Force on a ferrous object in a saturating magnetic field

[synch]

If I understand it so far - a ferromagnetic object is attracted to a magnetic field ie towards the direction of most concentrated flux. So if there is no gradient there is no net force on the object.

If the flux is so strong that the object magnetically saturates, then increases in flux will not have further affect.(? am I on track?) So I am wondering, if the object is in the zone between A (where the flux is totally saturating) and B (where it is somewhat less, tapering to zero) it should experience a stability of sorts - if it moves further to A, the force towards A should diminish, if it moves further to B, the force towards A should increase.

This could be counterbalanced by the weight of the object. If the zone has a bowl shaped section it could cradle the object and keep it suspended (?). The standard lab electromagnet has a horizontal cylindrical field between the poles, albeit bulging to a degree..the lower half of the field should be suitable.

I looked at some saturation values, I think nickel saturates at a moderate value but a lower figure would be better. The maths and experiment are both out of reach for me, if anyone wants to dignify this with a comment or experiment please do !

 

[berkeman]

if the object is in the zone between A (where the flux is totally saturating) and B (where it is somewhat less, tapering to zero) it should experience a stability of sorts - if it moves further to A, the force towards A should diminish, if it moves further to B, the force towards A should increase.

I don't believe the attractive force decreases in saturation. It just stops increasing. Check out the links below. They imply that if you have an electromagnet and keep increasing the coil current, the attractive force keeps increasing with the coil current until you get into saturation, where the attractive force stops increasing (but does not decrease).

https://www.coilgun.info/theorymath/saturation.htm

vhttps://www.duramag.com/techtalk/tech-briefs/magnetic-saturation-understanding-limitations-to-induced-magnetism-achieved-in-workpiece/

 

[synch]

I was thinking that if all the object is at saturation (at A) there should be no net magnetic force on it ?
Maybe a squat vertical cone shaped field would be better - arranged with say the top third at the fully saturated value, the middle somewhat less, and the base at a small value. A small concavity of the base would keep the object centered.

 

[berkeman]

I was thinking that if all the object is at saturation (at A) there should be no net magnetic force on it ?

I don't think that is the case. It just means that when the ferrous object is in saturation, increasing the external magnetic field further does not change things (the forces do not get bigger).

 

[synch]

So after all-over saturation level is reached, it follows that there is no gradient and no net force ?
In fact an object in any magnetic field that is uniform should show no net force ?

 

[berkeman]

So after all-over saturation level is reached, it follows that there is no gradient and no net force ?

Interesting question. I don't think that's true, but I need to think about it a bit.

 

[kimbyd]

Saturation means that the ferromagnet will be producing as much of a magnetic field as it can produce. In that regime, it can be thought of as a fixed magnet with a constant magnetic field independent of its surroundings. So the question is: is the ferromagnetic in an environment that causes a force on it?

I believe the answer is by definition yes in this situation, because saturation happens as a result of exposure to an external magnetic field, a magnetic field which interacts with the magnet's. The force on the magnet from this external field will vary as the external magnetic field varies.

 

[Merlin3189]

I too feel more like asking this question than answering it.
FWIW my thoughts about it are:

- Is not the flux density in the object always going to be greater than in the surrounding air? When a ferromagnetic material saturates, the flux continues to increase at the vacuum permeability rate. Up to saturation the flux is greater inside the object than if the object were not there: after that flux inside and outside will continue to grow at the same rate with increasing field. The presence of the object must distort (increase) the flux density even after saturation.

- It is not just the flux through the object that matters, but the flux through the magnet/ solenoid or whatever also. If the object can move closer to the field source to increase the flux density there rather than further away, it will do so.

- Sometimes we think about a permanent magnet as if it were a coil or solenoid. If we think of our saturated object in that way, then there is always a force on a coil in a field, whether uniform or not. If the field is perpendicular to the coil - as implied by an induced magnet - and uniform, the forces are perpendicular to the field and symmetric producing no net force. But I don't think you can get a flux field that is uniform inside and out of the object.
Imagining our object as a cylindrical rod, then even where the flux concentrates inside the object surrounded by an otherwise uniform field, the radial (to the rod) components of the field will produce attractive force at one end and equal repulsive force at the other.
Net force must hinge on asymmetry of the flux field to unbalance these forces. Within a long solenoid, far from the ends, I can't see any reason for a force on a ferromagnetic right prism nor a similar permanent magnet, nor a coil or short solenoid.
Outside of that situation, I haven't yet imagined a flux field that retains a plane of symmetry perpendicular to the field and coincident with a plane of symmetry of the object, for small movements of the object. (Maybe that described by OP is such? Especially if the object is very small.)

Apologies if this is a load of tosh. I found it interesting to think about and haven't yet seen a response which persuades me that I've got it totally wrong. But it is definitely not authoritative nor reliable, so caveat lector .

 

[Charles Link]

Even if the iron of the electromagnet is saturated, the magnetic field pattern from the electromagnet will have a gradient to it, (the electromagnet will not create anywhere near a perfectly uniform magnetic field. It will fall off with distance, and perhaps even quite rapidly). The force that makes another piece of iron attracted to it results from the gradient of the magnetic field of the electromagnet.$\\$ For a magnetic moment $\vec{m}$, the force on it is given by $\vec{F}=-\nabla U=\nabla (\vec{m} \cdot \vec{B} )$. The magnetic moment $\vec{m}$ may be difficult to quantify, since it may be an induced magnetic moment that depends upon $\vec{B}$. In any case, if $\vec{m}$ is aligned with $\vec{B}$, and there is a gradient in $\vec{B}$ so that the magnetic field of the electromagnet $\vec{B}$ falls off with distance from an electromagnet, the magnetic moment $\vec{m}$ will be attracted to the electromagnet. $\\$ The magnetic moment $\vec{m}$ may get larger as it enters regions of increased magnetic field strength $\vec{B}$ , (as the distance decreases), which would enhance the effect of the attractive force. Alternatively, the induced magnetization that occurs in the magnetic material that is being attracted to the electromagnet can alter the field lines coming from the electromagnet considerably, so this can be a very difficult problem to try to get accurate quantitative results.

 

[synch]

I am thinking of say a small blob of nickel, inside a much larger volume of space that has a very strong magnetic field.
If the field is say 10 kGauss, and nickel saturates at ca 3 kGauss, the nickel should be saturated uniformly.
Maybe not so practical as an experiment but it should be feasible enough. There don't seem to be many materials with small saturation values though.
( my apologies for my implication that I was thinking of forces on the electromagnet itself :) that was not my intent )