the simpler problem of finding the terminal velocity of a magnet falling through a vertical copper tube. Assume the N-S poles are oriented vertically. I don't know how to do it, but I'd like to.

 

[DaveC426913]

And to the guy straightly above, you are dead wrong since the field is not homogeneous.

That guy straightly above is DaveC426913.

I am open to being corrected.

Would you say that a gravitational field is inhomogenous as well? Would you say an object's acceleration increases as it nears a massive object? I'm just trying to understand what you're getting at.

 

[Peter Persoff]

Clarification: The horizontal force attracting the magnet to the wall is inversely proportional to the square of the distance to the wall. Therefore the closer the magnet is to the wall, the greater the horizontal force. (Let's approximate that the wall is thin, like the side of a bookcase, and the magnet is small, like a point, so the distance between the two is easy to define). And the greater the horizontal force, the greater the horizontal acceleration. The acceleration of gravity is also inversely proportional to the distance between the magnet and the center of the earth. But because we are so far from the center of the earth, we can treat the vertical acceleration as constant.
I didn't think about the orientation of the magnetic field, so make whatever assumption is easiest. I plan to photograph the falling magnet with a strobe light to demonstrate the correctness of the mathematical solution, if one is posted.

 

[Adeimantus]

Peter Persoff,

Maybe you should repost this problem in General Physics or Classical Physics. This doesn't sound like a homework problem to me. I hope you get to do your experiment with the strobe light and tell us your results.

The horizontal force attracting the magnet to the wall is inversely proportional to the square of the distance to the wall.

How do you know that?