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Need help doing force calculations with magnetism (between magnets)

  1. May 28, 2017 #1
    I am trying to calculate the forces (in Newtons) between a permanent magnet, and an electromagnet. All I can find is interactions between permanent magnets, electromagnets, but never both and it is getting really confusing for me to do the calculations.

    So basically, if I have a permanent magnet of strength X (in Teslas), and an electromagnet of strength Y (again, in Teslas) and a distance Z (in meters), what will the force be between them? If more variables are needed, let me know.
  2. jcsd
  3. May 28, 2017 #2
    "How much force" depends upon each magnet's field strength, where they are in relation to one another, the magnetic permeability of what ever is in between them, and their "geometry" (physical shape, dimension and construction). The math is easy enough when considering ideal magnetic point charges, but this last part is where most of the complexity resides, and renders easy answers to real world situations impossible.
  4. May 28, 2017 #3
    Very well, I will try to simplify it further. Let us say that the magnetic field strength is B in Teslas. Also the size of the filed is sufficiently large such that it appears to be linear locally, therefore the effects of curvature are unnoticeable. So if we were to place a magnetic coil where the field is strength B, with a radius of r, current of A, and N number of loops, what will the force F be? And don't worry about angles, it will be aligned to provide the maximum force given these conditions.
  5. May 29, 2017 #4
    This is valid only for the case when both magnets have the same area, and have a small air gap between them, but,

    gif-latex-f-3d-frac-b-2-2-mu-20_-0-cdot-20a-gif.gif where B= flux density in Teslas, A = area (square meters), and μ0 is permeability (4π×10−7 T·m/A in free space)

    The general form for point interaction is:

    [​IMG]where qm1 and qm2 are magnetic pole moments in ampere-meters, r is separation distance in meters, and μ is the permeability.

    You already know the flux density of both the electromagnet and permanent magnets. Nearly everything else depends on the geometry between them.

    How about building a spring scale test rig, and measuring it?
  6. May 29, 2017 #5
    No no no, that will not do. I need something where I have an electromagnet with a radius of r, coil windings of N, and current of I. Now the size of the permanent magnet is huge, say, around the size of a planet. Let us use the magnetic field of the earth for example. So since we know the approximate value of the magnetic field strength of the Earth in Teslas, what would the force be given these conditions?

    And I wish I could test something like this but I don't have the money.
  7. May 30, 2017 #6
    Would it be fair to say you are looking for an equation you can plug the above values into that yields an answer for the amount of force?
    AFAIK, no such equation exists.
  8. May 30, 2017 #7


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    Since the planetary field is uniform over the size of your electromagnet, there is indeed an equation for this situation: F = 0. There is no net force on a loop of wire, or an assembly of loops, in a uniform field.

    There is a torque that will tend to align the coil axis with the incident field.
  9. May 30, 2017 #8
    What do you mean when you say uniform field? And would an electrical coil create non- uniformities? You can't tell me there is no force between electromagnets and ordinary magnets. If so electrical generators would not work.

    I know there would be a torque, but what if it is pole facing pole?
  10. May 30, 2017 #9


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    That the direction and strength of the H field is constant at all points across your electromagnet. That is what you have when you specify using the earth's magnetic field.
    I won't try to tell you anything you don't want to hear.
  11. Jun 1, 2017 #10
    Well sorry if my frustration is coming through in this. However, science does not care about how either of us FEEL about things. But that is alright. The sooner we know what is wrong the sooner we know what is right and start adapting.

    But I think my problem is in how I phrased my question. So I will split it into two parts.

    1) If you were to stand at either the north or south pole, and you have a magnet with you and you and you face it having the same pole facing the geological one of the earth (north/north or south/south) are you saying no upward (away from the earth) force will be created? And if it can be done, why can't it be done with an electromagnet?

    2) Let us say we have two bar magnets and one is attached to the other by means of a lever that pivots around the center of one of them. One of the magnets were free to rotate while the other has one of the poles facing the magnet and the other is facing away. Now let us say the bar magnet that the lever is hinged to is not allowed to rotate because it is held stationary, or is much larger and more massive, or both. This leaves only the lever and the smaller magnet free to rotate. Now keep in mind that the lever can freely rotate around the more massive magnet, but not the smaller one relative to the lever therefore both the lever and smaller magnet must rotate as a single component. Now if this lever were rotated to the side of the larger magnet resulting in a 90 degree angle between the poles of the smaller magnet and the larger one, what would happen when it is released? How will it rotate?
  12. Jun 1, 2017 #11
    I got lost. Diagram please (labeled).
  13. Jun 1, 2017 #12
    I'll load a diagram later, but perhaps I can have another way of explaining it.

    Say we have a quadcoptor drone hovering above the magnetic equator of the earth with a sufficiently powerful electromagnet mounted to it. Now keep in mind that the poles of the electromagnet is pointed straight up and down. However when the electromagnet activates, it runs on DC power and it creates a torque. However, when a torque is created, the quadcoptor adjusts its engines to counteract the torque exerted while still maintaining altitude. So will it just hover there or will it move to the north or south based upon polarity?
  14. Jun 1, 2017 #13

    jim hardy

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    I think zero in direction of fields, but there is torque as has been said earlier.

    A permanent magnet is a dipole so one end of it pushes and the other pulls against earth's field netting zero.
    But it will try to align like a compass because of the torque..


  15. Jun 1, 2017 #14
    So wait, you are telling me that two magnets will with their poles facing one another will not be attracted or repulsed? Really? You mean all those elementary school experiments with magnets are just my imagination?
  16. Jun 1, 2017 #15

    jim hardy

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    oops, of course not

    i was back to earth's field. If your permanent magnet is located at earth's center and your electromagnet at earth's surface
    you can't make much force, see Asymptotic's equation in post #4
    Calculate force on each end of your electromagnet. What is difference between r's for its two ends?
    If it's a meter tall,
    r1 = 6.371 X 106 meters
    r2 = 6.371 X 106 + 1 meters

    here's what i get for the ratio of the two forces


    Can you feel two magnets even at arm's length apart ?

    Best i ever did was build a magnetometer that from my kitchen table could sense a car in my driveway about twenty feet away.

    old jim
  17. Jun 2, 2017 #16


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    CCatalyst, what is your education in physics, particularly electromagnetism? Do you know vector calculus? The Lorentz force? Your questions imply an approach that is not well grounded in physics principles and math.
  18. Jun 2, 2017 #17
    Really? I was educated in aerospace engineering. I WAS asking for the arrangement of variables.

    Anyway I've slowly learned over the course of this thread that magnetic repulsion/attraction rely upon non-linear magnetic field lines. And yes, I am aware of the Lorentz force. (current_x*magnetic field_y=force_z) But I didn't think I needed to focus on it until now.

    So here is a new scenario. We take a completely uniform magnetic field until we insert a superconducting plate at a normal angle relative to the field allowing a maximum magnetic field deflection for its shape thanks to the Meissner effect. Once that is done, we place a solenoid in front of the superconducting plate where the magnetic field is no longer linear because of the Meissner effect. Now, if we were to send a direct current through the solenoid, what would happen? Would there be a force exerted on the magnetic field generator? Would it be exerted upon the superconducting plate? Would it be on both? Let me know.
  19. Jun 3, 2017 #18


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    I asked because your posts contained no equations, no math and no apparent understanding of physics, and referenced elementary school experience. If you have some background, then put it to use instead of concocting ever more byzantine scenarios with levers and whatnot. The vector form of the Lorentz force is [itex]\mathbf F=q\mathbf v \times \mathbf B[/itex] (don't write just one component, and use symbols instead of words). If you apply it to a current loop whose plane is normal to that of the uniform field, you should be able to show yourself that F=0 when integrated around the loop (think of the right-hand rule if you can't do the integral). The same is true for each of a stack of loops, naturally. The currents interconnecting the loops to form a solenoidal coil lie parallel to the field, so the Lorentz force equation tells you what force they contribute (hint: zero). Now reason for yourself what happens if the electromagnet coil is in a nonuniform field coming from a localized source. Then apply some physics reasoning to the half-dozen other scenarios you've made up.
  20. Jun 4, 2017 #19
    First of all, this is not the place to judge people based upon assumptions and speculation. Second, how am I supposed to know what the equation is before asking what it is? How is that even possible? You honestly think I did not try to look this up first? And I was starting to get the feeling this may be a vector calculus application, and if so just say so. Plus I already knew about the Lorentz force long before this thread. That calculation is EASY! Third, I was not implying that I have an only elementary school level experience of magnets. I was pointing out how it almost sounded like people were saying that larger magnets (next to the one of the same size) were actually weaker. And that is what I felt contradicted even elementary school level knowledge on the subject. Now I know, thanks to Jim Hardy here, that is is actually a bit more complicated than that. He actually explained things to me and actually succeeded in advancing my knowledge of the subject. Fourth and finally, just because I have a background in aerospace doesn't mean I know everything, and there is no arrogance in admitting that, quite the opposite in fact. Presently there is not much overlap between aerospace and electrical engineering. But I think I may have hit on something that would need that to change someday and that is why I made this topic.

    So could you please stop treating me like I'm faking knowledge for attempting to further my own? It would be appreciated.

    Now getting back on topic, I think I may have figured something else out. I'll make a diagram of this soon. Let's start with a plate made of a superconducting material with a coil in front and behind that carry counter-rotating currents. The superconducting plate is placed at a 90 degree angle to a magnetic field, causing great curvature of the field much like a plate deflecting an aerodynamic flow. Now, is it possible to place the coils in such a way that would result in a net Lorentz force parallel to the magnetic field lines if they were undisturbed? And more importantly, as per Newton's third law, what would this force push against? The magnetic field source? The plate? Both?
  21. Jun 5, 2017 #20


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    Ok, sorry. We sometimes have troubles with posters who ask a lot of questions just to hear themselves talk.
    You can analyze this. Assume two identical single-turn loops (because they are easiest to analyze and because it's easy to find field plots online) that are coaxial. Since interactions fall off quickly with separation, place them fairly close together--separate them by, say, one diameter. Omit the superconductor to start with. Now, look at the B field from loop 1 here
    or in the plot of your choice. Draw coil 2 one diameter to the right of coil 1, and notice how the field lines curve at the wire of loop 2. Keeping in mind the opposite current flows, apply the Lorentz force rule and tell us whether the force is attractive or repellent.

    To take step towards including a superconducting plate, think about what the field is in the plane parallel to the loops and halfway between them (you'll get the answer from symmetry and from the opposite signs of the currents).
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