Electrostatic energy of a dielectric sphere

[libelec]

1. Find the electrostatic energy of a neoprene sphere or ratio R, charged with Q if:

a) Q is uniformly distributed in surface

The Attempt at a Solution

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

 

[libelec]

Anybody?

 

[libelec]

Does anybody know how I can get P of polarization?

 

[gabbagabbahey]

[
So, I can calculate the displacement field (so that I can use the expresion U= $$\int \vec{D}.\vec{E} dV$$), 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 $r\leq R$?

Then, given that D=$$\epsilon$$E, I can find the electric field for r>R.

doesn't $\epsilon=\epsilon_0$ 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.

You've already given the reason why...just assume that neoprene is a linear dielectric, then you know $\textbf{D}=\epsilon\textbf{E}$, so if $\textbf{D}=0$, then so does the electric field!

 

[libelec]

Yes, thank you. I thought I had to find the polarization vector P.