Which of the following statements is correct for a charged metallic shell?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → The electric field intensity is zero inside the shell and decreases outside the shell as we move away from the shell.
By Gauss's law, a Gaussian sphere inside the shell encloses no charge, so the field inside is zero. Outside, the shell behaves like a point charge at its centre.
\( \displaystyle E_{\mathrm{in}} = 0, \qquad E_{\mathrm{out}} = \frac{Q}{4\pi\varepsilon_0\,r^{2}} \)
\( \displaystyle V_{\mathrm{in}} = \frac{Q}{4\pi\varepsilon_0\,R} \ (\text{constant}), \qquad V_{\mathrm{out}} = \frac{Q}{4\pi\varepsilon_0\,r} \)
Option (1) The electric field intensity is zero inside the shell and decreases outside the shell as we move away from the shell. — Correct. The field is zero inside and falls as \( 1/r^{2} \) outside.
Option (2) The electric field intensity is uniform inside the shell and decreases outside the shell as we move away from its center. — Incorrect. The field inside is zero, not some uniform non-zero value.
Option (3) The electric potential is zero inside the shell and decreases outside the shell as we move away from its center. — Incorrect. Inside the shell the potential is constant, equal to its surface value \( Q/(4\pi\varepsilon_0 R) \), not zero.
Option (4) The electrostatic potential increases linearly with the distance from its center inside the shell. — Incorrect. Since \( E = 0 \) inside, the potential does not change with distance there.
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 – “… However, in this case, the Gaussian surface encloses no charge. Gauss’s law then gives
\( \displaystyle E \times 4\pi r^2 = 0 \quad \text{i.e.,} \quad E = 0 \quad (r \lt R) \qquad (1.35) \)
that is, the field due to a uniformly charged thin shell is zero at all points inside the shell.”