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Induced Magnetic Field

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data

    A parallel-plate capacitor has circular plates with radius 49.0 cm and spacing 2.20 mm. A uniform electric field between the plates is changing at the rate of 1.90 MV/m/s. Find the magnitude of the magnetic field between the plates at a point 12.1 cm from the axis (entirely inside the capacitor).


    2. Relevant equations

    Ampere's Law for induced current

    B(2∏r) = (μ-naught)(ε-naught)(A/d)(dV/dt)

    r = .121m
    μ-naught = 4∏x10^-7
    ε-naught = 8.85x10&-12
    d = .0022m
    dV/dt = 1.9x10^6 V/(m/s)
    A = ∏(.49m)^2

    3. The attempt at a solution

    the answer is B = 1.28x10^-12 T, but i can't seem to get that answer using my equation. i'd appreciate it if someone could direct me toward my error

    thanks
     
  2. jcsd
  3. Mar 31, 2012 #2

    tiny-tim

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    Hi George! :smile:

    (try using the X2 button just above the Reply box :wink:)

    Show us your full calculations.

    (In particular, what did you get for the current through the cylinder of radius 0.121 m ?)
     
  4. Mar 31, 2012 #3
    @tiny-tim

    sure.

    Id = [ (E[itex]\circ[/itex]A)/d ] * (dV/dt)

    Id = [ (E[itex]\circ[/itex]*(∏(.492))/.0022 ] * (1.9x106)

    Id = .005765 A

    i guess :smile:
     
  5. Mar 31, 2012 #4

    tiny-tim

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    mmm … your formula seems to be correct, but i'm not getting the result of 1.28 10-12 T either :confused:
     
  6. Mar 31, 2012 #5
    i got the right answer using the following equation (googled the question)

    B = [ (1/2)(r)(dV/dt) ] / C2

    C = 3x108 = speed of light in vacuum
    dV/dt = 1.9x106
    r = .121m

    not sure how the 2 equations are related tho
     
  7. Apr 1, 2012 #6

    tiny-tim

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    ah! :rolleyes: i took your word for it instead of looking at the original question …
    noooo :redface: … that wasn't dV/dt, it was dE/dt !! :biggrin:

    is everything clear now? :smile:

    (and c2 = 1/µoεo, which btw would have have been a lot easier for you to use :wink:)
     
  8. Apr 2, 2012 #7
    wow i'm slow
    it's a miracle i've even made it this far

    so for r < R,

    B = (1/2)µoεo(r)(dE/dt)

    thus B = [ (1/2)(r)(dE/dt) ] / C2

    guess i got mixed up with all these equations/derivations in front of me

    thanks tiny-tim
     
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