Chapter 2.3, Problem 2.30P

(a)

To determine

The $E_{above}-E_{below}=\frac{\sigma }{{\epsilon }_o}\widehat{n}$ , $\Delta E=\frac{\sigma }{{\epsilon }_o}\widehat{n}$ and $\Delta E=\frac{\sigma }{{\epsilon }_o}\widehat{r}$ are consistent with $E_{out}-E_{in}=\frac{\sigma }{{\epsilon }_o}\widehat{r}$

(b))

To determine

The field inside and outside a long hollow cylinder tube, which carries a uniform surface charge $\delta$ .

(c)

To determine

The $V_{outside}=\frac{R^2\sigma }{{\epsilon }_{o}r}$ and $V_{inside}=\frac{R\sigma }{{\epsilon }_o}$ are consistent with boundary conditions $\frac{\partial V_{out}}{\partial r}-\frac{\partial V_{in}}{\partial r}=-\frac{\sigma }{{\epsilon }_o}$