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(B) Let $\rho$ be the uniform volume charge density of the solid sphere. By the principle of superposition,the electric field at any point $P$ inside

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Non-zero and uniform

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(B) Let $\rho$ be the uniform volume charge density of the solid sphere. By the principle of superposition,the electric field at any point $P$ inside the cavity is the vector sum of the electric field due to the original solid sphere (with charge density $+\rho$) and the electric field due to a smaller sphere of the same size as the cavity (with charge density $-\rho$).The electric field inside a uniformly charged sphere at a position vector $\vec{r}$ from its center is given by $\vec{E} = \frac{\rho \vec{r}}{3\epsilon_0}$.Let $\vec{r}$ be the position vector of point $P$ from the center of the large sphere,and $\vec{r}'$ be the position vector of point $P$ from the center of the cavity. Let $\vec{a}$ be the vector from the center of the cavity to the center of the large sphere,such that $\vec{r} = \vec{a} + \vec{r}'$,or $\vec{r} - \vec{r}' = \vec{a}$.The net electric field at $P$ is:$\vec{E}_{net} = \vec{E}_{large} + \vec{E}_{cavity} = \frac{\rho \vec{r}}{3\epsilon_0} - \frac{\rho \vec{r}'}{3\epsilon_0} = \frac{\rho}{3\epsilon_0} (\vec{r} - \vec{r}') = \frac{\rho \vec{a}}{3\epsilon_0}$.Since $\rho$,$\vec{a}$,and $\epsilon_0$ are constants,the electric field inside the cavity is non-zero and uniform.

$A$ 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

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