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


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.

libelec

Anybody?

libelec

Does anybody know how I can get P of polarization?

gabbagabbahey

How are you calculating the displacement field? And why can't you calculate it for [itex]r\leq R[/itex]?

doesn't [itex]\epsilon=\epsilon_0[/itex] for [itex]r>R[/itex]?

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

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