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Balancing a cylinder on an incline with a mag. field

  1. Nov 17, 2008 #1
    1. The problem statement, all variables and given/known data
    A cylinder with radius R, length l, and density ro has a 10 turn coil of wire wrapped lengthwise. The cylinder is placed on the ramp tilted at an angle theta, with edge of the coil parallel to the ramp's slope. A uniform mag. field points straight up.

    For what loop current will the cylinder rest on the ramp. Assume static friction is large enough to keep the cylinder from sliding down the ramp.


    2. Relevant equations



    3. The attempt at a solution

    So, here are my thoughts. I need to find the current such that the torques exerted by the magnetic field on the wires balance the torque exerted by the force of gravity

    on a slope F = mgsin(theta), = ro*pi*R^2 * l, so the force of gravity is parallel to slope of the ramp, I think.

    Then for a current-carrying wire F = IlBsin(theta) Is theta = 90?

    F = IlB Torque = IlBR

    I'm not sure what to do at this point because I think that the forces exerted on the two wires by the magnetic field are equal and in opposite directions. I haven't done dynamics for awhile, so I could use a push in the right direction.

    Thanks
     
  2. jcsd
  3. Nov 17, 2008 #2
    Any ideas?
     
  4. Nov 19, 2008 #3
    Please?
     
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