Question

A spherical portion has been removed from a solid sphere having a charge distributed
uniformly in its volume as shown in the figure. The electric field inside the emptied
space is :

• A. zero everywhere
• B. non-zero and uniform
• C. non-uniform
• D. zero only at its center

Answer 1

Answer: (B)

non-zero and uniform

If a Gaussian surface is constructed within the cavity then by Gauss Law $\oint E.dS=0$ . This does not mean that $E=0$.

From the image, consider a point P inside the cavity and let $\rho$ be the charge density. Then, after applying superposition principle the net electric field at point P will be:

$E=\frac{\rho }{3{ϵ}_0}\overrightarrow{b}-\frac{\rho }{3{ϵ}_0}\overrightarrow{a}$

$=\frac{\rho }{3{ϵ}_0}\overrightarrow{r}$ (Since $\overrightarrow{r}=\overrightarrow{b}-\overrightarrow{a}$)

which for a given cavity is independent of the position of a point within the cavity.

Therefore, Electric field is non-zero and uniform within the cavity.