Correct Answer is: (c) \(\mathrm{R} / 3\)
Using the expression of the previous question's answer, for \(r=0\), potential at the centre \(=\mathrm{V}_{\mathrm{c}}=\mathrm{k} 3 \mathrm{Q} / 2 \mathrm{R}\).
We require a point where \(V=V_{d} / 2=k 3 Q / 4 R\).
This point cannot lie inside the sphere where \(V \geq k Q / R\).
Let the point lie outside the sphere, at a distance r from the centre. Then, \(V=k Q / r=k 3 Q / 4 R\)
or \(r=4 / 3 \mathrm{R}\)
Distance from the surface \(=r-R=R / 3\).
