1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dielectric Boundary Condition Question

  1. Jun 9, 2013 #1

    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

    k\frac{\partial \Phi}{\partial n_i} = \frac{\partial \Phi}{\partial n_e}

    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
    \frac{\partial \Phi}{\partial x} = -E_x

    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.


    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook