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Electromagnetic Induction and rectangular loop

  1. Oct 23, 2006 #1
    the question is that:
    A rectangular loop with width L and a slide wire with mass m are as shown in Fig. A uniform magnetic field [itex]\vec B[/itex] is directed perpendicular to the plane of the loop into the plane of the figure. The slide wire is given an initial speed of [itex]v_0[/itex] and then released. There is no friction between the slide wire and the loop, and the resistance of the loop is negligiblein comparison to the resistance R of the slide wire. a) Obtain an expression for F, the magnitude of the force exerted on the wire while it is moving at speed v. b). Show that the distance x that the wire moves before coming to rest is [itex] \frac{m v_0 R}{a^2 B^2}[/itex]

    i have done part a ,
    the ans. is [itex] \frac{B^2 L^2 v}{R}[/itex]
    but for part b ,
    i can just calculate half of the value of x mentioned in the question.
    i did it in this way

    subt. F from a to [itex]F=ma[/itex] to find the acceleration
    then subt. the ans. to
    [itex]v^2=u^2+2as[/itex] by taking v=0 and u=v.
    is there any mistake?

    Attached Files:

    Last edited: Oct 23, 2006
  2. jcsd
  3. Oct 23, 2006 #2


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    You have a force that is proportional to the velocity. As the wire slows, the force diminishes. You cannot use the initial acceleration as a constant.
  4. Oct 24, 2006 #3
    then , what should i do , can u give me some hints?
  5. Oct 24, 2006 #4


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    F = ma = mdv/dt = m(dv/dx)(dx/dt) = mvdv/dx

    You can separate variables and integrate.
  6. Oct 24, 2006 #5
    thx so much~
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