Question

# A spherical portion has been removed from a solid sphere having a charge distributeduniformly in its volume as shown in the figure. The electric field inside the emptiedspace is :

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

Solution

## The correct option is A non-zero and uniformIf 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: $$E=\dfrac{\rho}{3 \epsilon_0}\overrightarrow{b}-\dfrac{\rho}{3\epsilon_0}\overrightarrow{a}$$$$=\dfrac{\rho}{3 \epsilon_0}\overrightarrow{r}$$  (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. Physics

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