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Electrostatic energy of a dielectric sphere

by libelec
Tags: dielectric, electrostatic, energy, sphere
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libelec
#1
Oct10-09, 05:40 PM
P: 176
1. Find the electrostatic energy of a neoprene sphere or ratio R, charged with Q if:

a) Q is uniformly distributed in surface



3. The attempt at a solution

So, I can calculate the displacement field (so that I can use the expresion U= [tex]\int \vec{D}.\vec{E} dV[/tex]), but only for those points in space where r>R. Then, given that D=[tex]\epsilon[/tex]E, I can find the electric field for r>R.

But I don't know how to get the electric field inside the sphere, since D=0 there because there're no free charges inside. It could also happen that E doesn't exist inside the sphere either, but I woundn't know the reason why.

Any ideas? Thanks.
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libelec
#2
Oct11-09, 10:13 AM
P: 176
Anybody?
libelec
#3
Oct11-09, 04:20 PM
P: 176
Does anybody know how I can get P of polarization?

gabbagabbahey
#4
Oct12-09, 06:10 AM
HW Helper
gabbagabbahey's Avatar
P: 5,003
Electrostatic energy of a dielectric sphere

Quote Quote by libelec View Post
[
So, I can calculate the displacement field (so that I can use the expresion U= [tex]\int \vec{D}.\vec{E} dV[/tex]), but only for those points in space where r>R.
How are you calculating the displacement field? And why can't you calculate it for [itex]r\leq R[/itex]?

Then, given that D=[tex]\epsilon[/tex]E, I can find the electric field for r>R.
doesn't [itex]\epsilon=\epsilon_0[/itex] for [itex]r>R[/itex]?

But I don't know how to get the electric field inside the sphere, since D=0 there because there're no free charges inside. It could also happen that E doesn't exist inside the sphere either, but I woundn't know the reason why.
You've already given the reason why.....just assume that neoprene is a linear dielectric, then you know [itex]\textbf{D}=\epsilon\textbf{E}[/itex], so if [itex]\textbf{D}=0[/itex], then so does the electric field!
libelec
#5
Oct12-09, 08:41 AM
P: 176
Yes, thank you. I thought I had to find the polarization vector P.


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