UPSC NDA I 2017 General Ability Solved Paper

Concept:Electrostatic shielding: Inside a conductor in electrostatic equilibrium, the electric field is zero everywhere.Explanation:A hollow metallic sphere (conductor) has inner radius $a$ and outer radius $b$.A positive charge $+q$ is placed at its centre.Due to induction, an equal negative charge $-q$ appears on the inner surface at radius $a$, and $+q$ on the outer surface at radius $b$.For points inside the conducting material itself (region $a < r < b$), a Gaussian surface lying in the metal encloses both the central $+q$ and the inner surface $-q$.The net enclosed charge is zero, so by Gauss's law the electric field $E$ inside the metal is zero.For $r < a$ (inside the cavity), the field is due to the central charge alone: $E = \frac{q}{4\pi\varepsilon_0 r^2}$.For $r > b$ (outside the sphere), the field is as if the entire charge $+q$ were at the centre: $E = \frac{q}{4\pi\varepsilon_0 r^2}$.Thus, the only region where $E = 0$ is $a < r < b$.Answer:Option A: $E = 0$ for $a < r < b$