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Integration of V(t) using faraday's law

  1. Mar 9, 2006 #1
    Ok the question is with a U-shaped conductor and a bar that slides across. There is a battery and a switch, the switch is open for a long time then closed at t=0. Im supposed to find the velocity as a function of time. Im mostly having trouble with the integration, i know the answer but i cant seem to integrate it right.

    We have to integrate the first term from 0 to v, and the second from 0 to t

    dv/(E-BLv) = (LB/mR)dt

    E=voltage of battery
    B=magnetic field
    L=length of rod

    i get to the formula above and then try u-substitution and i cant seem to get it right, could someone integrate this and show me? thanks
  2. jcsd
  3. Mar 10, 2006 #2


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    Make the sub

    [tex] E-Blv= u [/tex]

    You get

    [tex] dv=-\frac{du}{Bl} [/tex]

    And i'm sure you know how the limits of integration transform...

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