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Induced current from changing magnetic field

  1. Apr 15, 2015 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    emf = i (induced) R
    emf = - d(Ф)/dt
    Ф = B (dot) A
    B = μi/(4piR)

    3. The attempt at a solution

    emf = - d(Ф)/dt
    emf = - d( B (dot) A )/dt
    emf = - d[ (μi/(4piR) * A ]/dt, A and B are perpendicular

    Really not sure how to proceed from here as there are multiple derivatives (di/dt dR/dt and dA/dt) that I don't quite get.

    Thank you very much.
  2. jcsd
  3. Apr 15, 2015 #2


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    Science Advisor

    You have to calculate the total flux φ through the loop. Since B is a function of R, you have to integrate to find the total flux, which will be a function of i. In terms of your question about time derivatives, the only thing changing with time is i. A and R are constant in time.
  4. Apr 15, 2015 #3
    Got it! Thank you very much.
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