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## Homework Statement

A solid metal cylinder of radius ##R## and length ##L##, carrying a charge ##Q##, is surrounded by a thick coaxial metal shell of inner radius ##a## and outer radius ##b##. The shell carries no net charge.

a) Find the surface charge desnities ##\sigma## at ##R##, at ##a##, and at ##b##.

b) Find the potential at the center using ##r=b## as the reference point.

## Homework Equations

##\sigma=q/A##, ##A_{cyl}=2\pi rh##, ##V(r)=-\int_{r_1}^{r_2} \frac{\sigma}{r} da##

## The Attempt at a Solution

a) ##\sigma_R=\frac{Q}{2\pi RL}## ##\sigma_a=\frac{Q}{2\pi aL}## ##\sigma_b=\frac{Q}{2\pi bL}##

b) ##V=-\int_b^a \frac{\sigma_b}{r}da-\int_a^R \frac{\sigma_a}{r}da-\int_R^0 \frac{\sigma_R}{r}da##

##da=2\pi RLdr##