Question

A solid sphere of radius $R$ has a charge $+2Q$. A hollow spherical shell of radius $3R$ placed concentric with the first sphere has net charge $-Q$. Find the electric field between the spheres at a distance $r$ from the centre of the inner sphere. $[R<r<3R]$ :

• A. $\frac{Q}{4\pi {\epsilon }_0{r}^2}$
• B. $\frac{Q}{2\pi {\epsilon }_0{r}^2}$
  
• C. $\frac{2Q}{\pi {\epsilon }_0{r}^2}$
• D. $0$

Answer 1

Answer: (B)

$\frac{Q}{2\pi {\epsilon }_0{r}^2}$

The electric field inside a spherical shell of charge is $0$

and the electric field outside a sphere of charge is $E=\frac{Q}{4\pi {ϵ}_0{r}^2}$

In the given system of charges, if $R<r<3R$, then the point lies outside the sphere of charge 2Q but lies inside the shell of charge -Q.

Thus, $E=E_{\text{sph}}+E_{\text{shell}}=\frac{2Q}{4\pi {ϵ}_0{r}^2}+0=\frac{Q}{2\pi {ϵ}_0{r}^2}$