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## Homework Statement

Consider a spherical shell with uniform charge density ρ.

The shell is drawn as a donut with inner (R1) and outer (R2) radii.

Let r measure the distance from the center of the spherical shell, what is the electric field at r>R2, R1<r<R2, and r<R1.

I am working on the r > R2 part right now.

I'll work on R1<r<R2 later.

The question says spherical shell so I would have assumed that we would multiply ρ by the area of the shell instead of the volume, however my professor's solution uses volume for the total charge. I solved the problem, I just don't understand why we would use volume and not the shell area. Although, it DOES give ρ which is the density per unit of volume.

It just doesn't make sense to me. What am I missing? Am I misunderstanding something?

## Homework Equations

E = Qenclosed/ (ε0A)

## The Attempt at a Solution

For r > R2 [/B]

Qenclosed = ρ*4/3π(R2^3-R1^3)

A = 4πr^2

R2 is the outer radius of the shell and r is the distance from the center.

E = ρ(R2^3-R1^3)/(3ε0*r^2)

I already know that r<R1 =0 from the center of the shell to R1, there is no charge (it is a hole).

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