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Magnetic Field Induced Current

  1. Apr 15, 2016 #1
    1. The problem statement, all variables and given/known data
    A uniform magnetic field Barrowitalic.gif is perpendicular to the plane of a circular loop of diameter 18 cm formed from wire of diameter5.0 mm and resistivity 1.69 ✕ 10−8 Ω · m. At what rate must the magnitude of Barrowitalic.gif change to induce a 10 A current in the loop

    2. Relevant equations
    Φ = ∫ B ⋅ dA (in vector form)
    φ= BA
    ε= -dΦ/dt
    R= ρL/A

    3. The attempt at a solution
    Current is given, so I fould the Emf using ε=IR
    ε= (10) x ((1.69E-8)(2π⋅0.09))/(π⋅0.0052)) = 0.001217

    Then using the value obtained for ε,
    0.001217 = dΦ/dt
    Φ= BA

    0.001217⋅A = dB/dt

    wouldn't dB/dT be the rate that B is changing?
  2. jcsd
  3. Apr 15, 2016 #2


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    2017 Award

    Staff: Mentor

    It is, but the units are not Ampere. In general, working with units helps to find most errors.
    Be careful with diameter and radius of the wire.
  4. Apr 15, 2016 #3
    Oh I see, my mistake was actually I used diameter instead of radius. Thank you!
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