The volume of this spherical shell \(=4 \pi r^{2} d r\). 

The charge enclosed within shell

\(=\frac{Q r}{\pi R^{4}}\left[4 \pi r^{2} d r\right]\)

The charge enclosed in a sphere of radius \(r_{1}\) is

\(=\frac{4 Q}{R^{4}} \int_{0}^{r_{1}} r^{3} d r=\frac{4 Q}{R^{4}}\left[\frac{r^{4}}{4}\right]_{0}^{r}=\frac{Q}{R^{4}} r_{1}^{4}\)

\(\therefore \) The electric field at point \(p\) inside the sphere at a distance \(r_{1}\) from the centre of the sphere is

\(E=\frac{1}{4 \pi \epsilon_{0}}-\frac{\left[\frac{Q}{R^{4}} r_{1}^{4}\right]}{r_{1}^{2}}=\frac{1}{4 \pi \epsilon_{0}} \frac{Q}{R^{4}} r^{2}\)