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Metal bar on conducting rails

  1. Jun 30, 2007 #1
    1. The problem statement, all variables and given/known data

    This is a Problem 7.7 fom Griffiths Introduction to Electrodynamics (3ed)

    A metal bar of mass m slides frictionlessly on two parallel conducting rails a
    distance l apart. A resistor R is connected across the rails and a uniform magnetic field B, pointing into page, fills the entire region.

    If the bar moves to the right at speed v, what is the current in the resistor ?

    2. Relevant equations


    3. The attempt at a solution

    my reasonig is:

    magnetic flux is:

    A0 is initial surface, and A1 is surface which bar makes moving to the right with spead v.

    A1=x*l=v*t*l , but v is also function of t, so: A1=v(t)*t*l

    I know that equation for A1 is wrong, becouse when I try to get electromotive froce
    I get this:


    in solution manual it's:


    Can someone explain why my reasoning is wrong, it seams logical to me.
  2. jcsd
  3. Jun 30, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Setting x = v*t assumes that v is constant.

    In any case, what matters is the rate at which flux changes, which depends on the speed at the moment in question:
    d(A1) = l*v*dt
    d(A1)/dt = l*v, even if v is changing.
    Last edited: Jun 30, 2007
  4. Jun 30, 2007 #3
    Ok, than you.
    That will help me to answer other question from that problem.
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