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Calculating the magnitude of the electric field

  1. Oct 22, 2015 #1
    1. The problem statement, all variables and given/known data
    A uniform magnetic field pointing in the positive z-direction fills a cylindrical volume of space of radius R whose central axis is the z axis. Outside this region, there is no magnetic field. The magnitude of the magnetic field in changes with time as B = Bmax sin(ωt).

    a. Calculate the magnitude of the electric field that accompanies this changing magnetic field as a function of time t and radial distance rfrom the center of the magnetic field for r < R.

    b. Calculate the magnitude of the electric field that accompanies this changing magnetic field as a function of time t and radial distance rfrom the center of the magnetic field for r>R.

    2. Relevant equations
    I'm not exactly sure which equations to use.

    3. The attempt at a solution

    a)

    E(2*pi*r) = pi*r^2 (dB/dt)
    E = r/2 (dB/dt)
    E = [omega*r*Bmax(sin(omega*t))]/2

    This however is incorrect.


    b)

    E(2*pi*r) = pi*R^2 (dB/dt)
    E = R^2/2r (dB/dt)
    E = [omega*R^2*Bmax (cos(omega*t))]/2r

    Which also appears to be incorrect. Where did I go wrong?
     
  2. jcsd
  3. Oct 22, 2015 #2

    andrewkirk

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    The Maxwell-Faraday equation describes the electric fields arising from time-varying magnetic fields. It easily gives you the curl of E and the EMF around a loop at the given radius. I forget how one extracts the E vector from that but no doubt it is straightforward.
     
  4. Oct 25, 2015 #3

    vela

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    Probably just a typo, but the sine should be a cosine. You're also missing a negative sign (Lenz's law).

     
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