Chapter 25, Problem 38PQ

(a)

To determine

To show that $\overrightarrow{E}=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}\widehat{r}$ and $\overrightarrow{E}=\frac{1}{4\pi {\epsilon }_0}\frac{q}{R^3}r\widehat{r}$ are identical at $r=R$.

(b)

To determine

The plot for the equations $\overrightarrow{E}=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}\widehat{r}$ and $\overrightarrow{E}=\frac{1}{4\pi {\epsilon }_0}\frac{q}{R^3}r\widehat{r}$.