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Rotating loop - Faraday's Law

  1. May 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Plate is rotating on the yz plane, so perpindicular to x-plane. It is rotating at angular velocity, W = 10 [rad/s]. If B = 0.2ay [T] and phi = 0 @ t = 0, find the current i, which is flowing up the portion of the loop that is along the z-axis (current is directed toward increasing values of z). A 10 ohm resistor also lies on the positive z-axis that the current goes through. Assume loop inductance is neglibile

    2. Relevant equations
    Faraday's Law, net voltage around a closed path is equal to the net time-varying mag. flux passes through the surface of your choosing.

    3. The attempt at a solution
    So, using Faraday's Law, I can break down the magnetic field integral into two components, the motional EMF minus the transformer EMF. The B-field is not changing with respect to time so the tranformer EMF goes to zero. The formula for motional EMF is:[(u x B) • dl]. Because the velocity around the edge of the rotating plate that is standing up straight on yz plane, u = W*p*aphi. Taking the cross product of u/B] x B, and then multiplying the different displacement vector (dl), I determine the current to be i(t) = 2.4-4sin(Wt). I have checked my calculations through these steps (i.e. making sure I multiplied centimeters by centimeters), and I don't see where I am going wrong. The correct answer is i(t) = 2.4-6sin(Wt). How can I be off by a factor of 2?! Please help!
  2. jcsd
  3. May 2, 2010 #2
    [PLAIN]http://img263.imageshack.us/img263/4404/75662244.jpg [Broken]

    Attached is an image to help clarify what I am asking. Now has been the first opportunity for me to gain access to a scanner. Thanks again for all help!
    Last edited by a moderator: May 4, 2017
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