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Rate of decrease of the magnetic fields

  1. Aug 23, 2010 #1
    Let V_B be the rate of decrease of the magnetic fields


    For the 3rd path:
    [tex]\oint E\cdot ds = -\frac{d\phi _B}{dt} = -\frac{{d\phi _B}_1 + {d\phi _B}_2}{dt}[/tex]

    [tex]\phi _B_{(t)} = A_{(t)}B_{(t)}[/tex]
    The area is constant, it's only the magnetic field that's changing:
    [tex]\phi _B_{(t)} = \pi R^2(B_0 - V_Bt)[/tex]

    Since B1 and B2 are in opposite directions, give one of them a minus sign:
    [tex]{\phi _B}_1 + {\phi _B}_2 = \pi R_1^2(B_0 - V_Bt) - \pi R_2^2(B_0 - V_Bt) = \pi (B_0 - V_Bt)(R_1^2 - R_2^2)[/tex]
    Take the derivative of that:
    [tex]\frac{{d\phi _B}_1 + {d\phi _B}_2}{dt} = -\pi V_B(R_1^2 - R_2^2)[/tex]

    And therefore:
    [tex]\oint E\cdot ds = \pi V_B(R_1^2 - R_2^2)[/tex]
    1. The problem statement, all variables and given/known data

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  2. jcsd
  3. Aug 23, 2010 #2
    Re: bnxcnxcmn

    We appreciate that you know latex, but the title is useless, and you didn't follow the template. You also don't describe the problem. Don't expect an answer.
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