Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dielectric with net charge

  1. Dec 12, 2007 #1
    Let's say we have a sphere, radius R, which has a uniform volume charge density. Then we wrap it around with a dielectric with a frozen in polarizability of kz in the z direction. This dielectric goes from R to a radius A. The total surface bound charge on either surface of the dielectric is zero; however, the volume bound charge total is -4/3(A^3-R^3)*pi*k. Now I would think that this net charge would change the E field outside the dielectric. Looking at it through the electric displacement vector shows that in a region outside the dielectric, the E field would be determined only by the free charge on the sphere. Which would say that the charge of the dielectric has no effect. Anybody who would know which of these scenarios is actually happening and why?
     
  2. jcsd
  3. Dec 13, 2007 #2

    clem

    User Avatar
    Science Advisor

    Although the total bound surface charge (bsc) is zero, the bsc varies with angle.
    Therefor, you cannot use Gauss's law.
    The problem requires a Legendre polynomial expansion.
     
  4. Dec 14, 2007 #3

    mda

    User Avatar

    The external field will be non-zero, because the central sphere is a monopolar source and the coating is essentially a dipolar source.

    As a first attempt at the answer I would add the fields from: monopole sphere (radius R) + dipole sphere (radius A) - dipole sphere (radius R)

    I would guess given the geometry that this is actually correct but this would need to be proven properly.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Dielectric with net charge
Loading...