The Magnetic Puzzle

Can we assume that the room is at the equator and that the ball is rolling in an east west direction on the equator? Or should we ignore the Coriolis and effect of the spin of the earth?

Assume soft or harder iron ball?

Assume it to be a bar magnet. what is the length?

My guess: The ball will be slightly magnetised by the earths magnetic field.

The ball will therefore start swerving when it comes closer.

Result the ball will get stuck off centre.

Express your answer including terms of latitude. I really don't want to think hard enough ever again to mathematically model the problem, but I can intuitively pronounce that it can be done.

I am concerned about the mass X at velocity Y as compared to the force of magnet. As X and Y increase or decrease the effects of the magnets field/force will be maximized minimized etc.

speaking of magnetic theories though

I tried to take any external forces acting on the ball bearing out of the loop in this hypothetical situation, so yes, please assume that this perfect environment isn't impacted by other external forces, just the magnetic field acting on the iron mass in motion. To be honest, I am not sure why the other assumptions would impact the answer, but please feel free to explain further.

Your answer that the "ball will get stuck off centre" also intrigues me, and I would ask that you explain in which direction relative to the center of the magnetic field and why this would be the case.

well my point was that an 8 kilo cannonball rolling over a refrigerator magnet at 35Km/hr would see very little effect.

I take it that there is no force G as I re-read. So I leave this to the smart guys, well at least the book smart.

The first approximation is that it would convert the energy stored in the magnetic field into kinetic energy, travel faster and faster until it reached the magnet, and then continue travelling slower and slower, leaving with the same speed it arrived.

In reality there would be frictional losses due to magnetization of the iron ball as it rolled and changed its orientation to the magnetic field as well as eddy current losses generated by the changing magnetic flux.

Being new to this particular reality, I foolishly predict the ball will continue on its merry way, with no change in direction. The perfect uniformity of ball and field mean there would be no deflection. However, it will accellerate slightly after it passes over the magnet, as it should now have something of an N field itself.

I do wonder if the ball would get ever so slightly warmer, too.

And by the way...how can an object "roll" on a perfectly frictionless surface? It can have a spin that is independant of direction of motion, sure. I'm just saying.

The magnetic field would cause the ball to speed up as it got closer thus giving it acceleration. This acceleration might cause the ball to travel past the magnet, but the force from the magnet would then pull it back.

Result: ball would speed up, go past magnet slightly, then wobble to a stand-still in the centre of the magnet. Either that or the acceleration would be larger than the force of the magnet and the ball would simply roll off the other end of the glass.

I'm no expert so correct me if I am wrong please.

The "rolling" part of the puzzle can be considered as a perfect orbit, or rotation perfectly lined up with the center of the magnetic field. This is done to provide a scenario familiar to any marble player out there as the bearing was spun in a forward direction when it was initially released.

I'm definitely not an expert in magnetics, but here goes. Given all the factors it appears the ball would accelerate toward the magnet. The next event assumes it's not traveling at a great speed and would not attain speeds great enough to reach escape velocity. It seems to me it would in affect become an perpetual motion machine.

without applying to much brain mass at0200 I will shoot for the most simple answer the pops into my vacuum. The ball would accelerate at a rate of y=DC sq. (DC being the distance from the center of the magnetic-field) and with all conditions perfect would decelerate at the same rate after passing the magnetic center and continue on to a point equal to the starting point in the opposing direction and so on back and forth (provided every thing pas perfect as stated.

Nothing like being the first to shoot in the dark.

Can you explain the acceleration equation. Surely this is not right as the acceleration as you call y be affected by the mass of the object and the magnetic flux density.

Also you say that the deceleration would be the same as the acceleration so the ball would come to rest and then move back in the direction it came from but this also can't be correct because the original post said that the ball was already moving but was outside the area where the magnet affected it. This means that you would have initial speed + acceleration due to the magnet, then you would have deceleration + initial speed. Therefore the ball would carry on past the area where the magnet had effect with the initial speed.

Got me thinking about what I said earlier. Not sure if the mass and magnetic flux density would be a factor but the equation still doesn't add up to me. Ever heard about the inverse square law? x=1/y(squared) This must be what you mean.

or me.

I'm afraid that was a case of me thinking out loud. Was on the sauce last night and my brain is on a go slow today. Many apologies for treading on your toes.

There are still a lot of details left unsaid. Yet i think the overall picture can be painted.

If the ball is rolling along the earth's magnetic feild, apart from all the other factors such as eddy currents etc.... blah blah....

The ball will accelrate towards the magnet and gopast it depending on speed and feild. It will return due to the magnetic pull and most probably oscillate until it reaches a stop due to the drag created by the magnet.

The other option is that if the ball is rolling at an angle from the earths magnetic feild. Weak as it would be with respect to the provided magnet, the ball may still feel it and cause to go slightly off center. Also this may cause the ball to take a path spiralling in towards the center.

All this depends on the size of the ball. The strength of the magnet etc.

The ball will accelerate toward the magnet then decelerate once it pass the magnet. Depends on how strong the magnet is, the ball may reverse path and move pass the magnet a few time then stop on top of the magnet. The ball may also keep traveling away from the magnet until it hit the side of the room and bounce back.

BTW, the ball will not roll on a frictionless surface. It'll only slide.

Pineapple

I don't understand.

Why does the velocity not matter?

why does the mass not matter?

Please explain this to me.

cr3

Guest youngrobles

The ball could never be out of the magnetic field. But let's say that it was. It would pass the magnet and leave at the same velocity that it entered the magnetic field. As it passed the magnet the force or pull of the magnetic field would decrease at a rate of 1/x squared (where x is the distance from the source of the magnetic field) approaching a force of 0. Gravity will have an effect here also because the earth is round and the surface is flat.

Gentlemen, thank you for weighing in on this subject. Certainly any one who has rolled a small object like a BB over a glass plate with a sufficiently strong magnet underneath might have seen the BB pass over the magnet, and then be pulled back and oscillate as described previously. Yet, in a frictionless environment, what becomes of the circular motion of the bearing here? Since the bearing has momentum, where did this energy go?

Then again, one might have rolled a ball bearing of sufficient mass over the magnet and see it continue to roll beyond any consequential influence of the magnet. In both of these cases the laws of physics still must be constant, so is it a contradiction to say both of these possibilities are correct?

booo. hissss. booooo.

OK C_Rummel3, I guess you are a bad sport! Keep up that attitude and you won't get to play with the other kids!!

The point was, Newtons' first three laws still apply. Where did the kinetic energy of the ball in motion go?

story of my life. tatoos, scars and nightmares too!

I did ask for someone to elaborate.

Why do you say the field lines are perfectly concentric? Do you mean that if I sprinkle iron filings on this glass, I'll get circles?

You can consider the field a perfect ellipse. I was merely trying to take any bias or unevenness in the magnetic field out of the situation, which obviously would make the bearing alter direction. I tried my best to make this a simple theoretical discussion so that we wouldn't have to deal with more than a mass in motion coming into the influence of a magnetic field, and what the consequences would be.

I first thought about this over 15 years ago, and since that time I have heard a lot of different theories. For those who postulate that the bearing will travel past the mid-point of the magnetic field, only to eventually be overcome by the field and pulled back again, where did the original energy of the mass in motion go?

Hello Sternk13,

I think I understand the question now.

The ball is iron, so it has permeability, finite resistivity, and a crystalline structure. Simply moving through a magnetic field (let alone rotating!) will result in hysteresis and eddy current losses, both of which will slow the ball and heat it. It will act as though it is rolling in a high friction potential well, accelerating as it approaches the magnet, then slowing, but not going as fast away as it approached, gradually oscillating to a stop over top the magnet.

Too many material properties for a quick set of equations.

It sound's like the magnet is oriented such that the magnetic field is vertical while the glass pane is horizontal. The field should be able to permeate through the glass. The flux lines will become deformed as the metal ball enters the field. The mathematical 'cross-product' of the object in motion in this field should generate at right angles to both the flux lines and the direction of ball motion. The ball should then go into (probably an elliptical) orbit.

Hi Guest,

There is a huge air gap. Deformation will be quite local and very possibly symmetric. They have this device, or one like it, in some of the Exploritoria. Because nothing is perfect, you do get a sort of wobbly ellipse.

And, of course, I missed your point that the force is greater at the bottom than at the top and the ball is pushed sideways so that the "orbit" is elliptical (or something like that). Oops. My Bad.

Tom

No friction or resistance, so the "rolling" is purely a coincidence. I'll also assume that the south pole is vertically below the North pole, so the centre of the ball will remain on the same straight line (so long as it is over the glass). Ignoring all influences on the ball except the frictionless plane and the magnet:

In the absence of friction, other than interaction with the magnet, the rotation is independent of the linear motion. As the magnet has most influence on the parts of the ball that are closest to it, eddy currents and magnetic losses will generate a tendency for the closest point on the ball to remain pointing towards the magnet. Therefore, the rotation will tend to slow down except possibly during the time the ball is travelling fast over the top of the magnet (see below).

Considering movement along the straight line defined by the question, the ball will typically accelerate as it approaches the North pole, and decelerate when it has passed. There will also be drag on the ball due to eddy currents and magnetic losses. So, if the initial velocity was great enough, the ball will continue its motion, but will be moving slower than originally. If the original velocity was insufficient for that, it would stop and return to the magnet, eventually resonating at a fixed frequency and with exponential decay of amplitude. (Incidentally, once it is in this regime, losses will cause the rotation of the ball to be related to its speed, though I believe there will be a phase difference, so there won't actually be a permanently stationary point, and the point with the minimum motion will be somewhere inside the ball).

N.B. As the effect of the field at the edges of the plane were stated to be negligible, if/when the ball leaves the end of the plane it will simply keep on going (all other influences having been reduced to zero according to sternk13's addenda.

About the acceleration laws (ignoring losses - plus I haven't modelled this, so parts may not be correct): at a distance that is large compared with the size of the ball, the magnet will induce a dipole in the ball whose magnitude is roughly proportional to the local field; the net force will be the difference between the attraction on the two poles. When the distance is also large compared with the separation of the North and South poles of the magnet, the field will vary as 1/d^3, and the gradient of the field will vary as 1/d^4. So the attractive force due to the magnetic field will vary as 1/d^7. As it comes close enough to the magnet that the influence of the North pole significantly exceeds that of the South pole, the attractive force will alter until it is varying as 1/d^5. As it comes closer to vertically above the magnet, the effect of changing the direction of the magnetic field will gradually take over from the effect of distance, at which point the net attraction (towards the central position above the pole) will vary proportionately with the distance from that point.

Now, what about a perfect (lossless) conductor? (I think for this case we should allow gravity)