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Finding volume and surface densities of bound charge

  1. May 11, 2016 #1
    1. The problem statement, all variables and given/known data
    A slab of material has parallel faces. One coincides with the xy plane (z = 0), while the other is given by z = zt . The material has a nonuniform polarization P = P(1 + αz)zˆ where P and α are constants. Fin the volume and surface densities of bound charges


    3. The attempt at a solution
    I think that cramster-equation-20101110855506342497615036712447177.gif holds for this case. However, I couldn't any further. Please, help asap. Will appreciate so much!
     
  2. jcsd
  3. May 12, 2016 #2
    Locally the surface density of bound charge is ##\vec P. \hat n ##. Here ##\vec P## is polarization and ##\hat n## is the unit vector along the direction of local surface area. Now integrate it over the whole surface to get the total bound surface charge. Similarly the local volume density of surface charge is ##- \vec \nabla.\vec P ##. Integrate it over the whole volume to get the total bound volume charge.
     
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