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 ?
[amp_mcq option1=”E = 0 for a < r < b" option2="E = 0 for r < a" option3="E = q/4πε₀r for a < r < b" option4="E = q/4πε₀a for r < a" correct="option1"]
This question was previously asked in
UPSC NDA-1 – 2017
– For r < a (inside the cavity but outside the point charge): The electric field is due to the point charge +q. Using Gauss's Law with a spherical surface of radius r < a centered at +q, the enclosed charge is +q. So, E * 4πr² = q/ε₀, which gives E = q/(4πε₀r²). Thus, E is not zero for r < a. - For a < r < b (inside the metallic material): In electrostatic equilibrium, the electric field inside a conductor is always zero. The presence of the charge +q at the center induces a charge of -q on the inner surface of the metallic sphere (at r=a) and a charge of +q on the outer surface (at r=b). The induced charges arrange themselves such that the field inside the conductor material (a < r < b) is zero. - For r > b (outside the sphere): The total enclosed charge within a spherical surface of radius r > b centered at +q is +q (the original charge) + (-q on inner surface) + (+q on outer surface) = +q. Using Gauss’s Law, E * 4πr² = q/ε₀, so E = q/(4πε₀r²).
Based on this analysis, the statement E = 0 for a < r < b is correct.