A positive charge +q is placed at the centre of a hollow metallic sphere of inner radius a and outer radius b. The electric field at a distance r from the centre is denoted by E. In this regard, which one of the following statements is correct ?

The correct answer is Option 1. This conclusion is based on the fundamental principles of electrostatics regarding conductors and Gauss’s Law.

• Inside the cavity (r < a): The electric field is non-zero because the Gaussian surface encloses the central charge +q.
• Within the metallic shell (a < r < b): Metals are ideal conductors. In electrostatic equilibrium, the free electrons in the metallic sphere redistribute themselves. The positive charge +q at the centre induces a charge -q on the inner surface (r = a) and +q on the outer surface (r = b).
• Electric Field Zero: For any point a < r < b, the net enclosed charge within a Gaussian surface is zero (+q - q = 0). Consequently, the electric field E is 0 inside the bulk of the conductor.

Option 1 correctly identifies that E = 0 (notated as Q in some contexts of the question) in the region between the inner and outer radii. Options 3 and 4 are incorrect as they suggest a non-zero field within the conductor or incorrect field distributions.