Question

There are three concentric thin spheres of radius $a,b,c$ $(a>b>c)$. The total surface charge densities on their surfaces are $\sigma ,-\sigma ,\sigma$, respectively. The magnitude of electric field at $r$ (distance from centre) such that $a>r>b$ is

• A. 0
• B. $\frac{\sigma }{{\epsilon }_0{r}^2}\left(b^2-c^2\right)$.
• C. $\frac{\sigma }{{\epsilon }_0{r}^2}\left(a^2+b^2\right)$
• D. none of these

Answer 1

Answer: (B)

Electric field at a distance $r(a>r>b)$ will be due to charges enclosed in $r$ only, and since a sphere acts as a point charge for points outside its surface,
$\therefore E=\frac{k{Q}_c}{r^2}+\frac{k{Q}_b}{r^2}=\frac{k}{r^2}\left(\sigma \times 4\pi c^2+(-\sigma )4\pi b^2\right)$|
$=\frac{\sigma }{{\epsilon }_0{r}^2}\left(c^2-b^2\right)$