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Current loop rotating to give magnetic moment

  1. Nov 7, 2012 #1
    1. The problem statement, all variables and given/known data
    A uniform non-conducting ring of radius
    0.816 cm and total charge 6.76 µC rotates
    with a constant angular speed of 1.73 rad/s
    around an axis perpendicular to the plane of
    the ring that passes through its center.
    What is the magnitude of the magnetic
    moment of the rotating ring?

    r = .00816 m
    q = 6.76E-6 C
    ω = 1.73 rad/s



    2. Relevant equations
    μ = IA
    I = dq/dt
    A = [itex]\pi[/itex]r^2



    3. The attempt at a solution
    I took the current and said it was equal to qω/2∏, since that gives charge/time. Then I multiplied by area. When that didn't work I decided to take the same approach but integrating from 0 to ∏/2 with r replaced with (rcosθ), to be the radius of any point on the loop, making a circle as a function of angle. Then I said charge was equal to λr dθ, since the charge is uniform. I took that function and integrated it: λω(r^2)/2∫(cosθ)^2 dθ, 0,∏/2. Then I multiplied by 4, for each of the quarters of the loop.
    The idea is that each infinitesimally small point on the loop has a charge and will behave like a charge orbiting and integrating over all of the possible radii gives the combined magnetic moment. However, this didn't work and I lost points. I don't understand why.
     
  2. jcsd
  3. Nov 7, 2012 #2

    Delphi51

    User Avatar
    Homework Helper

    qω/2∏ * area should be correct. Did you get 3.89 E-10 ?
     
  4. Nov 7, 2012 #3
    I had almost that...but not quite within 1%. Which is what our online homework requires. So my approach was correct, just not some value.
    Thanks.
     
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