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Quick question on direction of dl in motional emf integral

  1. May 20, 2015 #1
    1. The problem statement, all variables and given/known data
    u = velocity
    B = magnetic flux density

    2. Relevant equations
    ∫ (uxB)⋅dl

    3. The attempt at a solution
    From my understanding, the direction of dl depends on the resulting direction of (uxB). How will I know if my dl is in positive or negative?
     
  2. jcsd
  3. May 21, 2015 #2

    BvU

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    Hi Ed,

    Little response so far eh? Perhaps because there is no problem statement ? And your equation isn't an equation ?
    Attempts at solution usually look different also.

    On the constructive side: in something like$$
    X =\int_a^b (...) \cdot \vec {dl}$$ the direction of ##l## is established by the path to be followed from ##\vec a## to ##\vec b## : positive is towards ##\vec b##.

    Since ##\vec u \times \vec B## is generally perpendicular to ##\vec u##, and ##\vec u## is generally along ##\vec {dl}##, the dot product is generally zero: magnetic fields have a tendency to change the direction of velocities but not the magnitude.
     
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