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Magnetic Torque

  1. Mar 8, 2010 #1
    I am a mechanical engineer and am having to do some calculations concerning magnets and solenoids for a project I am on.

    I have a solenoid (defined by number loops, current and cross sectional area).

    Inside the solenoid is a rare earth bar magnet of some length, initial mis alignment (degrees). The magnet is only free to rotate. I have the manufactures information for the magnet seen below.
    remanence (Br), which measures the strength of the magnetic field = 1.2 teslas
    energy product (BHmax), the density of magnetic energy = 300 Kj/m^3

    How do I calculate the torque on this magnet when the solenoid is turned on? I have looked and looked online but I don't know how to convert the manufactures data into a magnetic moment or a magnetic field or anything else I could find of use.

    Please any help would be greatly appreciated I have already spent way to much time on this.

  2. jcsd
  3. Mar 8, 2010 #2


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    Staff: Mentor

    Welcome to the PF. The way I have it pictured in my head, there will be no torque on the bar inside the solenoid coil. Their magnetic fields are parallel or anti-parallel. You may get some force pushing the magnet either partially out or all the way out of the solenoid, and you may partially demagnitize the magnet (if the 2 fields are anti-parallel), but I don't see a torque anywhere (except maybe from the few degrees of misalignment you mention).

    Could you post a picture, and describe the moment arm and where the force would be applied to give you a torque?
  4. Mar 8, 2010 #3
    I plan on ensuring the mis-alignment to be somewhat large to induce the needed torque. I need to be able to rotate the magnet 40-60 degrees one way and then reverse the solenoid and rotate it back to the original positions. I am curious at my minimum mis alignment how much torque can I get probably between 10 and 30 degrees.
  5. Mar 9, 2010 #4


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    Staff: Mentor

    Please post a sketch. Thanks.
  6. Mar 9, 2010 #5
    The magnetic "charge" qm of a bar magnet pole is given in Eqn (1) in

    http://instruct.tri-c.edu/fgram/WEB/Mdipole.htm [Broken]

    The dipole moment of the bar magnet is p = qmL where L is the length of the bar magnet

    the torque is τ = p x B

    where p x B is the vector cross product (= the magnitude of p and B times the sine of the included angle), and B is the magnetic field inside the solenoid.

    If you know the moment of inertia of the magnet, you can calculate the oscillation period of the magnet in the solenoid.

    I could help you more if you give complete details of both the bar magnet and the solenoid.

    Do all of your calculations in mks units, and you will get the torque in Newton-meters.

    Bob S
    Last edited by a moderator: May 4, 2017
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