Consider the following statements about the electric fields found with Gauss’s law:
(A) The electric field of a uniformly charged infinite plane sheet does not depend on the distance from the sheet.
(B) The electric field due to a uniformly charged thin spherical shell is zero at all points inside the shell.
(C) For an infinitely long straight charged wire, the field found by Gauss’s law at a point is due only to the charge enclosed by the Gaussian cylinder.
(D) The electric field of a uniformly charged infinite plane sheet points towards the sheet when \(\sigma\) is positive.
Which of the above statements are incorrect? Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (C) and (D) only
Gauss’s law gives the field in a simple way when the charge has symmetry. The Gaussian surface is chosen to match that symmetry.
(A) The electric field of a uniformly charged infinite plane sheet does not depend on the distance from the sheet. — True. Gauss’s law gives \( E=\sigma/2\varepsilon_0 \). No distance appears in this result.
(B) The electric field due to a uniformly charged thin spherical shell is zero at all points inside the shell. — True. A sphere drawn through a point inside the shell encloses no charge. Its flux \( E\times4\pi r^{2} \) is zero, so \( E=0 \).
(C) For an infinitely long straight charged wire, the field found by Gauss’s law at a point is due only to the charge enclosed by the Gaussian cylinder. — False. Only the enclosed charge \( \lambda l \) appears in Gauss’s law. The field itself is produced by the charge on the whole wire.
(D) The electric field of a uniformly charged infinite plane sheet points towards the sheet when \( \sigma \) is positive. — False. For positive \( \sigma \) the field points away from the sheet. It points towards the sheet only when \( \sigma \) is negative.
NCERT (2026-27):
Field due to a uniformly charged infinite plane sheet – “… the above application of the Gauss’ law has brought out an additional fact: E is independent of x also.”
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.”
Field due to an infinitely long straight uniformly charged wire – “Also note that though only the charge enclosed by the surface (λl) was included above, the electric field E is due to the charge on the entire wire.”
Field due to a uniformly charged infinite plane sheet – “E is directed away from the plate if σ is positive and toward the plate if σ is negative.”