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Homework Help: Laplacian for hyperbolic plates

  1. Dec 23, 2017 #26
    I don't see how you could sketch it without working out ##\sigma##

    Could we not have a non zero volume charge though? To satisfy the conservation of charge
     
  2. Dec 23, 2017 #27

    TSny

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    Sketch E-field lines in the region of the origin. Look for symmetry. This should help you see any symmetry of the surface charge density.

    Usually, it is assumed that the susceptibility ##\chi_e## is constant inside the material (i.e., does not depend on position). From ##\bf D = \epsilon_0 \left( 1 + \chi_e \right) \bf E##, deduce that ##\nabla \cdot \bf D## ## = \epsilon_0 \left( 1 + \chi_e \right)\nabla \cdot \bf E##. But we know ##\nabla \cdot \bf D## ## = 0## (assuming no free volume charge density ##\rho_f##). Hence, ##\nabla\cdot \bf E## ## = 0##. And this implies zero total volume charge density ##\rho_f + \rho_b##. Hence, what can you conclude about any bound charge density ##\rho_b##?
     
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