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Oscillations in a magnetic field

  1. Mar 10, 2009 #1
    1. The problem statement, all variables and given/known data
    A long, narrow bar magnet that has magnetic moment [tex]\vec{\mu}[/tex] parallel to its long axis is suspended at its center as a frictionless compass needle. When placed in a region with a horizontal magnetic field [tex]\vec{B}[/tex], the needle lines up with the field. If it is displaced by a small angle theta, show that the needle will oscillate about its equilibrium position with frequency f= (1/2pi)*sqrt(uB/I), where I is the moment of inertia of the needle about the point of suspension.


    2. Relevant equations
    No specific equations


    3. The attempt at a solution
    I remember from my mechanics physics class that I need to figure out what the restoring force is. However, that is where I run into my first problem. I do not know how to model an equation to show how the magnetic field will restore the magnet to equilibrium.
     
  2. jcsd
  3. Mar 10, 2009 #2
    This equation looks the exact same as the equation for the oscillation frequency of a spring f=(1/2pi)*sqrt(k/m). I know it is a harmonic oscillator, but can anyone get me started on how to change from sqrt(k/m) to sqrt(uB/I). Any help on how to start would be greatly appreciated.
     
    Last edited: Mar 10, 2009
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