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Induced Current problem from review

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  1. Dec 11, 2014 #1
    1. The problem statement, all variables and given/known data
    A 40 turn circular coil of a 4.0 cm radius and a total resistance of 0.20 Ω is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies with time as B = 50*sin(10π*t) mT where t is measured in s. What is the induced current in the coil at 0.10 s?

    2. Relevant equations
    I believe these are the equations needed:
    ε = -N*d(ΦB)/dt
    I = V/R
    ΦB = ∫B*dA


    3. The attempt at a solution
    The way I did it was start off with I = V/R, then knowing that V is the emf, I plugged in ε = -N*d(ΦB)/dt.

    Then I used the flux equation, but modified it since we were given dB (or what I assume is dB) and I thus get I = (-N* ∫dB*A)/ R.

    From there I get I = (-N*50*sin(10π*t)*10-3 *πr2)/R

    I solve this, but I don't get the correct answer (which is known since this is from an older exam that I'm doing as additional practice for my fnal).

    Am I missing something key here, or did I improperly set up the mag. field equation?
     
  2. jcsd
  3. Dec 12, 2014 #2

    rude man

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    Homework Helper
    Gold Member

    Why did you bring dB into the picture? The problem does not allude to dB in any way.
    This problem could have been made really interesting if B = 0 for t < 0. But you don't want to consider that possibility. Just assume the B field has been there for a long time and then when the field is zero and starting to increase (B=0, dB/dt > 0) that defines t=0. Then you want the current 0.1sec. later.
     
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