A thin spherical shell of radius 15 cm has a charge spread uniformly over it. The electric field at a point 30 cm from the centre of the shell is \(8\times10^{4}\ \mathrm{N\,C^{-1}}\). The magnitudes of the electric field at points 10 cm and 60 cm from the centre are, respectively,
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → zero and \(2\times10^{4}\ \mathrm{N\,C^{-1}}\)
The radius of the shell is 15 cm, so the point at 10 cm lies inside it. The field of a uniformly charged shell is zero at every point inside. The points at 30 cm and 60 cm lie outside. There the field is as if the whole charge sits at the centre, so \( E\propto1/r^{2} \).
\( \begin{aligned} \frac{E_{60}}{E_{30}} &= \left(\frac{30}{60}\right)^{2} \\ &= \frac{1}{4} \end{aligned} \)
\( \begin{aligned} E_{60} &= \frac{8\times10^{4}}{4} \\ &= 2\times10^{4}\ \mathrm{N\,C^{-1}} \end{aligned} \)
Therefore, the field is zero at 10 cm and \( 2\times10^{4}\ \mathrm{N\,C^{-1}} \) at 60 cm.
NCERT (2026-27):
Field due to a uniformly charged thin spherical shell – “… Thus for points outside the shell, the field due to a uniformly charged shell is as if the entire charge of the shell is concentrated at its centre.”
Summary – “… The field is zero at all points inside the shell.”