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Homework Help: Angular speed in terms magnetic field

  1. Aug 5, 2012 #1
    1. The problem statement, all variables and given/known data
    3. A particle with magnetic dipole moment of magnitude μ (be careful—this is not a magnetic
    permeability) and spin angular momentum of magnitude S is immersed in a magnetic field
    of magnitude B. For simplicity, assume that the spin and magnetic-moment vectors (which
    are either in the same or opposite directions) are perpendicular to the magnetic field. The
    particle will precess, i.e., its spin angular momentum vector will rotate about the direction
    of the magnetic field, with angular speed Ωp.
    Find Ωp, in terms of the properties of the particle and the magnetic field. HINT: Remember
    that Newton’s Second Law for rotation states that the torque equals the rate of change of
    angular momentum.

    2. Relevant equations

    I did have to substitute in the variable notation given in the problem for the following equations.
    Im not entirely sure what equations to use. But I've jotted down these.
    angular momentum (S)= moment of inertia (I) x angular speed (Ωp)
    precession angular velocity= T/L= ωr/Iω
    Magnetic Field: B= mΩp/q

    b]3. The attempt at a solution[/b]

    B = mΩp/q
    = m (S/I)/ q

    I solve B for Ωp and Ωp= Bq/m

    μ= q/2m S S is the angular momentum
    solve μ for q then but that in Ωp equation

    so I then got:

    Ωp= B2μ/S

    Does this make any sense?
  2. jcsd
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