I have a problem that I can not do after searching the net and looking through my notes and text book. I think it is a basic electomagnetic field question but i just cant get my head around it.

The question is:

The electric field E inside a dielectric sphere placed between the plates of a large parallel-plate capacitor is uniform. Given that the sphere has a relative dielectric constant "epsilon"(r) and radius r, find an expression for the total electric energy of the sphere.

I was considering using the relationship

U=1/2*"EPSILON(0)"E^2

Where U is the energy density and "EPSILON(0)" is the permitivity of free space and E is the electric field.

But I dont know how to take this to get an expression for the total energy of the dielectric.

Can anyone help me? I would really appreciate it

Thanks

hhh79bigo

## Answers and Replies

The idea here is a basic boundary value problem. You know the field is constant outside, how does it change at the boundary of the dielectric? Once you have the equation of the electric field inside, integrate it over the volume of the sphere then plug it into your equation for the total energy U.

(hint: what are the boundary equations on the E and D field between the vacuum and the dielectric? Or... do it from a potential standpoint... lots of ways to do this problem)

cheers for that I shall be pondering on this later on

Thanks