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Dielectric Boundary Condition Question

  1. Jun 9, 2013 #1
    Hi,

    I have a question regarding the boundary condition present for a dielectric immersed in a static field. I hope one of you physics guru's can shed some light on this.

    Suppose we have a dielectric in space subjected to some external static electric field.

    I have read (without explanation) that at the boundary of the dielectric the potential [itex]\Phi[/itex] satisfies

    [itex]
    k\frac{\partial \Phi}{\partial n_i} = \frac{\partial \Phi}{\partial n_e}
    [/itex]

    where [itex]\frac{\partial}{\partial n}[/itex] represent the derivatives along the outward unit normal just interior, [itex]i[/itex], and just exterior, [itex]e[/itex], of the dielectric and [itex]k[/itex] is the dielectric constant.

    can anyone shed some light on why this is so?
     
    Last edited: Jun 9, 2013
  2. jcsd
  3. Jun 9, 2013 #2
    The equation relates the normal component of the electric fields on either side of the boundary
    [itex]
    \frac{\partial \Phi}{\partial x} = -E_x
    [/itex]

    The boundary condition is

    [itex]\epsilon_1 E^\perp_1 - \epsilon_2 E^\perp_1 = \sigma_q[/itex]

    where [itex]\sigma_q[/itex] is the charge density on the surface.

    This can be shown by using Gauss's law with a "pillbox" surface.

    http://www.scribd.com/doc/136393324/27/Boundary-conditions-for-perpendicular-field-components

    This corresponds to your equation when [itex]\frac{\epsilon_i}{\epsilon_e} = k[/itex] and [itex]\sigma_q = 0[/itex]
     
    Last edited: Jun 9, 2013
  4. Jun 9, 2013 #3
    MisterX you are amazing!
    I am grateful. Thank you.
     
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