Question

A solid insulating sphere of radius a carries a net positive charge $3Q$, uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius $n$ and outer radius $c$ and having a net charge $-Q$, as shown in figure. The electric field in the region $b>r>a$ is _____

Answer 1

Consider a hypothetical sphere of radii $r$ as shown in the figure.
Total charge enclosed by hypothetical sphere is $Q_{en}=3Q$
By Gauss's law, $E.4\pi r^2=\frac{Q_{en}}{{ϵ}_0}=\frac{3Q}{{ϵ}_0}$
or $E=\frac{3Q}{4\pi {ϵ}_0{r}^2}$