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Time dependence of induced emf in a loop

  1. Jan 22, 2014 #1
    1. The problem statement, all variables and given/known data

    A uniform magnetic field B is perpendicular to the plane of a circular wire loop of radius R. The magnitude of the field varies with time according to B=B0exp(-t/τ) where B0 and τ are constants. The time dependence of the induced emf in the loop is
    a) exp(-t22)
    b) 1+exp(-t22)
    c) 1-exp(-t/τ)
    d) -exp(-t/τ)

    2. Relevant equations

    emf=-dΘ/dt
    Θ=∫B.dA

    3. The attempt at a solution

    εdt=-dΘ
    ∫εdt=-∫dΘ
    ∫εdt=-Θ
    ∫εdt=-∫B.dA
    ∫εdt=-B∏R2
    ∫εdt=-B0.exp(-t/τ)∏R2

    So with this I guessed that the time dependence would be option d) -exp(-t/τ)
    Is this the correct answer?
     
  2. jcsd
  3. Jan 22, 2014 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hello, JonNash.

    The question asks for the time dependence of ε. So you need to find an expression for ε as a function of time.
     
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