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EMF in loop, given magnetic field

  1. Jul 8, 2011 #1
    1. The problem statement, all variables and given/known data

    In the figure below, a circular loop of wire 12 cm in diameter (seen edge on) is placed with its normal at an angle θ = 30° with the direction of a uniform magnetic field B of magnitude 0.60 T. The loop is then rotated so that N rotates in a cone about the field direction at the rate 160 rev/min; angle θ remains unchanged during the process. What is the emf induced in the loop?

    Figure: http://imageshack.us/photo/my-images/854/webassign.jpg/

    2. Relevant equations

    EMF = BAcos(theta)


    EMF = d(BAcos(theta))/dt

    3. The attempt at a solution

    I converted 160 rev/min to rev/sec and then to rad/sec, getting 16.755 rad/sec. I then plugged the given data into the 2nd equation above (trying both positive and negative signs) and it's still incorrect. Any help would be appreciated.
  2. jcsd
  3. Jul 8, 2011 #2


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    Homework Helper

    Interesting. The EMF is proportional to the change in flux through the loop. Is there a change? You have the flux as BAcos(theta), which looks correct to me. The B is constant. The A is constant. So is theta. Looks like the flux is constant, so its derivative will be zero.
  4. Jul 8, 2011 #3
    I'm confused. Are you saying the EMF is zero? I only have one guess left before the problem is marked wrong.
  5. Jul 8, 2011 #4
    Anyone have any ideas?
  6. Jul 8, 2011 #5


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    Homework Helper

    Yes, it looks like EMF = 0 to me. There are some B field lines cutting through the wire, but it looks like an equal number cutting in and out, so that approach also yields zero for the EMF.
  7. Jul 9, 2011 #6
    That was the right answer, but could you please explain the reasoning again? Is it that magnetic flux has to be increasing/decreasing to create an EMF, and if the flux is constant then EMF is zero? Because I had another homework problem which I already solved that said, "An electric generator contains a coil of 110 turns of wire formed into a rectangular loop 60.0 cm by 30.0 cm, placed entirely in a uniform magnetic field with magnitude B = 3.50 T and with B initially perpendicular to the coil's plane. What is the maximum value of the emf produced when the coil is spun at 1000 rev/min about an axis perpendicular to B?" For this one I just used the formula EMF=NABomega (where omega = 104.7) and got the correct answer of 7,257 V. Can you explain why the two problems are different?
  8. Jul 9, 2011 #7
    In one problem the net flux linking the loop changes with time. In the other it doesn't.
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