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Electromagnetics: Moving loop in a static magnetic field

  1. Oct 30, 2015 #1
    1. The problem statement, all variables and given/known data
    A conducting square loop (L × L) moving with velocity vo ay m/s where the magnetic flux density is B=Bo ax Wb/m2 in 0 < y < 2L, and is equal to zero when 0 > y and y > L. Determine the current in the loop and plot its magnitude as a function in the loop's position in the y-axis. Assume the loop's front at y=0 and t=0 (time), and its resistance is R Ω.
    5MKxNMk.png

    2. Relevant equations
    I=V/R (Ohm's law)
    Vemf=u × B × dl (× refers to cross product, u is the velocity)

    3. The attempt at a solution
    Vemf=- vo B l V
    I=Vemf/R = ( - vo B l )/ R A

    wtAqScx.png


    I don't know whether I am doing OK or not. I feel like I've missed up with dl. Can anyone clarify?
     
  2. jcsd
  3. Oct 31, 2015 #2

    rude man

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    Homework Helper
    Gold Member

    This formula is wrong, in fact, it's not a formula at all since you can't write "a x b x c". Plus, you're equating a differential quantity with a finite quantity. You need to be more careful with your vector math. But express V as a differential and fix your "u × B × dl" term, and you're there.
    As for your "Vemf=- vo B l V", that is OK in magnitude but you need to get the vector formula right to determine the direction of the current. Or use Lenz's law.
    And BTW V is not a vector.
     
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