Question

Three concentric conducting spherical shells of radii $R,2R$ and $3R$ carry charges $Q,-2Q$ and $3Q$, respectively. Compute the electric field at $r=\frac{5}{2}R$.

• A. $\frac{+Q}{25\pi {\epsilon }_0{R}^2}\hat{r}$
• B. $\frac{-Q}{25\pi {\epsilon }_0{R}^2}\hat{r}$
• C. $\frac{-Q}{5\pi {\epsilon }_0{R}^2}\hat{r}$
• D. $\frac{+Q}{5\pi {\epsilon }_0{R}^2}\hat{r}$

Answer 1

The correct option is B $\frac{-Q}{25\pi {\epsilon }_0{R}^2}\hat{r}$

There will be no electric field inside the metallic sphere due to the charge present on its either inner or outer surface.

Inside the metallic sphere, hence electric field will only be present due to the charge present at the center. Therefore, field at a point $r=5R/2$ inside the outer sphere and outside the inner two spheres, field is due to the net charge on sphere of radius $R$ and $2R$. Therefore field is

$\frac{1}{4\pi {ϵ}_o}\frac{Q-2Q}{25R^2/4}=\frac{1}{25\pi {ϵ}_0}\frac{-Q}{R^2}$