1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

  2. jcsd
  3. Mar 31, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    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


    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook