Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    2. Relevant equations

    3. The attempt at a solution
  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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook