Should I Consider the Electric Field Outside a Uniformly Charged Sphere?

[guyvsdcsniper]

Homework Statement

The goal of this problem is to find the total electrostatic energy stored in a uniformly charge
sphere of radius R and total charge Q. Note that the charge is uniformly distributed throughout the whole volume –this is not a shell.

Express your answer in terms of Q, R, and constants of nature. There are many different ways to do this, you might want to use two different methods so you can check your result.

Relevant Equations

W= ϵ /2 ∫ E²dt

I solved this problem on my own using the Energy formula. When I compared my answer to online answers (attached) as well as the griffiths solution manual, I noticed they also include the Electric field outside the sphere into their calculations. I did not and only use the Electric Field inside.

Am I wrong for just considering the Electric Field inside the sphere? The problem explicitly states "find the total electrostatic energy stored IN a uniformly charge sphere". I don't see how E outside is relevant to the question.

 

[ergospherical]

The energy of a static charge distribution is an integral of the energy density $(1/2) \epsilon_0 E^2$ over all space, which reflects the idea that said energy is stored in the electromagnetic field (which extends over all space) rather than the charges themselves.

 

[guyvsdcsniper]

The energy of a static charge distribution is an integral of the energy density $(1/2) \epsilon_0 E^2$ over all space, which reflects the idea that said energy is stored in the electromagnetic field (which extends over all space) rather than the charges themselves.

Thank you that makes sense. I actually just got done re reading my book and forgot about the "all space" part of this equation. It makes sense now.