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Homework Help: Faraday's law and a uniform magnetic field

  1. Apr 23, 2008 #1
    [SOLVED] faraday's law

    1. The problem statement, all variables and given/known data
    A uniform magnetic field [itex]\mathbf{B}(t)[/itex] in the z-direction, fills a circular region in the x-y plane. If B is changing with time, what is the direction of [itex]\mathbf{E}[/itex]/


    2. Relevant equations



    3. The attempt at a solution
    My book says it is circumferential, just like the magnetic field inside a long straight wire carrying a uniform current density.

    Apparently they are using the analogy between Faraday's Law and Ampere's Law. But I do not see the logic at all.

    This is Griffiths Example 7.7.
     
  2. jcsd
  3. Apr 23, 2008 #2

    Ben Niehoff

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    They are mathematically very similar. Faraday's law:

    [tex]\nabla \times \vec E = -\frac{\partial \vec B}{\partial t}[/tex]

    And Ampere's Law (for electrostatics):

    [tex]\nabla \times \vec B = \mu_0 \vec J[/tex]
     
  4. Apr 23, 2008 #3
    I know, but why does that imply that the E-field is circumferential?
     
  5. Apr 23, 2008 #4

    Ben Niehoff

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    Because [itex]\partial \vec B / \partial t[/itex] is vertical.
     
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