Question

Which of the following statements is not true about Gauss’s law?
(A) Gauss’s law is true for any closed surface.
(B) The term $q$ on the right side of Gauss’s law includes the sum of all charges enclosed by the surface.
(C) Gauss’s law is not very useful in calculating electrostatic fields when the system has some symmetry.
(D) Gauss’s law is based on the inverse square dependence on distance contained in the coulomb’s law.

Answer 1

Hint: As we know that, “In electrostatics, Gauss's law holds true for any closed surface, regardless of its shape or size.” As it allows the quantity of confined charge to be calculated by mapping the field on a surface outside the charge distribution.

Complete Step By Step Answer:
Gauss's law is often useful towards a much easier calculation of the electrostatic field when the system has some symmetry. This is facilitated by the choice of a suitable Gaussian surface.
So, option (C) Gauss’s law is not very useful in calculating electrostatic fields when the system has some symmetry, and is incorrect about Gauss’s law.
According to Gauss's law, the total charge inside any closed surface is measured by the flow through it. As a result, the Gauss law holds true for closed surfaces. Only symmetric body charge distributions, such as spherical, cylindrical, and plane symmetry, are valid for Gauss's law. Other valid mediums, such as dielectric media, are also valid. Therefore, option (A) is the correct statement about Gauss’s law.
The sum of all charges encompassed by the surface is included in the term $q$ on the right side of Gauss's law. The charges could be anywhere within the surface. When the surface is designed in such a way that some charges are inside and some are outside, the electric field [whose flux is shown on the left side of $Eq$ . Therefore, option (B) is also a correct statement about Gauss’s law.
The electrostatic field of a symmetric system can be calculated using Gauss's law. The inverse square dependence on distance inherent in Coulomb's law is the basis for Gauss's law. Any deviation from the inverse square law will be indicated by a violation of Gauss' law. Therefore, option (D) is also a correct statement about Gauss’s law.
Hence, the correct option is (C) Gauss’s law is not very useful in calculating electrostatic fields when the system has some symmetry.

Note:
“In electrostatics, Gauss's law holds true for any closed surface, regardless of its shape or size.” The net electric flux through a closed surface is independent of the shape or size of the surface. This is a consequence of Gauss's law.