A ball of radius R carries a positive charge whose volume density depends on a separation $r$ from the ball’s centre as $\rho ={\rho }_0(1-\frac{r}{R}),$ where ${\rho }_0$ is a constant. If the permittivities of the ball and the environment is equal to unity, then

The magnitude of electric field strength as a function of distance $r(>R)$ outside of the ball is $\frac{{\rho }_0{R}^3}{12{\epsilon }_0{r}^2}$

The magnitude of the electric field strength as a function of the distance $r$ (<R) inside the ball is $\frac{{\rho }_{0}r}{3{\epsilon }_0}(1-\frac{3r}{4R})$

The maximum intensity $E_{\max }$ and the corresponding distance $r_m$ is $\frac{{\rho }_{0}R}{9{\epsilon }_0}$

The magnitude of the electric field strength as a function of the distance $r$ (<R) inside the ball is $\frac{{\rho }_{0}r}{{\epsilon }_0}(1+\frac{3r}{4R})$