question_answer

A spherical portion is removed from a solid sphere having a charge distribution uniformly in its volume. The electric field inside the emptied space is

A) zero everywhere

B) non-zero and uniform

C) non-uniform

D) zero, only at the centre

Correct Answer: B

Solution :

Consider the diagram. Let P is a point inside cavity whose distance from O and O' are i and i' respectively. \[a=(r-r')\] The net electric field at point P is given by \[{{E}_{P}}=\frac{\rho }{3{{\varepsilon }_{0}}}r-\frac{\rho }{3{{\varepsilon }_{0}}}r'=\frac{\rho }{3{{\varepsilon }_{0}}}(r-r')\] \[\Rightarrow \]\[{{E}_{P}}=\frac{\rho }{3{{\varepsilon }_{0}}}a=\]uniform