A point charge Q is placed inside a cavity within a solid isolated conducting sphere. Consider points A (inside cavity), B and C (outside the sphere, equidistant from its centre) with field magnitudes E_A,E_B,E_C. The correct option is:

Solution & Explanation

Point A is inside the cavity: the point charge Q produces a field there that the conductor cannot cancel, so E_A ≠ 0. The conductor responds by inducing −Q on the cavity wall and +Q on its outer surface. Key fact: that induced +Q spreads UNIFORMLY over the outer surface, completely independent of where Q sits inside the cavity — the conductor screens the interior arrangement. So outside the sphere the field is exactly that of a point charge +Q located at the geometric centre. Points B and C are stated to be equidistant from the centre, so they lie on the same equipotential/field-magnitude shell: E_B = E_C. Therefore E_A ≠ 0 and E_B = E_C, which is answer (B). Key trap: even though Q may be off-centre in the cavity, the external field stays symmetric, so B and C are NOT different.