Question
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is
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Answer
$a=$ distance between center of both spheres By principle of superposition the net electric field at point $\mathrm{P}$
$\overrightarrow {\rm{E}} = \frac{{\overrightarrow {\rho {\rm{r}}} }}{{3{{\rm{e}}_0}}} - \frac{{{{\overrightarrow {\rho {\rm{r}}} }^\prime }}}{{3{{\rm{e}}_0}}}$
$\therefore \quad \overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{r}}^{\prime}=\overrightarrow{\mathrm{a}}$
$\therefore \overrightarrow {\rm{E}} = \frac{{\rho \overrightarrow {\rm{a}} }}{{3{ \in _0}}} = $ uniform
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