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 centre

Answer 1

Answer: (B)

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:
$\vec{E}=\frac{\rho \vec{b}}{3 \varepsilon_{0}}-\frac{\rho \vec{a}}{3 \varepsilon_{0}} \vec{E}=\frac{\rho}{3 \varepsilon_{0}}(\vec{b}-\vec{a}) \vec{E}=\frac{\rho}{3 \varepsilon_{0}} \vec{r}$
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.