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Energy Dissipated in Loop (Magnetic Field)-

  1. Apr 2, 2012 #1
    Energy Dissipated in Loop (Magnetic Field)-- Please Help!

    1. The problem statement, all variables and given/known data

    What is the energy dissipated as a function of time in a circular loop of N turns of wire having a radius of r and a resistance of R if the plane of the loop is perpendicular to a magnetic field given by
    B(t)=B0e-t/tau


    2. Relevant equations

    P=I^2*R=EMF^2/R
    EMF=-d/dt(flux)=-dB/dt*NA

    3. The attempt at a solution

    I first wanted to calculate the EMF, and since the B field varies, I found the derivative of the B field, times the number of turns times the area:
    EMF=NA*(t/tau)Be^(-t/tau)
    Then squaring this term and multiplying it by 1/R will equal the time-derivative of the energy dissipated
    dE/dt = (NA)^2*(t/tau)^2*(B^2)e^(-2t/tau)

    Bringing dt over and integrating from 0 to t I find (and substituting pi*r^2 for A):
    E=(N*pi*r^2)^2*(B^2)(tau^2-e^(-2t/tau))(2t^2+2t*tau + tau^2)/(4R*tau)

    This is not the correct answer, though.

    Any help??? Please!
     
  2. jcsd
  3. Apr 2, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    Re: Energy Dissipated in Loop (Magnetic Field)-- Please Help!

    Your derivative of the B field doesn't look right. Since you're taking the derivative w.r.t. time the t shouldn't be coming down from the exponent.
     
  4. Apr 2, 2012 #3
    Re: Energy Dissipated in Loop (Magnetic Field)-- Please Help!

    Oh-duh! Thank you--got it now.
     
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