• # question_answer                 A hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is 2 m ?                                                                                   A)                 Zero    B)                 $5\,\mu \,C{{m}^{-2}}$                               C)                 $20\,\mu \,C{{m}^{-2}}$                            D)                 $8\,\mu \,C{{m}^{-2}}$

Key Idea: No charge is enclosed by the hollow insulated conducting sphere.                                 Charge resides on the outer surface of a conducting hollow sphere of radius R (say). We consider a spherical surface of radius r < R. By Gauss theorem                 $\int\limits_{s}^{{}}{\vec{E}\,.\,\overrightarrow{ds}}=\frac{1}{{{\varepsilon }_{0}}}\times$charge enclosed or            $E.4\pi {{r}^{2}}=\frac{1}{{{\varepsilon }_{0}}}\times 0$ $\Rightarrow E=0$                 i.e., electric field inside a hollow sphere is zero.