Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find Flux Density On One Side of Dielectric Boundary Given Boundary Conditions

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data
    A dielectric interface is defined as 4x + 3y = 10 m. The region including the origin is free space, where D1 = 2ax - 4ay + 6.5az nC/m2. In the other region, εr2 = 2.5. Find D2 given the previous conditions.


    2. Relevant equations
    an12 = ± grad(f)/|grad(f)|

    D2n = D1n = an(D1 · an)

    D1t = D1 - D1n

    ε = ε0εr

    D2t = (D1t)(ε2)/ε1

    D2 = D2n + D2t


    3. The attempt at a solution
    f = 4x + 3y - 10 = 0

    an12 = ± grad(4x + 3y - 10)/|grad(4x + 3y - 10)| = ± (4ax + 3ay)/5 = ± (.8ax + .6ay) Since the vector points in the positive x and y directions, I choose the plus sign to get: an12 = .8ax + .6ay

    D2n = D1n = (.8ax + .6ay)((2ax - 4ay + 6.5az) · (.8ax + .6ay)) nC/m2 = (.8ax + .6ay)(-.8) nC/m2 = -.64ax - .48ay nC/m2

    D1t = (2ax - 4ay + 6.5az nC/m2) - (-.64ax - .48ay nC/m2) = 2.64ax - 3.52ay + 6.5az nC/m2

    ε1 = ε0εr1 = ε0 = 8.854 pF/m (since the region is free space)

    ε2 = ε0εr2 = (8.854 pF/m)(2.5) = 22.135 pF/m

    D2t = (2.64ax - 3.52ay + 6.5az nC/m2)(22.135 pF/m)/(8.854 pF/m) = (2.64ax - 3.52ay + 6.5az nC/m2)(2.5) = 6.6ax - 8.8ay + 16.25az nC/m2

    D2 = (-.64ax - .48ay nC/m2) + (6.6ax - 8.8ay + 16.25az nC/m2) = 5.96ax - 9.28ay + 16.25az nC/m2

    The answer in the back of the book, however, is given as D2 = .416ax - 1.888ay + 2.6az nC/m2, which is completely different than what I got. I'm not sure where I went wrong. I followed one of my teacher's examples that he has posted (you can find it here), which is very similar to this question, but I still come up with the wrong answer. Can someone please show me where I went wrong? Thanks.
     
    Last edited: Nov 19, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted
Similar Discussions: Find Flux Density On One Side of Dielectric Boundary Given Boundary Conditions
  1. Boundary Conditions (Replies: 2)

Loading...