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Homework Help: Bound charge inside and outside a dielectric

  1. Nov 23, 2008 #1


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    1. The problem statement, all variables and given/known data
    A conducting wire of length a and charge density lambda is embedded inside a dielectric cylinder of radius b. To Show: a) Bound charge on the outer surface is equal in magnitude to the bound charge inside the surface.
    b) volume density of bound charge is 0 in the dielectric.
    c) what is the net charge along the axis?

    2. Relevant equations

    3. The attempt at a solution
    I calculated D and E outside the dielectric which came out to be
    D = lambda/(2*pi*s) along axial (s) direction
    E = lambda/(2*epsilon_0*pi*s) along axial (s) direction
    Using Gauss's Law I found out free charge enclosed and total charge enclosed using D and E. Then subtracting free charge from the total charge, I got the total bound charge enclosed, which came out to be 0. I don't know if it make sense or not. I need help in understanding the question.

  2. jcsd
  3. Nov 23, 2008 #2


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    I think I know what I am supposed to do conceptually but still I don't know how to write down everything in a systematic and scientific way. So, the bound charge enclosed came out to be 0 outside the cylinder. To satisfy this case, the bound charge inside the surface should be equal to the bound charge outside the surface.

    For the third part of the question, E inside the dielectric will be lambda/(2*epsilon_0*epsilon_r*pi*s) along axial (s) direction
    So, if we use Gauss's law, then we will get q enclosed to be lambda * l/epsilon_r, therefore charge per unit length will be lambda/epsilon_r

    i don't know about the third part of the question. would anyone please help me with this problem? thanks
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