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## Homework Statement

A point charge +Q is placed at the center of a spherical insulator of radius a. The insulator completely fills three cavity of a spherical conducting shell of radius b. Find the inner and outer surface charge density of the conductor and the bound surface charge density of the conductor.

I've the electric field for each region Im having a hard time figuring out how to find the charge densities though.

I know how to find the total charge on each surface but again, Im hazy on how EXACTLY it relates to charge density.

**Relevant equations**

##E_{sphere}={\frac{Q_{enc}}{4πε_0r^2}}{\hat{r}}##

Field in conductor= 0

## The Attempt at a Solution

My thought is that it should just be ##Q_{enc}=σA## Where A is the surface area. But I cant find anything in my book to confirm this.

Another thought was to use Gaussian pillboxes, but I don't think those apply to spherical systems.

I have a picture of the problem but I'm having trouble uploading it.

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