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Homework Help: Faraday's law

  1. Jun 5, 2013 #1
    A magnetic field of B=0.5B0z^ is present when a loop with radius r is rotated around the y axis with angular velocity of w=9 rad/s. What is the induced emf?

    Well: flux = SB*dA = SBdAcosq(t) = Bcosq(t)SdA = 0.5B0*pi*r^2cosq(t)

    d(flux)/dt = 0.5B0*pi*r^2*-sinq(t)*dq(t)/dt = 0.5B0*pi*r^2*-sinq(t)*9.

    But I'm still stuck with the angle q which isn't given to me... What should I do?

    Attached Files:

  2. jcsd
  3. Jun 5, 2013 #2
    The attachment shows ##B=(1/2)B_0 t^2## and you use ##B=(1/2)B_0##.

    And what is S?
  4. Jun 5, 2013 #3
    I think you are mostly correct. However, what should the argument of cosq(t) be? could it be cosq(9t)?
  5. Jun 5, 2013 #4
    The first magnetic field is from another part of the question - if you look at the bottom you'll see the field I wrote here. S in the sign of integration ∫, forgot about the operators here :P
  6. Jun 5, 2013 #5
    You're right! It's analoug to x=vt for constant speed movement... thanks!
  7. Jun 5, 2013 #6
    Ah ok but I don't think you need to deal with integrals here.

    You know ##\phi=\vec{B}.\vec{A}##. The direction of A is perpendicular to plane of ring. When the area vector rotates by an angle ##\theta##, evaluate ##\phi##.

    PS: Can you post the answer so that I can check my working?
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