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Dielectric lens

  1. May 6, 2012 #1
    1. The problem statement, all variables and given/known data

    In the figure the left surface of a dielectric lens is that of a circular
    cylinder, and the right surface is a plane. If E1 at point P(r,45,z) in
    region 1 is [tex]5\hat{a}_{r}-3\hat{a}_{\phi }[/tex], what must be the dielectric
    constant of the lens if the electric field in the 3rd region is parallel to
    the x axis?

    2. Relevant equations

    3. The attempt at a solution

    The coordinate systems are confusing me.

    First region
    Tangential componet [tex]E_{1t}=-3\hat{a}_{\phi }[/tex]

    Normal component [tex]E_{1n}=5\hat{a}_{r}[/tex]
    (boundary is charge free,i think)

    second region

    Tangential componet [tex]E_{2t}=-3\hat{a}_{\phi } [/tex]

    Normal component [tex]E_{2n}=\dfrac{5}{\varepsilon _{r}}\hat{a}_{r} [/tex]

    Now what to do ?
  2. jcsd
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