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Homework Help: Field of a Polarized Object

  1. Oct 24, 2012 #1
    ρ1. The problem statement, all variables and given/known data

    A sphere of radius a has a radial polarization P = krn[itex]\hat{r}[/itex] where k and n are constants and n [itex]\geq[/itex] 0.

    a.) Find the volume and surface charge densities of bound charge.

    b.) Find E outside and inside the sphere. Verify that you results for E satisfy the appropiate boundary conditions.

    c.) Find V (potential) outside and inside the sphere.

    d.) Sketch the results.

    2. Relevant equations

    σb = P [itex]\cdot[/itex] [itex]\hat{n}[/itex]

    ρb = -[itex]\nabla[/itex] [itex]\cdot[/itex] P

    3. The attempt at a solution

    I got

    σb = krn


    ρb = -(n+2)krn-1

    which I'm pretty sure is right, but then for E I get

    Einside = -krn[itex]\hat{r}[/itex]0

    which seems okay and then

    Eoutside = 0

    which doesn't seem right.

    Can anybody tell if this is right or not? And if not how to do it?
    Last edited: Oct 24, 2012
  2. jcsd
  3. Oct 24, 2012 #2


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    I think everything is correct, except you need to specify a specific value of r in your expression for σb.

    To see if it's reasonable that E = 0 outside the sphere, calculate the net charge of the sphere due to both the bound volume charge density and the bound surface charge density.
    Last edited: Oct 24, 2012
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