Two thin concentric spherical shells have radii 5 cm and 15 cm. The inner shell carries a charge of 3 nC and the outer shell a charge of 6 nC, each spread uniformly. The magnitude of the electric field at a point 10 cm from the common centre is (take \(\frac{1}{4\pi\varepsilon_0}=9\times10^{9}\ \mathrm{N\,m^2\,C^{-2}}\))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(2700\ \mathrm{N\,C^{-1}}\)
The point is inside the outer shell but outside the inner shell. A thin shell gives no field at points inside it, so the outer shell adds nothing here. Outside the inner shell, its field is the same as if its whole charge were at the centre.
Given:
\( q_1=3\ \mathrm{nC}=3\times10^{-9}\ \mathrm{C} \)
\( r=10\ \mathrm{cm}=0.10\ \mathrm{m} \)
\( \begin{aligned} E &= \frac{1}{4\pi\varepsilon_0}\frac{q_1}{r^2} \\ &= \frac{9\times10^{9}\times3\times10^{-9}}{(0.10)^2} \\ &= \frac{27}{0.01} \\ &= 2700\ \mathrm{N\,C^{-1}} \end{aligned} \)
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.”
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 …”