Let $\mathrm{\rho }\left(\mathrm{r}\right)=\frac{\mathrm{Qr}}{{\mathrm{\pi R}}^4}$ be the charge density distribution for a solid sphere of radius R and total charge Q for a point ‘p’ inside the sphere at distance r₁ from the centre of the sphere, the magnitude of electric field is

Point inside the charged solid sphere E cannot be zero. We know that
$\mathrm{Q}=\frac{4}{3}\pi {\mathrm{r}}^4\rho ;\mathrm{dq}=4\pi {\mathrm{r}}^2\mathrm{dr}.\rho$
Total charge on the sphere of radius r
$\begin{array}{c}\mathrm{q}={\int }_0^{{\mathrm{r}}_1} 4\pi {\mathrm{r}}^2\mathrm{dr}\cdot \rho ={\int }_0^{{\mathrm{r}}_1} 4\pi {\mathrm{r}}^2\mathrm{dr}\cdot \frac{\mathrm{Qr}}{\pi {\mathrm{R}}^4}\\ =\frac{4\mathrm{Q}}{{\mathrm{R}}^4}{\int }_0^{{\mathrm{r}}_1} {\mathrm{r}}^3\mathrm{dr}=\frac{4\mathrm{Q}}{{\mathrm{R}}^4}\frac{{\mathrm{r}}_1^4}{4}=\frac{{\mathrm{Qr}}_1^4}{{\mathrm{R}}^4}\\ \mathrm{E}=\frac{1}{4\pi {\epsilon }_0}\frac{\mathrm{Q}}{{\mathrm{r}}_1^2}=\frac{1}{4\pi {\epsilon }_0}\frac{{\mathrm{Qr}}_1^4}{{\mathrm{r}}_1^2{\mathrm{R}}^4}=\frac{1}{4\pi {\epsilon }_0}\frac{{\mathrm{Qr}}_1^2}{{\mathrm{R}}^4}\end{array}$