Which of the following are true statements?
(A) Electric field due to a single charge is cylindrically symmetric.
(B) Gauss's theorem holds good for any closed surface.
(C) Electric field due to an electric dipole is spherically symmetric
(D) The field due to a uniformly charged spherical shell is zero at all points inside the shell.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
A field is spherically symmetric when it depends only on the distance from a centre, the same in every direction; it is cylindrically (axially) symmetric when it looks the same on rotation about one axis only.
(A) Electric field due to a single charge is cylindrically symmetric. — Incorrect. The field of a point charge, \( E = kq/r^{2} \), is the same in every direction at a given distance, so its symmetry is spherical.
(B) Gauss's theorem holds good for any closed surface. — Correct. Gauss's law \( \oint \vec{E}\cdot d\vec{A} = q_{\mathrm{enc}}/\varepsilon_{0} \) is true for every closed surface, whatever its shape or size.
(C) Electric field due to an electric dipole is spherically symmetric — Incorrect. The dipole field is different along the axis and on the equatorial line at the same distance, so it is only symmetric about the dipole axis.
(D) The field due to a uniformly charged spherical shell is zero at all points inside the shell. — Correct. A Gaussian sphere drawn inside the shell encloses no charge, so the field inside is zero.
NCERT (2026-27):
Gauss’s Law – “… (i) Gauss’s law is true for any closed surface, no matter what its shape or size.”
Field Due to a Uniformly Charged Thin Spherical Shell – “… 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.”