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Inducing EMF by changing area

  1. Nov 8, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm answering a question which describes a situation in which a metal ring is dropped through a magnetic field such that, when it falls, its area is perpendicular to the magnetic field.
    I need to find its terminal velocity given:
    Mass : 2.66 x 10-4 kg
    Magnetic flux density : 2.00 T
    Radius : 2.00 cm
    Resistance : 2.48 m(ohms)

    2. Relevant equations
    Emf = dBA/dt
    V = IR
    F = BILsin(theta)

    3. The attempt at a solution

    At terminal velocity, the magnetic force as a result of the ring's current must equal its weight:

    mg = BIL

    I'm confused about how to introduce v into the equation E.m.f = dBA/dt.
    My thoughts were as follows:

    If A is the area through which the ring moves in time dt then
    A = pi r2vdt

    e.m.f = (dBpi r2vdt)/dt
    e.m.f = dBpi r2v

    Dividing both sides by R :

    I = (dBpi r2)/ R
    I would then set this equal to mg / BL to find v.
    However, in previous questions 'L' has always been a straight wire. Would you use the diameter of this metal ring or its circumference? My feeling is the circumference but I'm not 100% sure.
    Also, is the way I've approached this question right?
     
  2. jcsd
  3. Nov 8, 2015 #2

    andrewkirk

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    Gold Member

    What does this mean? Do you mean that the disc that has the ring as boundary has a normal that is perpendicular to the mag field lines?

    Is the magnetic field uniformly linear and self-parallel within the region of interest?
     
  4. Nov 9, 2015 #3
    I mean the plane of the area of the metal ring is perpendicular to the plane of the magnetic field lines. The magnetic field is uniform. I don't have a clue what self parallel within the region of interest means.
     
  5. Nov 9, 2015 #4
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