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Torque and Force due to an external magnetic field

  1. Mar 20, 2009 #1
    Torque N = μ ∧ B

    where μ is the dipole moment of the loop,
    and B is an external magnetic field.

    Q1 Is it true that we can only write the Torque due to an external magnetic field in this form if and only iff B is a constant? What happens, say, if B = B * x (in the z-direction) where x is a variable, is it still possible to write Torque in this form, where μ is a constant.

    Q2 Why is it that Force = 0 but Torque is not = 0 when the external magnetic field is constant?

    Cheers guys
  2. jcsd
  3. Mar 20, 2009 #2


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    Science Advisor

    1. The torque is given by the cross product [tex]\mu\times B[/tex] even if B is a function of position.
    2. The force on a magnetic dipole is given by
    [tex]{\vec F}=\nabla(\mu\cdot}{\vec B}[/tex],so it vanishes if B is constant.
    As a simple model, think of a bar magnet. The force on the N and S ends will be equal and opposite in a constant magnetic field.
  4. Mar 20, 2009 #3
    The torque on a magnetic dipole, like a compass needle, is non-zero whenever it is in a constant magnetic field B (and if the dipole is not aligned with B). There is no net translational force on the needle, however.

    If B is non constant, specifically B = B * x, where B is along z, there can also be a net translational force on a magnetic dipole. A good example is the magnetic force on a beam of neutral silver atoms, which are now known to have a magnetic moment. Because the atoms did have a magnetic dipole moment, the beam was deflected (transverse force) in a magnetic field. This was the basis of the Stern Gerlach experiments in 1921-23, which later won the Nobel Prize in physics.
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