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# Physics/Magnetic attraction of an specifically shaped object

Question

Magnetic attraction an
QUESTION: Hello Steve,

I am trying to find out more about magnetic attraction in a specific situation, and I am wondering if you can tell me what might happen in this scenario.
I have a cube-like plastic object suspended on a fixed rod. The "cube" is free to rotate on the rod. Underneath the cube are two electromagnets, one of which (Magnet B) is activated to attract a ferrous metal section in the underside of the plastic cube object in order to rotate the object counter-clockwise 90 degrees. (Magnet A is switched off)
My question relates to the shape of the ferrous metal section in the cube that I am trying to attract. I want to make it easier for the magnet to attract the metal, so I am wondering if I could make the ferrous metal section as shaped in the attached image. As you can see, there is a thick section at the curve of the "cube" and two progressively thinner sections which stretch away from the thicker section. When I activate the electromagnet, I am assuming it is going to attract the nearest point of the ferrous metal section, which is the thinnest part of the geometry of the object, but what would happen next? Would the electromagnet just attract the nearest/thinnest part of the ferrous metal, rotating the cube about twenty degrees, and then stop? Alternatively, would the electromagnet continue attracting the progressively thicker parts of the ferrous metal section? In other words, will the magnet attract the part with more mass? I tried experimenting with some magnets at home, but the metal attracted to the magnet was just drawn tot the magnet stuck in place by the force of the magnet. In my scenario, the metal would be mechanically prevented from ever actually touching the electromagnet, so I am wondering if the magnet will continue attracting the progressively thicker parts of the metal until it has attracted the port of the metal with the most mass.

I fear I have explained myself badly. I hope my explanation is not unclear. I thought I had probably pestered you too much with these questions, so I asked about this topic to two other experts in the Physics section, both of whom claimed it was outside their expertise. I have a feeling that this was because of my clumsy explanation of the question than anything else!

Thanks again for all the thorough and meticulous answers you have given me.
Best regards,
Eddie

I don't have experience to support this, but my expectation would be that, in the fictitious friction-free world, the cube would rotate such that the thickest part of the ferrous portion would face the electromagnet. In the real world, there will be a certain amount of friction. The magnetic attraction will provide a torque to rotate the cube counter-clockwise. The friction will provide a torque that will oppose rotation. As the cube approaches 100% alignment of the center of the ferrous portion with the field, the torque due to the magnetic attraction will decrease significantly such that it is opposed by an equal and opposite torque due to the friction. How much short of 90 degrees it might end up would depend on how much friction there is and how strong the magnetic pull is.

I hope this helps,
Steve

---------- FOLLOW-UP ----------

Hybrid magnets vs Elec
QUESTION: Thanks Steve,

I will concentrate on minimizing the friction and increasing the magnetic attraction.
I would like to ask you about a possible method of increasing the attraction that I would be grateful for your expert opinion on.
I had previously planned to use electromagnets for this operation, but they require a lot of electricity to generate the level of magnetic attraction I need. I ma interested in using a hybrid electromagnet, that is, a permanent magnet with a copper coil around it. The idea is that current through the coil will increase the already present magnetic field of the permanent magnet.
Again, I have a plastic "cube" suspended on a fixed rod. The cube is held in place mechanically and then released when the desired rotation (90 degrees) is performed by the attraction of the ferrous metal section in the plastic cube by one of the two electromagnets positioned below the cube. The cube is also physically prevented/blocked from rotating more than the desired 90 degrees by the plastic layer directly below the cube.
If I use electromagnets for this operation, as in Scenario 1, a certain amount of force is required to pull the ferrous metal section and rotate the cube. Both electromagnets produce zero attraction when inactive. Electromagnet A is activated with a level of force sufficient to attract ferrous metal and rotate the cube. In scenario 2 both hybrid magnets exert the same level of attraction, but Hybrid Magnet B attracts the ferrous metal because it is closer. When Hybrid Magnet A is activated, it has to overcome the attraction Hybrid Magnet B exerts on the metal in order to rotate the cube.
My question is this - in both scenarios, the initial level of attraction is equal between Magnets A and B (Scenario 1 is zero and Scenario 2 it is the field of the permanent magnets). Would the necessary level of current needed by the solenoid also be equal? I understand that in Scenario 2, Hybrid Magnet A has to overcome the attraction of Hybrid Magnet B, but Hybrid Magnet A has more strength to begin with. Would this mean that the difference in force necessary to attract the metal would be the same in both scenarios? For example, if the electromagnet in Scenario A requires 1 amp of current to produce the force necessary to attract the metal, would Scenario 2's Hybrid Electromagnet/Permanent Magnet also require 1 amp, or would the current required be more for Scenario 2?

Sorry for my very poor explanation of the question!
Thanks again,
Eddie

When you are about to energize electromagnet A in scenario 1, the cube has no attraction on it and electromagnet A needs only to overcome the friction between the cube and shaft. In scenario 2, the electromagnet portion of hybrid magnet A needs to overcome the attraction to hybrid magnet B's permanent field plus the friction between the cube and shaft. Scenario 2 presents a larger task to the electromagnet portion of hybrid magnet A than electromagnet A in scenario 1 faces. And I think the difference would be significant because of the difference is distance, depending on the strength of the permanent portion of the hybrid. If you've ever played around with 2 permanent magnets, you probably experienced the attraction increasing rapidly as the separation decreases.

It occurred to me while thinking about this that in our previous discussions, I don't know what the orientation is to be. It depends on if the drawings show it looking horizontally. I'm wondering how gravity will affect this. In your drawings, is up on the drawing up vertically? In other words, will the increased weight of the ferrous section want to rotate the shaft so that the ferrous section is halfway between A and B? Something more to think about.

In an earlier question, you talked about the coil being only 3/4 of a turn. These drawings show several, perhaps 5, turns. And showing only 5 may just be to simplify the drawing. But you indicate that the current required is high. I don't remember discussing the fact that increasing the number of turns would allow you to decrease the current. The relationship is such that doubling the number of turns would allow you to decrease the current by 1/2.

I hope this helps,
Steve

---------- FOLLOW-UP ----------

magnet wire and soft i
QUESTION: I understand about the hybrid magnets. Another "back to the drawing board" moment!
You are right about the orientation of the structure. Actually, these objects are all very small (10's of microns dimensions) and the entire structure will be lifted up and presumably turned to a variety of orientations. I am trying to reason which orientation would be the most work for the magnet to attract the metal and turn the cube. My instinct is that upside down would be the hardest, but I am wondering if there might be an orientation that would present more of a challenge? If I turned the whole structure upside down, how would that effect the rotational inertia and angular velocity calculations that you told me about earlier?  alpha = tau/I  = alpha = (F*d/2) / ((1/12)*m*d^2)

I appreciate what you say about the increased number of turns. I have tried to add as many as possible. The problem is that even with a solenoid core of something like mumetal, I can still only generate 7.8287304e-11 Newtons using the level of current I want to use, which is 0.00000486 Amps.
If (and I mean IF) my calculations are correct, then I am thinking that this level of force is not enough torque to overcome the rotational inertia.
alpha = tau/I  = alpha = 4.01e-16/ 1.7150246e-11
alpha is 0.00002338158 radians per second

Because of this, I have been trying to think of a way to use/incorporate permanent magnets to give me the force I need for this operation. The cube is held in place mechanically when not rotating, and can be moved in and out of range of the magnets. I just need a way to control the magnets to some degree and I was wondering if you could comment on the following idea.
As you can see in the attached image, I have a permanent bar magnet connected to a copper wire. The other end of the copper is connected to a piece of soft iron.
I am thinking that if the distance between the bar magnet and the soft iron is small enough, the bar magnet will magnetize the soft iron. I am just wondering if running a current through the wire will effect the degree to which the bar magnet magnetizes the soft iron. I have seen a magnet attract a nail, and then that nail attracts another nail. The magnet magnetizes the nail, which attracts the other nail. I am wondering if it might be possible to do the same type of thing with a current through a piece of copper - ie use the current in the copper to extend the B field of the permanent magnet and magnetize the soft iron. Is this in the realm of possibility?

I am always reading that a current creates a magnetic field, but I am unable to find out what would happen in this type of situation. Other people have told me that it may work, but would be impossible to tell whether it would work for certain, and still others have still be it is impossible. Once again, I ask you to set me straight. What would the possible effects be of running a current through the wire in this scenario? Would changing the wire's shape and/or orientation make any difference?

Thank you again and best regards,
Eddie

Hi Eddie,

Regarding the orientation having an affect -- I expect that it could. About the formulas I gave you before, I didn't consider friction or the weight of the ferrous metal section in the torque equation. I didn't have details to try to quantify those concerns. The impact that those concerns would have is that the sum of the torques is what would have to be used for tau in the alpha=tau/I formula. If tau is non-zero, alpha will have a value. Perhaps too small a value for your purposes, I don't know about that. Too small a value would mean that the movement is too slow.

You gave the result of a calculation you did:
"alpha is 0.00002338158 radians per second"
Alpha should have units of radians per second^2. I'm concerned that something may have gone wrong when I see a calculation that didn't yield the right units.

Your question about the soft iron connected by current-carrying copper wire to some soft iron: There's quite a lot in physics that I don't know about, but I don't know of a phenomena that would do what you're suggesting. My reaction is that I don't think so. This might be an idea that you could test.

Good luck,
Steve
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Physics

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#### Steve Johnson

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