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Homework Help: Metal ring in magnetic field

  1. Dec 14, 2011 #1
    1. The problem statement, all variables and given/known data

    A metal ring of radius a is located in a region with the homogenous magnetic flux density:

    [itex]\hat{B} =\hat{z}B_0 cos(\omega t)[/itex]

    The metal ring coincides with the plane z=0. The frequency w is very low.

    Use Faraday´s Law to determine the electric field where the metal ring is located

    2. Relevant equations

    Faraday´s Law

    [itex]\nabla \times E= -\frac{dB}{dt}[/itex]

    3. The attempt at a solution

    Cylindrical coordinates.

    The Electric field is directed in the [itex]\varphi[/itex] direction around the ring.

    Rotation of E then becomes:

    [itex]-\frac{dE_{\varphi}}{dz}\hat{r} + \frac{1}{r} \frac{d(rE_{\varphi})}{dr}\hat{z}[/itex] = [itex]\hat{z}B_0 \omega sin(\omega t)[/itex]

    Is this a correct beginning, and how do i proceed from this point?
  2. jcsd
  3. Dec 14, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    It's admirable to start from the Maxwell relations explicitly. Most people probably would not.

    hint: what is Faraday's law?
    hint: what relates emf and electric field?

    I'm actually looking at your approach, it should of course yield the same result, will be either fun or frustration for me.
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