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Faraday's Law of Induction - Current in Multiple Wires

  1. Sep 25, 2012 #1
    1. The problem statement, all variables and given/known data

    A 7.40 cm diameter coil consists of 15 turns of circular copper wire 2.3 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 7.29×10^−3 T/s . Determine the current in the loop. Express your answer using two significant figures.

    2. Relevant equations

    magnetic flux = BA
    ε = -N Δmagnetic flux / ΔT

    3. The attempt at a solution

    I'm still a little confused as what to do with the 7.40 cm and 2.3 mm (other than convert them to SI units).

    What I've done so far:

    -15 (7.29 * 10^-3 T/s) = ε
    ε = -0.109 V

    Was that a good place to start?
     
  2. jcsd
  3. Sep 25, 2012 #2
    The two radii are given so that you could determine the resistance of the wire in coil.
     
  4. Sep 26, 2012 #3
    Would it make sense if I :

    ε = - N (ΔB) / (Δt) * ∏r^2

    This would provide a voltage.

    R = ρl / a

    This would provide a resistance.

    I = V / R

    This would provide a current.
     
  5. Sep 27, 2012 #4
    The equation for EMF seems correct. In the equation for resistance, what are all those constants? How do they correspond to the data in the problem?
     
  6. Sep 27, 2012 #5
    R is resistance.

    ρ is the resistivity of the material (copper) = 1.72 * 10^-8 Ωm

    l = length of wire = (0.0740 m?)

    A = cross sectional area of wire = ∏(0.00115 m)

    I'm unsure about the last two.
     
  7. Sep 27, 2012 #6
    The values you listed for the last two are incorrect.

    How would you compute the length of wire in a coil?

    What about its cross-sectional area?
     
  8. Sep 27, 2012 #7
    To calculate the length of a wire in a coil:

    A coil is a circle. The circumference of a circle is ∏d. The coil has 15 turns so in this case

    l = d∏ * 15

    To calculate the cross sectional area of the copper wires:

    A = ∏(0.00115 m)^2 * 15 (now I'm considering all of the turns).
     
  9. Sep 27, 2012 #8
    The length looks good. But I don't understand why you multiply the cross-sectional area by the number of turns.
     
  10. Sep 27, 2012 #9
    Wow! A = ∏r^2 . I just noticed in one of the comments I left off the "square" part.

    A = ∏(0.00115 m)^2
     
  11. Sep 27, 2012 #10
    So I think you have all it takes to solve the problem.
     
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