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(C) Inside a uniformly charged sphere,the electric field is given by $E = \frac{\rho r}{3\epsilon_0}$,where $r$ is the distance from the centre. In th

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remains constant

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(C) Inside a uniformly charged sphere,the electric field is given by $E = \frac{\rho r}{3\epsilon_0}$,where $r$ is the distance from the centre. In the overlapping region between $C$ and $D$,the net electric field is the vector sum of the electric fields due to $S_1$ and $S_2$. Let $r_1$ be the distance from $O_1$ and $r_2$ be the distance from $O_2$. The field due to $S_1$ is $E_1 = \frac{\rho r_1}{3\epsilon_0}$ (directed away from $O_1$) and the field due to $S_2$ is $E_2 = \frac{\rho r_2}{3\epsilon_0}$ (directed towards $O_2$). Since both fields are in the same direction (from $O_1$ towards $O_2$) in the overlapping region,the net field is $E_{net} = E_1 + E_2 = \frac{\rho}{3\epsilon_0} (r_1 + r_2)$. Since the distance between the centres $O_1$ and $O_2$ is constant $(d = r_1 + r_2)$,the net electric field $E_{net} = \frac{\rho d}{3\epsilon_0}$ is constant throughout the overlapping region.

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