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Finding the charge density

  1. Feb 10, 2017 #1
    1. The problem statement, all variables and given/known data
    IMG_2504.JPG
    ##e_{r1}=2##
    ##e_{r2}=10##
    ##α_1=\pi /4##
    ##D_1=100 nC/m^2##
    ##ρ_s=0##
    On the borderline of two dielectrics there is no free charge. Calculate the surface bond charge density of both dielectrics.
    ##ρ_{bs1}=?##
    ##ρ_{bd2}=?##
    2. Relevant equations
    3. The attempt at a solution

    So with the information i was given i am able to calculate some things.
    Since there is no free charge ##D_{1n}=D_{2n}## so ##D_1\cos α_1=D_2 \cos α_2##
    And since ##E_{1t}=E_{2t}##, ##\frac{D_1 \sin α_1}{e_{r1}}=\frac{D_2 \sin α_2}{e_{r2}}##
    Dividing these equations i get ##\tan α_2=\frac{e_{r1}}{e_{r2}} \tan α_1## and i get some crazy number.
    The bond charge density is ##D=e_0E+P##, ##P_1=D_1-e_0E_1##, ##P=e_0(e_r-1)E_1##
    So how do i get this to work?
     
  2. jcsd
  3. Feb 12, 2017 #2

    rude man

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    Homework Helper
    Gold Member

    If you express Gauss's law in terms of E instead of D you can determine that there exist different bound surface charge densities at the dielectric discontinuity.
     
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