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Inductance of a loop in a nonuniform magnetic field

  1. May 5, 2008 #1
    1. The problem statement, all variables and given/known data
    A square loop made of wire with negligible resistance is placed on a horizontal frictionless table. The mass of the loop is m and the length of each side is b. a nonuniform vertical magnetic field B=B0(1+kx) exists in the region, where B0 and k are constants. The loo is given a quick push with initial velocity v along x-axis. The loop stops after a time interval T. Find the inductance of the loop.

    2. Relevant equations

    emf(ind) = -L*dI/dT
    emf= -delta flux/delta t

    3. The attempt at a solution

    well, I am sort of in a loss for this one.
    I tried to get the induced emf by finding dflux/dt:

    =integral ( B0*(1+kx) * b dX )
    = b*B0*(b*2*k*x+b^2*k+2*b)/2

    change of flux in regards with time = dphi/dx * dx/dt
    = b^2*k*B0*v (because velocity= dx/dt)

    so emf is b^2*k*B0

    now Im not sure what to do, since the resistance is negligble and i cant find the current from it....

    also the whole time interval thing, where does it come into play (kinematics ?)
    and should I use conservation of energy here ?
    1/2 * m * v^2 = 1/2 * L * I^2 ? for some reason I don't think its the right way

    just thoroughly confused with this one. please help !
  2. jcsd
  3. May 6, 2008 #2
    anyone ? any hints/suggestions ?
  4. May 6, 2008 #3
    I don't think you got the right equation for emf, you are trying to use the emf generated by a solenoid.

    Also, you don't need to find any current (you can't, since there is no resistance), you only need to find the emf.
  5. May 6, 2008 #4
    can you possibly expand on your answers ?

    what do you mean I dont have the right expression for the emf ? and what does a solenoid have to do with this problem ?

    the textbook I use states that the self-induced emf in any closed loop of current is -L*dI/dT...

    I saw a similar problem done in a portable ta guide the way I described.... only there resistance wasnt negligible and the field was Bz=C/x and not B=B0*(1+kx)....
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