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!

Polarized cylinder

  1. Nov 22, 2006 #1
    Griffith's problem 4.13 page 173

    A very long cylinder of radius a carries a uniform polarization P perpendicular to its axis. Find the electric field inside the cylinder. Show taht the field outside the cylinder can be expressed in the form

    [tex] \vec{E}(\vec{r}) = \frac{a^2}{2 \epsilon_{0} s^2} [2(\vec{P}\bullet\hat{s})\hat{s} - \vec{P}] [/tex]

    I m wondering if this is in any way similar to that of a sphere in that we can find the potnetial (from the solution of Laplace's equation) and from there we can find the electric field both inside and outside.

    Is there a shorter method, though?

    problem 4.14
    When you polarize a neutral dielectric, charge moves a bit, but the total remains zero. Thi fact should be reflected i nteh bound charges simga b and rho b. Prove from the given equations taht the total bound charge vanishes
    [tex] \sigma_{b} = \vec{P} \bullet \hat{n} [/tex]
    [tex] \rho_{b} = - \vec{\nabla} \bullet \vec{P} [/tex]

    wel ok
    [tex] \sigma_{b} = (P_{x},P_{y},P_{z}) \bullet (n_{x},n_{y},n_{z}) [/tex]
    and we know that
    [tex] \frac{\partial P}{\partial n} = \vec{P}\bullet\hat{n} [/tex]
    but the thing is does this hold??

    [tex] \frac{\partial P}{\partial n_{x}} = \frac{\partial P}{\partial x} [/tex]??
     
    Last edited: Nov 22, 2006
  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?



Similar Discussions: Polarized cylinder
Loading...