Question

There are two non conducting spheres having uniform volume charge densities $\rho$ and $-\rho$. Both spheres have equal radius R. The spheres are now laid down such that they overlap as shown in the figure. The electric field $\overrightarrow{E}$ in the overlap region is :

• A. non uniform
• B. zero
• C. $\frac{\rho }{3{ϵ}_0}\overrightarrow{d}$
• D. $\frac{\rho }{3{ϵ}_0}\overrightarrow{r}$

Answer 1

The correct option is B zero

The filed lines are directed outward from the surface of sphere for $+\rho$ and inner ward for $-\rho$.

Thus the electric filed due to $+\rho$ at the over lap region is equal and opposite direction of the filed due to $-\rho$. So the net electric field is zero in overlap region.