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KeyToMyFire
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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.
σb = P [itex]\cdot[/itex] [itex]\hat{n}[/itex]
ρb = -[itex]\nabla[/itex] [itex]\cdot[/itex] P
I got
σb = krn
and
ρb = -(n+2)krn-1
which I'm pretty sure is right, but then for E I get
Einside = -krn[itex]\hat{r}[/itex]/ε0
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?
Homework Statement
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.
Homework Equations
σb = P [itex]\cdot[/itex] [itex]\hat{n}[/itex]
ρb = -[itex]\nabla[/itex] [itex]\cdot[/itex] P
The Attempt at a Solution
I got
σb = krn
and
ρb = -(n+2)krn-1
which I'm pretty sure is right, but then for E I get
Einside = -krn[itex]\hat{r}[/itex]/ε0
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?
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