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? [AIPMT 1998]

A) Zero

B) \[5\,\mu \,C{{m}^{-2}}\]

C) \[20\,\mu \,C{{m}^{-2}}\]

D) \[8\,\mu \,C{{m}^{-2}}\]

Correct Answer: A

Solution :

[a] 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.