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 Uniform Field

  1. Jun 8, 2013 #1
    Hi,

    One of the boundary conditions when solving for the potential, [itex]\Phi[/itex], outside a dielectric sphere placed within a uniform electric field is
    [itex]\lim_{r→0}\Phi(r,θ)<\infty[/itex]

    Can anyone explain/prove why this so.

    Thanks,
     
  2. jcsd
  3. Jun 9, 2013 #2

    Jano L.

    User Avatar
    Gold Member

    If the charges are contained in some finite volume ##V##, then the Coulomb formula applies:

    $$
    \Phi(\mathbf x) = \int_V \frac{\rho(\mathbf r)}{4\pi |\mathbf x-\mathbf r|}\,d^3\mathbf r.
    $$

    If total charge in the volume ##V## is finite, the integral can be estimated by (is lower than) ##Q/(4\pi |\mathbf x-\mathbf r|)## for some ##Q##. As the latter expression falls off to zero as distance increases, so does the potential.
     
  4. Jun 9, 2013 #3
    Thank you Jano!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Dielectric Sphere in Uniform Field
Loading...