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Homework Help: Lenz's Law, 2nd opinion wanted

  1. Apr 5, 2004 #1
    Please look for flaws in my reasoning, any help would be appreciated.
    Question:
    HRW CH31 #28P(if you have the book handy)
    A long rectangular conducting loop of width L, resistance R, and mass m, is hung in a horizontal, uniform magnetic field B that is directed into the page and exists only above line aa. The loop is then dropped; during its fall, it accelerates until it reaches a certain terminal speed. Ignoring air resistance, what is this terminal speed?
    Answer:
    For the falling loop to reach a constant terminal speed the force of gravity pulling it downward must be cancelled by a Lorentz Force pullint it upward

    F(Lorentz)=mg eqn 1

    To find F(L) we must first find the induce EMF, then the induced current and finally use this to determine F(L).

    Magnetic Flux:(MF)=Integral[B*dot*dA] Let x equal verticle length of loop in B field.
    (MF)=B*L*x

    EMF=d/dt*(MF)=d/dt*BLX=BL*dx/dt=BLv

    Now taking the derivative of both sides with respect to t:
    d/dt*EMF=dv/dt*BL=abL

    intergrate both sides with respect to t:
    Integral[d/dt*EMF*dt=aBL*Integral[dt]
    EMF=aBLt
    This sounds reasonable because EMF should be increasing with time since change of flux is increasing with time.

    Now in terms of current:
    i=EMF/R=abLt/R

    and Force:
    F=aB^2*L^2*t/R

    Subbing g for a and rewriting eqn 1 from way above:
    mg=gB^2*L^2*t/R

    solving for t:
    t=MR/(M^2*L^2)

    Using kinematics equation:
    V(terminal)=g*t

    Sound Plausible? Thanks for your time.
     
  2. jcsd
  3. Apr 5, 2004 #2
    Here, I think, is a problem:

    (You could have saved yourself some time by simply claiming that v = at, which in effect is what you have done.)

    Problem is you are assuming that a is constant. I think you will agree that this is the case here. The magnetic force exerted on the coil is increasing as v increases.

    In fact, if you just remember that you are looking for a terminal velocity, it will be obvious that ai=g, and af=0.
     
  4. Apr 6, 2004 #3
    Ahhh :rolleyes: , thanks for pointing that out; I sensed a bit of redundancy(sp?), but wasn't sure enough to simplify. Then again, I can use the practice showing relationships via Calculus.
     
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