Physics - Electrostatics Question with Solution | TestHub

Charge on nucleus $=+Ze$ Total negative charge $=-\mathrm{Ze}$ ( $\because$ atom is electrically neutral) Negative charge density, $\rho =\frac{\text{ charge }}{\text{ volume }}=\frac{-Ze}{\frac{4}{3}\pi R^3}$
Consider a Gaussian surface with radius $r$. By Gauss's theorem,
Charge enclosed by Gaussian surface, $q=Ze+\frac{4\pi r^3}{3}\rho =Ze-Ze\frac{r^3}{R^3}$ (Using (i)) From (ii), $E(r)=\frac{q}{4\pi {\epsilon }_0{r}^2}=\frac{\mathrm{Z}e-\mathrm{Z}e\frac{r^3}{R^3}}{4\pi {\epsilon }_0{r}^2}=\frac{Ze}{4\pi {\epsilon }_0}\left[\frac{1}{r^2}-\frac{r}{R^3}\right]$