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Homework Help: Induced Magnetic Field in Dielectric

  1. Jan 11, 2005 #1
    I need a little help on an E&M problem I'm working on. A dielectric slab suspended in free space has a time dependant, non-uniform electric field inside of it (it was given in the problem, but I don't have it with me right now). For the material [tex]\mu=\mu_0[/tex] and [tex]\epsilon=2.56\epsilon_0[/tex]. I need to first find the magnetic field inside the material and then the magnetic and electric fields just above and below the material.

    For the first part, I tried using curl of E[tex]=-\frac{\partial{B}}{\partial{t}}[/tex] which gives me the partial time derivative of the magnetic field. Can I just integrate this to get the magnetic field? Since it is a partial derivative of B, I wasn't sure if that would be allowed.

    For the second part, how does the electric field change ouside of the material? Does the permitivity affect the magnetic or the electric field, or both? And could someone explain the difference between permitivity and permeability?

    E&M is a very weak subject for me, so expect to get a lot of questions this semester.
    Last edited: Jan 11, 2005
  2. jcsd
  3. Jan 14, 2005 #2
    The equation you try to apply is useless in this problem because it represents the Faraday law (for electromagnetic induction: variation of B => circular electric field). You have an inverse problem: variation of E => circular magnetic field, so.....

    I propose another Maxwell's equation:

    curl B=miu_0*j+miu_0*eps*dE/dt

    You do not have any currents, so j=0 and

    curl B=miu_0*eps*dE/dt

    If you replace B an E with sinusoidal functions (with the form A_0*exp[i*(k*r-w*t))] you'll find a relation between the magnitudes of the two alternative fields (electric and magnetic):


    where v=1/sqrt(miu_0*eps)

    or simpler (with your data)


    (c-velocity of light in vacuum)

    The magnetic and electric fields are allways perpendicular.

    In vacuum you have the same problem but eps=eps_0.
    Last edited: Jan 14, 2005
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