1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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 sphere in constant E-field

  1. Jan 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Given a dielectric sphere with relative permittivity = ε in a homogeneous E-field:

    [itex]\vec{E_{0}} = E \vec{e_{z}}[/itex].

    The E-field causes a homogeneous polarisation (dipole density) of

    [itex]\vec{p} = \frac{vec{P}}{V} [/itex] with big P the dipole moment vector. The total electric field outside is:

    [itex]\vec{E^{ex}} = \vec{E_{0} - \frac{1}{4 \pi \epsilon_{0}} ( \frac{\vec{P}{r^{3}} - \frac{\vec{3P}{r^{5}}} ) [/itex]

    Question: Use the continuous nature of the normal component of [itex]\vec{D}[/itex] at the surface to show that:

    [itex]\epsilon_{0} E^{in} = E_{0} + \frac{2P}{4\pi\epsilon_{0}}[/itex]

    2. Relevant equations

    Using [itex]\vec{D^{ex}_{n}} = \vec{D^{in}_{n}}[/itex] , e.g. normal component of D is continuous at surface
    and [itex]\vec{\frac{D^{ex}_{t}}{\epsilon_{0}}} = \vec{D^{in}_{t}}[/itex]


    3. The attempt at a solution

    I simply don't know what to do I've messed around with this and got nowhere. Please help!

    Latex isn't rendering properly - vector arrows are appearing as small boxes but please try and help!!
     
    Last edited: Jan 10, 2012
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted