A thin spherical shell of radius 10 cm has a charge of \(+4\ \mu\mathrm{C}\) spread uniformly over it. A point charge of \(+2\ \mu\mathrm{C}\) is placed at its centre. The magnitude of the electric field at a point 5 cm from the centre is (Take \(\frac{1}{4\pi\varepsilon_0}=9\times10^{9}\ \mathrm{N\,m^{2}\,C^{-2}}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(7.2\times10^{6}\ \mathrm{N\,C^{-1}}\)
The point is inside the shell. The field of a uniformly charged thin shell is zero at every point inside it. So the field at 5 cm comes only from the point charge at the centre.
\( \begin{aligned} q &= 2\times10^{-6}\ \mathrm{C} \\ r &= 5\ \mathrm{cm}=0.05\ \mathrm{m} \end{aligned} \)
\( \begin{aligned} E &= \frac{1}{4\pi\varepsilon_0}\frac{q}{r^{2}} \\ &= \frac{9\times10^{9}\times2\times10^{-6}}{(0.05)^{2}} \\ &= 7.2\times10^{6}\ \mathrm{N\,C^{-1}} \end{aligned} \)
NCERT (2026-27):
Field due to a uniformly charged thin spherical shell – “… that is, the field due to a uniformly charged thin shell is zero at all points inside the shell. …”